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# Statistics Surveys

Open Access. Projekt Euclid.

## Adaptive clinical trial designs for phase I cancer studies

Oleksandr Sverdlov, Weng Kee Wong, Yevgen Ryeznik. Source: Statistics Surveys, Volume 8, 2--44.Abstract:

Adaptive clinical trials are becoming increasingly popular research designs for clinical investigation. Adaptive designs are particularly useful in phase I cancer studies where clinical data are scant and the goals are to assess the drug dose-toxicity profile and to determine the maximum tolerated dose while minimizing the number of study patients treated at suboptimal dose levels.

In the current work we give an overview of adaptive design methods for phase I cancer trials. We find that modern statistical literature is replete with novel adaptive designs that have clearly defined objectives and established statistical properties, and are shown to outperform conventional dose finding methods such as the 3+3 design, both in terms of statistical efficiency and in terms of minimizing the number of patients treated at highly toxic or nonefficacious doses. We discuss statistical, logistical, and regulatory aspects of these designs and present some links to non-commercial statistical software for implementing these methods in practice.

2014/05/31 - 14:03

## Adaptive clinical trial designs for phase I cancer studies

Oleksandr Sverdlov, Weng Kee Wong, Yevgen Ryeznik. Source: Statistics Surveys, Volume 8, 2--44.Abstract:

Adaptive clinical trials are becoming increasingly popular research designs for clinical investigation. Adaptive designs are particularly useful in phase I cancer studies where clinical data are scant and the goals are to assess the drug dose-toxicity profile and to determine the maximum tolerated dose while minimizing the number of study patients treated at suboptimal dose levels.

In the current work we give an overview of adaptive design methods for phase I cancer trials. We find that modern statistical literature is replete with novel adaptive designs that have clearly defined objectives and established statistical properties, and are shown to outperform conventional dose finding methods such as the 3+3 design, both in terms of statistical efficiency and in terms of minimizing the number of patients treated at highly toxic or nonefficacious doses. We discuss statistical, logistical, and regulatory aspects of these designs and present some links to non-commercial statistical software for implementing these methods in practice.

2014/05/31 - 14:03

## Errata: A survey of Bayesian predictive methods for model assessment, selection and comparison

Aki Vehtari, Janne Ojanen. Source: Statistics Surveys, Volume 8, , 1--1.Abstract:

Errata for “A survey of Bayesian predictive methods for model assessment, selection and comparison” by A. Vehtari and J. Ojanen, Statistics Surveys , 6 (2012), 142–228. doi:10.1214/12-SS102.

2014/02/27 - 18:28

## Analyzing complex functional brain networks: Fusing statistics and network science to understand the brain

Sean L. Simpson, F. DuBois Bowman, Paul J. LaurientiSource: Statist. Surv., Volume 7, 1--36.Abstract:

Complex functional brain network analyses have exploded over the last decade, gaining traction due to their profound clinical implications. The application of network science (an interdisciplinary offshoot of graph theory) has facilitated these analyses and enabled examining the brain as an integrated system that produces complex behaviors. While the field of statistics has been integral in advancing activation analyses and some connectivity analyses in functional neuroimaging research, it has yet to play a commensurate role in complex network analyses. Fusing novel statistical methods with network-based functional neuroimage analysis will engender powerful analytical tools that will aid in our understanding of normal brain function as well as alterations due to various brain disorders. Here we survey widely used statistical and network science tools for analyzing fMRI network data and discuss the challenges faced in filling some of the remaining methodological gaps. When applied and interpreted correctly, the fusion of network scientific and statistical methods has a chance to revolutionize the understanding of brain function.

2013/10/29 - 17:33

## A survey of Bayesian predictive methods for model assessment, selection and comparison

Aki Vehtari, Janne OjanenSource: Statist. Surv., Volume 6, 142--228.Abstract:

To date, several methods exist in the statistical literature for model assessment, which purport themselves specifically as Bayesian predictive methods. The decision theoretic assumptions on which these methods are based are not always clearly stated in the original articles, however. The aim of this survey is to provide a unified review of Bayesian predictive model assessment and selection methods, and of methods closely related to them. We review the various assumptions that are made in this context and discuss the connections between different approaches, with an emphasis on how each method approximates the expected utility of using a Bayesian model for the purpose of predicting future data.

2012/12/28 - 17:06

## The theory and application of penalized methods or Reproducing Kernel Hilbert Spaces made easy

Nancy HeckmanSource: Statist. Surv., Volume 6, 113--141.Abstract:

The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $\sum_{j}(Y_{j}-\mu(t_{j}))^{2}+\lambda \int_{a}^{b}[\mu''(t)]^{2}\,dt$, where the data are $t_{j},Y_{j}$, $j=1,\ldots,n$. The minimization is taken over an infinite-dimensional function space, the space of all functions with square integrable second derivatives. But the calculations can be carried out in a finite-dimensional space. The reduction from minimizing over an infinite dimensional space to minimizing over a finite dimensional space occurs for more general objective functions: the data may be related to the function $\mu$ in another way, the sum of squares may be replaced by a more suitable expression, or the penalty, $\int_{a}^{b}[\mu''(t)]^{2}\,dt$, might take a different form. This paper reviews the Reproducing Kernel Hilbert Space structure that provides a finite-dimensional solution for a general minimization problem. Particular attention is paid to the construction and study of the Reproducing Kernel Hilbert Space corresponding to a penalty based on a linear differential operator. In this case, one can often calculate the minimizer explicitly, using Green’s functions.

2012/10/16 - 17:12

## Statistical inference for disordered sphere packings

Jeffrey PickaSource: Statist. Surv., Volume 6, 74--112.Abstract:

This paper gives an overview of statistical inference for disordered sphere packing processes. These processes are used extensively in physics and engineering in order to represent the internal structure of composite materials, packed bed reactors, and powders at rest, and are used as initial arrangements of grains in the study of avalanches and other problems involving powders in motion. Packing processes are spatial processes which are neither stationary nor ergodic. Classical spatial statistical models and procedures cannot be applied to these processes, but alternative models and procedures can be developed based on ideas from statistical physics.

Most of the development of models and statistics for sphere packings has been undertaken by scientists and engineers. This review summarizes their results from an inferential perspective.

2012/07/20 - 05:34

## Prediction in several conventional contexts

Bertrand Clarke, Jennifer ClarkeSource: Statist. Surv., Volume 6, 1--73.Abstract:

We review predictive techniques from several traditional branches of statistics. Starting with prediction based on the normal model and on the empirical distribution function, we proceed to techniques for various forms of regression and classification. Then, we turn to time series, longitudinal data, and survival analysis. Our focus throughout is on the mechanics of prediction more than on the properties of predictors.

2012/05/09 - 02:43

## A review of survival trees

This paper presents a non–technical account of the developments in tree–based methods for the analysis of survival data with censoring. This review describes the initial developments, which mainly extended the existing basic tree methodologies to censored data as well as to more recent work. We also cover more complex models, more specialized methods, and more specific problems such as multivariate data, the use of time–varying covariates, discrete–scale survival data, and ensemble methods applied to survival trees. A data example is used to illustrate some methods that are implemented in R.

2011/09/12 - 23:33

## Curse of dimensionality and related issues in nonparametric functional regression

Gery GeenensSource: Statist. Surv., Volume 5, 30--43.Abstract:

Recently, some nonparametric regression ideas have been extended to the case of functional regression. Within that framework, the main concern arises from the infinite dimensional nature of the explanatory objects. Specifically, in the classical multivariate regression context, it is well-known that any nonparametric method is affected by the so-called “curse of dimensionality”, caused by the sparsity of data in high-dimensional spaces, resulting in a decrease in fastest achievable rates of convergence of regression function estimators toward their target curve as the dimension of the regressor vector increases. Therefore, it is not surprising to find dramatically bad theoretical properties for the nonparametric functional regression estimators, leading many authors to condemn the methodology. Nevertheless, a closer look at the meaning of the functional data under study and on the conclusions that the statistician would like to draw from it allows to consider the problem from another point-of-view, and to justify the use of slightly modified estimators. In most cases, it can be entirely legitimate to measure the proximity between two elements of the infinite dimensional functional space via a semi-metric, which could prevent those estimators suffering from what we will call the “curse of infinite dimensionality”.

References:[1] Ait-Saïdi, A., Ferraty, F., Kassa, K. and Vieu, P. (2008). Cross-validated estimations in the single-functional index model, Statistics, 42, 475–494.[2] Aneiros-Perez, G. and Vieu, P. (2008). Nonparametric time series prediction: A semi-functional partial linear modeling, J. Multivariate Anal., 99, 834–857.[3] Baillo, A. and Grané, A. (2009). Local linear regression for functional predictor and scalar response, J. Multivariate Anal., 100, 102–111.[4] Burba, F., Ferraty, F. and Vieu, P. (2009). k-Nearest Neighbour method in functional nonparametric regression, J. Nonparam. Stat., 21, 453–469.[5] Cardot, H., Ferraty, F. and Sarda, P. (1999). Functional linear model, Stat. Probabil. Lett., 45, 11–22.[6] Crambes, C., Kneip, A. and Sarda, P. (2009). Smoothing splines estimators for functional linear regression, Ann. Statist., 37, 35–72.[7] Delsol, L. (2009). Advances on asymptotic normality in nonparametric functional time series analysis, Statistics, 43, 13–33.[8] Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications, Chapman and Hall, London.[9] Fan, J. and Zhang, J.-T. (2000). Two-step estimation of functional linear models with application to longitudinal data, J. Roy. Stat. Soc. B, 62, 303–322.[10] Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis, Springer-Verlag, New York.[11] Ferraty, F., Laksaci, A. and Vieu, P. (2006). Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models, Statist. Inf. Stoch. Proc., 9, 47–76.[12] Ferraty, F., Mas, A. and Vieu, P. (2007). Nonparametric regression on functional data: inference and practical aspects, Aust. NZ. J. Stat., 49, 267–286.[13] Ferraty, F., Van Keilegom, I. and Vieu, P. (2010). On the validity of the bootstrap in nonparametric functional regression, Scand. J. Stat., 37, 286–306.[14] Ferraty, F., Laksaci, A., Tadj, A. and Vieu, P. (2010). Rate of uniform consistency for nonparametric estimates with functional variables, J. Stat. Plan. Inf., 140, 335–352.[15] Ferraty, F. and Romain, Y. (2011). Oxford handbook on functional data analysis (Eds), Oxford University Press.[16] Gasser, T., Hall, P. and Presnell, B. (1998). Nonparametric estimation of the mode of a distribution of random curves, J. Roy. Stat. Soc. B, 60, 681–691.[17] Geenens, G. (2011). A nonparametric functional method for signature recognition, Manuscript.[18] Härdle, W., Müller, M., Sperlich, S. and Werwatz, A. (2004). Nonparametric and semiparametric models, Springer-Verlag, Berlin.[19] James, G.M. (2002). Generalized linear models with functional predictors, J. Roy. Stat. Soc. B, 64, 411–432.[20] Masry, E. (2005). Nonparametric regression estimation for dependent functional data: asymptotic normality, Stochastic Process. Appl., 115, 155–177.[21] Nadaraya, E.A. (1964). On estimating regression, Theory Probab. Applic., 9, 141–142.[22] Quintela-Del-Rio, A. (2008). Hazard function given a functional variable: nonparametric estimation under strong mixing conditions, J. Nonparam. Stat., 20, 413–430.[23] Rachdi, M. and Vieu, P. (2007). Nonparametric regression for functional data: automatic smoothing parameter selection, J. Stat. Plan. Inf., 137, 2784–2801.[24] Ramsay, J. and Silverman, B.W. (1997). Functional Data Analysis, Springer-Verlag, New York.[25] Ramsay, J. and Silverman, B.W. (2002). Applied functional data analysis; methods and case study, Springer-Verlag, New York.[26] Ramsay, J. and Silverman, B.W. (2005). Functional Data Analysis, 2nd Edition, Springer-Verlag, New York.[27] Stone, C.J. (1982). Optimal global rates of convergence for nonparametric regression, Ann. Stat., 10, 1040–1053.[28] Watson, G.S. (1964). Smooth regression analysis, Sankhya A, 26, 359–372.[29] Yeung, D.T., Chang, H., Xiong, Y., George, S., Kashi, R., Matsumoto, T. and Rigoll, G. (2004). SVC2004: First International Signature Verification Competition, Proceedings of the International Conference on Biometric Authentication (ICBA), Hong Kong, July 2004.

2011/04/14 - 23:22

## Data confidentiality: A review of methods for statistical disclosure limitation and methods for assessing privacy

Gregory J. Matthews, Ofer HarelSource: Statist. Surv., Volume 5, 1--29.Abstract:

There is an ever increasing demand from researchers for access to useful microdata files. However, there are also growing concerns regarding the privacy of the individuals contained in the microdata. Ideally, microdata could be released in such a way that a balance between usefulness of the data and privacy is struck. This paper presents a review of proposed methods of statistical disclosure control and techniques for assessing the privacy of such methods under different definitions of disclosure.

2011/02/04 - 19:06

## Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules

Michael P. Fay, Michael A. ProschanSource: Statist. Surv., Volume 4, 1--39.Abstract:

In a mathematical approach to hypothesis tests, we start with a clearly defined set of hypotheses and choose the test with the best properties for those hypotheses. In practice, we often start with less precise hypotheses. For example, often a researcher wants to know which of two groups generally has the larger responses, and either a t-test or a Wilcoxon-Mann-Whitney (WMW) test could be acceptable. Although both t-tests and WMW tests are usually associated with quite different hypotheses, the decision rule and p-value from either test could be associated with many different sets of assumptions, which we call perspectives. It is useful to have many of the different perspectives to which a decision rule may be applied collected in one place, since each perspective allows a different interpretation of the associated p-value. Here we collect many such perspectives for the two-sample t-test, the WMW test and other related tests. We discuss validity and consistency under each perspective and discuss recommendations between the tests in light of these many different perspectives. Finally, we briefly discuss a decision rule for testing genetic neutrality where knowledge of the many perspectives is vital to the proper interpretation of the decision rule.

2010/12/30 - 03:38

## A survey of cross-validation procedures for model selection

Sylvain Arlot, Alain CelisseSource: Statist. Surv., Volume 4, 40--79.Abstract:

Used to estimate the risk of an estimator or to perform model selection, cross-validation is a widespread strategy because of its simplicity and its (apparent) universality. Many results exist on model selection performances of cross-validation procedures. This survey intends to relate these results to the most recent advances of model selection theory, with a particular emphasis on distinguishing empirical statements from rigorous theoretical results. As a conclusion, guidelines are provided for choosing the best cross-validation procedure according to the particular features of the problem in hand.

2010/12/30 - 03:38

## Finite mixture models and model-based clustering

Volodymyr Melnykov, Ranjan MaitraSource: Statist. Surv., Volume 4, 80--116.Abstract:

Finite mixture models have a long history in statistics, having been used to model population heterogeneity, generalize distributional assumptions, and lately, for providing a convenient yet formal framework for clustering and classification. This paper provides a detailed review into mixture models and model-based clustering. Recent trends as well as open problems in the area are also discussed.

2010/12/30 - 03:38

## Discrete variations of the fractional Brownian motion in the presence of outliers and an additive noise

Sophie Achard, Jean-François CoeurjollySource: Statist. Surv., Volume 4, 117--147.Abstract:

This paper gives an overview of the problem of estimating the Hurst parameter of a fractional Brownian motion when the data are observed with outliers and/or with an additive noise by using methods based on discrete variations. We show that the classical estimation procedure based on the log-linearity of the variogram of dilated series is made more robust to outliers and/or an additive noise by considering sample quantiles and trimmed means of the squared series or differences of empirical variances. These different procedures are compared and discussed through a large simulation study and are implemented in the R package dvfBm.

2010/12/30 - 03:38

## Primal and dual model representations in kernel-based learning

Johan A.K. Suykens, Carlos Alzate, Kristiaan PelckmansSource: Statist. Surv., Volume 4, 148--183.Abstract:

This paper discusses the role of primal and (Lagrange) dual model representations in problems of supervised and unsupervised learning. The specification of the estimation problem is conceived at the primal level as a constrained optimization problem. The constraints relate to the model which is expressed in terms of the feature map. From the conditions for optimality one jointly finds the optimal model representation and the model estimate. At the dual level the model is expressed in terms of a positive definite kernel function, which is characteristic for a support vector machine methodology. It is discussed how least squares support vector machines are playing a central role as core models across problems of regression, classification, principal component analysis, spectral clustering, canonical correlation analysis, dimensionality reduction and data visualization.

2010/12/30 - 03:38

## Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview

A. Philip Dawid, Vanessa DidelezSource: Statist. Surv., Volume 4, 184--231.Abstract:

We consider the problem of learning about and comparing the consequences of dynamic treatment strategies on the basis of observational data. We formulate this within a probabilistic decision-theoretic framework. Our approach is compared with related work by Robins and others: in particular, we show how Robins’s ‘ G -computation’ algorithm arises naturally from this decision-theoretic perspective. Careful attention is paid to the mathematical and substantive conditions required to justify the use of this formula. These conditions revolve around a property we term stability , which relates the probabilistic behaviours of observational and interventional regimes. We show how an assumption of ‘sequential randomization’ (or ‘no unmeasured confounders’), or an alternative assumption of ‘sequential irrelevance’, can be used to infer stability. Probabilistic influence diagrams are used to simplify manipulations, and their power and limitations are discussed. We compare our approach with alternative formulations based on causal DAGs or potential response models. We aim to show that formulating the problem of assessing dynamic treatment strategies as a problem of decision analysis brings clarity, simplicity and generality.

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Journal of the American Statistical Association 95 407–448.Dawid, A. P. (2001). Separoids: A mathematical framework for conditional independence and irrelevance. Annals of Mathematics and Artificial Intelligence 32 335–372.Dawid, A. P. (2002). Influence diagrams for causal modelling and inference. International Statistical Review 70 161–189. Corrigenda, ibid ., 437.Dawid, A. P. (2003). Causal inference using influence diagrams: The problem of partial compliance (with Discussion). In Highly Structured Stochastic Systems ( P. J. Green, N. L. Hjort and S. Richardson, eds.) 45–81. Oxford University Press.Dawid, A. P. (2010). Beware of the DAG! In Proceedings of the NIPS 2008 Workshop on Causality. Journal of Machine Learning Research Workshop and Conference Proceedings ( D. Janzing, I. Guyon and B. Schölkopf, eds.) 6 59–86. http://tinyurl.com/33va7tmDawid, A. P. and Didelez, V. (2008). Identifying optimal sequential decisions. In Proceedings of the Twenty-Fourth Annual Conference on Uncertainty in Artificial Intelligence (UAI-08) ( D. McAllester and A. Nicholson, eds.). 113-120. AUAI Press, Corvallis, Oregon. http://tinyurl.com/3899qppDechter, R. (2003). Constraint Processing. Morgan Kaufmann Publishers.Didelez, V., Dawid, A. P. and Geneletti, S. G. (2006). Direct and indirect effects of sequential treatments. In Proceedings of the Twenty-Second Annual Conference on Uncertainty in Artificial Intelligence (UAI-06) ( R. Dechter and T. Richardson, eds.). 138-146. AUAI Press, Arlington, Virginia. http://tinyurl.com/32w3f4eDidelez, V., Kreiner, S. and Keiding, N. (2010). Graphical models for inference under outcome dependent sampling. Statistical Science (to appear).Didelez, V. and Sheehan, N. S. (2007). Mendelian randomisation: Why epidemiology needs a formal language for causality. In Causality and Probability in the Sciences, ( F. Russo and J. Williamson, eds.). Texts in Philosophy Series 5 263–292. College Publications, London.Eichler, M. and Didelez, V. (2010). Granger-causality and the effect of interventions in time series. Lifetime Data Analysis 16 3–32.Ferguson, T. S. (1967). Mathematical Statistics: A Decision Theoretic Approach. Academic Press, New York, London.Geneletti, S. G. (2007). Identifying direct and indirect effects in a non–counterfactual framework. Journal of the Royal Statistical Society: Series B 69 199–215.Geneletti, S. G. and Dawid, A. P. (2010). Defining and identifying the effect of treatment on the treated. In Causality in the Sciences ( P. M. Illari, F. Russo and J. Williamson, eds.) Oxford University Press (to appear).Gill, R. D. and Robins, J. M. (2001). Causal inference for complex longitudinal data: The continuous case. Annals of Statistics 29 1785–1811.Guo, H. and Dawid, A. P. (2010). Sufficient covariates and linear propensity analysis. In Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics, (AISTATS) 2010, Chia Laguna, Sardinia, Italy, May 13-15, 2010. Journal of Machine Learning Research Workshop and Conference Proceedings ( Y. W. Teh and D. M. Titterington, eds.) 9 281–288. http://tinyurl.com/33lmuj7Henderson, R., Ansel, P. and Alshibani, D. (2010). Regret-regression for optimal dynamic treatment regimes. Biometrics (to appear). doi:10.1111/j.1541-0420.2009.01368.xHernán, M. A. and Taubman, S. L. (2008). Does obesity shorten life? The importance of well defined interventions to answer causal questions. International Journal of Obesity 32 S8–S14.Holland, P. W. (1986). Statistics and causal inference (with Discussion). Journal of the American Statistical Association 81 945–970.Huang, Y. and Valtorta, M. (2006). Identifiability in causal Bayesian networks: A sound and complete algorithm. In AAAI’06: Proceedings of the 21st National Conference on Artificial Intelligence 1149–1154. AAAI Press.Kang, J. D. Y. and Schafer, J. L. (2007). Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22 523–539.Lauritzen, S. L., Dawid, A. P., Larsen, B. N. and Leimer, H. G. (1990). Independence properties of directed Markov fields. Networks 20 491–505.Lok, J., Gill, R., van der Vaart, A. and Robins, J. (2004). Estimating the causal effect of a time-varying treatment on time-to-event using structural nested failure time models. Statistica Neerlandica 58 271–295.Moodie, E. M., Richardson, T. S. and Stephens, D. A. (2007). Demystifying optimal dynamic treatment regimes. Biometrics 63 447–455.Murphy, S. A. (2003). Optimal dynamic treatment regimes (with Discussion). Journal of the Royal Statistical Society, Series B 65 331-366.Oliver, R. M. and Smith, J. Q., eds. (1990). Influence Diagrams, Belief Nets and Decision Analysis. John Wiley and Sons, Chichester, United Kingdom.Pearl, J. (1995). Causal diagrams for empirical research (with Discussion). Biometrika 82 669-710.Pearl, J. (2009). Causality: Models, Reasoning and Inference, Second ed. Cambridge University Press, Cambridge.Pearl, J. and Paz, A. (1987). Graphoids: A graph-based logic for reasoning about relevance relations. In Advances in Artificial Intelligence ( D. Hogg and L. Steels, eds.) II 357–363. North-Holland, Amsterdam.Pearl, J. and Robins, J. (1995). Probabilistic evaluation of sequential plans from causal models with hidden variables. In Proceedings of the 11th Conference on Uncertainty in Artificial Intelligence ( P. Besnard and S. Hanks, eds.) 444–453. Morgan Kaufmann Publishers, San Francisco.Raiffa, H. (1968). Decision Analysis. Addison-Wesley, Reading, Massachusetts.Robins, J. M. (1986). A new approach to causal inference in mortality studies with sustained exposure periods—Application to control of the healthy worker survivor effect. Mathematical Modelling 7 1393–1512.Robins, J. M. (1987). Addendum to “A new approach to causal inference in mortality studies with sustained exposure periods—Application to control of the healthy worker survivor effect”. Computers & Mathematics with Applications 14 923–945.Robins, J. M. (1989). The analysis of randomized and nonrandomized AIDS treatment trials using a new approach to causal inference in longitudinal studies. In Health Service Research Methodology: A Focus on AIDS ( L. Sechrest, H. Freeman and A. Mulley, eds.) 113–159. NCSHR, U.S. Public Health Service.Robins, J. M. (1992). Estimation of the time-dependent accelerated failure time model in the presence of confounding factors. Biometrika 79 321–324.Robins, J. M. (1997). Causal inference from complex longitudinal data. 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(2009). Intervening on risk factors for coronary heart disease: An application of the parametric g-formula. International Journal of Epidemiology 38 1599–1611.Tian, J. (2008). Identifying dynamic sequential plans. In Proceedings of the Twenty-Fourth Annual Conference on Uncertainty in Artificial Intelligence (UAI-08) ( D. McAllester and A. Nicholson, eds.). 554–561. AUAI Press, Corvallis, Oregon. http://tinyurl.com/36ufx2hVerma, T. and Pearl, J. (1990). Causal networks: Semantics and expressiveness. In Uncertainty in Artificial Intelligence 4 ( R. D. Shachter, T. S. Levitt, L. N. Kanal and J. F. Lemmer, eds.) 69–76. North-Holland, Amsterdam.

2010/12/30 - 03:38

## The ARMA alphabet soup: A tour of ARMA model variants

Scott H. Holan, Robert Lund, Ginger DavisSource: Statist. Surv., Volume 4, 232--274.Abstract:

Autoregressive moving-average (ARMA) difference equations are ubiquitous models for short memory time series and have parsimoniously described many stationary series. Variants of ARMA models have been proposed to describe more exotic series features such as long memory autocovariances, periodic autocovariances, and count support set structures. This review paper enumerates, compares, and contrasts the common variants of ARMA models in today’s literature. After the basic properties of ARMA models are reviewed, we tour ARMA variants that describe seasonal features, long memory behavior, multivariate series, changing variances (stochastic volatility) and integer counts. A list of ARMA variant acronyms is provided.