Author

# T. W. Anderson

Other affiliations: Columbia University, Carnegie Mellon University, University of Tokyo ...read more

Bio: T. W. Anderson is an academic researcher from Stanford University. The author has contributed to research in topic(s): Estimator & Autoregressive model. The author has an hindex of 52, co-authored 179 publication(s) receiving 42299 citation(s). Previous affiliations of T. W. Anderson include Columbia University & Carnegie Mellon University.

##### Papers published on a yearly basis

##### Papers

More filters

•

14 Sep 1984

TL;DR: In this article, the distribution of the Mean Vector and the Covariance Matrix and the Generalized T2-Statistic is analyzed. But the distribution is not shown to be independent of sets of Variates.

Abstract: Preface to the Third Edition.Preface to the Second Edition.Preface to the First Edition.1. Introduction.2. The Multivariate Normal Distribution.3. Estimation of the Mean Vector and the Covariance Matrix.4. The Distributions and Uses of Sample Correlation Coefficients.5. The Generalized T2-Statistic.6. Classification of Observations.7. The Distribution of the Sample Covariance Matrix and the Sample Generalized Variance.8. Testing the General Linear Hypothesis: Multivariate Analysis of Variance9. Testing Independence of Sets of Variates.10. Testing Hypotheses of Equality of Covariance Matrices and Equality of Mean Vectors and Covariance Matrices.11. Principal Components.12. Cononical Correlations and Cononical Variables.13. The Distributions of Characteristic Roots and Vectors.14. Factor Analysis.15. Pattern of Dependence Graphical Models.Appendix A: Matrix Theory.Appendix B: Tables.References.Index.

9,680 citations

••

7,404 citations

••

TL;DR: In this article, a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations.

Abstract: The statistical problem treated is that of testing the hypothesis that $n$ independent, identically distributed random variables have a specified continuous distribution function $F(x)$. If $F_n(x)$ is the empirical cumulative distribution function and $\psi(t)$ is some nonnegative weight function $(0 \leqq t \leqq 1)$, we consider $n^{\frac{1}{2}} \sup_{-\infty

2,788 citations

••

TL;DR: In this article, the authors present a statistical analysis of time series regression models for longitudinal data with and without lagged dependent variables under a variety of assumptions about the initial conditions of the processes being analyzed.

Abstract: This paper presents a statistical analysis of time series regression models for longitudinal data with and without lagged dependent variables under a variety of assumptions about the initial conditions of the processes being analyzed. The analysis demonstrates how the asymptotic properties of estimators of longitudinal models are critically dependent on the manner in which samples become large: by expanding the number of observations per person, holding the number of people fixed, or by expanding the number of persons, holding the number of observations per person fixed. The paper demonstrates which parameters can and cannot be identified from data produced by different sampling plans.

2,582 citations

••

TL;DR: In this paper, observations on N cross-section units at T time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit.

Abstract: Observations on N cross-section units at T time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit. Different assumptions about the initial conditions are (a) initial state fixed, (b) initial state random, (c) the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed, and (d) the unobserved individual effect independent of the unobserved dynamic process with initial value random. Asymptotic properties of the maximum likelihood and “covariance” estimators are obtained when T → ∞ and when N → ∞. The relationship between the pseudo and conditional maximum likelihood estimators is clarified. A simple consistent estimator that is independent of the initial conditions and the way in which T or N → ∞ is also suggested.

2,231 citations

##### Cited by

More filters

••

TL;DR: In this article, the adequacy of the conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice were examined, and the results suggest that, for the ML method, a cutoff value close to.95 for TLI, BL89, CFI, RNI, and G...

Abstract: This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and G...

63,509 citations

••

TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.

Abstract: The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.

42,619 citations

•

01 Jan 2001

TL;DR: This is the essential companion to Jeffrey Wooldridge's widely-used graduate text Econometric Analysis of Cross Section and Panel Data (MIT Press, 2001).

Abstract: The second edition of this acclaimed graduate text provides a unified treatment of two methods used in contemporary econometric research, cross section and data panel methods. By focusing on assumptions that can be given behavioral content, the book maintains an appropriate level of rigor while emphasizing intuitive thinking. The analysis covers both linear and nonlinear models, including models with dynamics and/or individual heterogeneity. In addition to general estimation frameworks (particular methods of moments and maximum likelihood), specific linear and nonlinear methods are covered in detail, including probit and logit models and their multivariate, Tobit models, models for count data, censored and missing data schemes, causal (or treatment) effects, and duration analysis. Econometric Analysis of Cross Section and Panel Data was the first graduate econometrics text to focus on microeconomic data structures, allowing assumptions to be separated into population and sampling assumptions. This second edition has been substantially updated and revised. Improvements include a broader class of models for missing data problems; more detailed treatment of cluster problems, an important topic for empirical researchers; expanded discussion of "generalized instrumental variables" (GIV) estimation; new coverage (based on the author's own recent research) of inverse probability weighting; a more complete framework for estimating treatment effects with panel data, and a firmly established link between econometric approaches to nonlinear panel data and the "generalized estimating equation" literature popular in statistics and other fields. New attention is given to explaining when particular econometric methods can be applied; the goal is not only to tell readers what does work, but why certain "obvious" procedures do not. The numerous included exercises, both theoretical and computer-based, allow the reader to extend methods covered in the text and discover new insights.

28,263 citations

•

01 Jan 1962TL;DR: In this article, the authors introduce the principles of estimation and inference: means and variance, means and variations, and means and variance of estimators and inferors, and the analysis of factorial experiments having repeated measures on the same element.

Abstract: CHAPTER 1: Introduction to Design CHAPTER 2: Principles of Estimation and Inference: Means and Variance CHAPTER 3: Design and Analysis of Single-Factor Experiments: Completely Randomized Design CHAPTER 4: Single-Factor Experiments Having Repeated Measures on the Same Element CHAPTER 5: Design and Analysis of Factorial Experiments: Completely-Randomized Design CHAPTER 6: Factorial Experiments: Computational Procedures and Numerical Example CHAPTER 7: Multifactor Experiments Having Repeated Measures on the Same Element CHAPTER 8: Factorial Experiments in which Some of the Interactions are Confounded CHAPTER 9: Latin Squares and Related Designs CHAPTER 10: Analysis of Covariance

25,574 citations

••

TL;DR: In this article, the generalized method of moments (GMM) estimator optimally exploits all the linear moment restrictions that follow from the assumption of no serial correlation in the errors, in an equation which contains individual effects, lagged dependent variables and no strictly exogenous variables.

Abstract: This paper presents specification tests that are applicable after estimating a dynamic model from panel data by the generalized method of moments (GMM), and studies the practical performance of these procedures using both generated and real data. Our GMM estimator optimally exploits all the linear moment restrictions that follow from the assumption of no serial correlation in the errors, in an equation which contains individual effects, lagged dependent variables and no strictly exogenous variables. We propose a test of serial correlation based on the GMM residuals and compare this with Sargan tests of over-identifying restrictions and Hausman specification tests.

23,658 citations