T. W. Anderson

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

The Statistical Analysis of Time Series

Abstract: The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold M. S. Coxeter Introduction to Modern Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Bruno de Finetti Theory of Probability, Volume 1 Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1 --Nuclear Structure J. L. Doob Stochastic Processes Nelson Dunford & Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory--Self Adjoint Operators in Hilbert Space Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Herman Fsehbach Theoretical Nuclear Physics: Nuclear Reactions Bernard Friedman Lectures on Applications-Oriented Mathematics Gerald d. Hahn & Samuel S. Shapiro Statistical Models in Engineering Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume I--Methods and Applications Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume II--Theory Peter Henrici Applied and Computational Complex Analysis, Volume 1--Power Series--lntegration--Conformal Mapping--Location of Zeros Peter Henrici Applied and Computational Complex Analysis, Volume 2--Special Functions--Integral Transforms--Asymptotics--Continued Fractions Peter Henrici Applied and Computational Complex Analysis, Volume 3--Discrete Fourier Analysis--Cauchy Integrals--Construction of Conformal Maps--Univalent Functions Peter Hilton & Yel-Chiang Wu A Course in Modern Algebra Harry Hochetadt Integral Equations Erwin O. Kreyezig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation All Hasan Nayfeh Introduction to Perturbation Techniques Emanuel Parzen Modern Probability Theory and Its Applications P.M. Prenter Splines and Variational Methods Walter Rudin Fourier Analysis on Groups C. L. Siegel Topics in Complex Function Theory, Volume I--Elliptic Functions and Uniformization Theory C. L. Siegel Topics in Complex Function Theory, Volume II--Automorphic and Abelian integrals C. L Siegel Topics in Complex Function Theory, Volume III--Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry J. J. Stoker Water Waves: The Mathematical Theory with Applications J. J. Stoker Nonlinear Vibrations in Mechanical and Electrical Systems

A Test of Goodness of Fit

Abstract: Some (large sample) significance points are tabulated for a distribution-free test of goodness of fit which was introduced earlier by the authors. The test, which uses the actual observations without grouping, is sensitive to discrepancies at the tails of the distribution rather than near the median. An illustration is given, using a numerical example used previously by Birnbaum in illustrating the Kolmogorov test.

Statistical Inference about Markov Chains

Abstract: Maximum likelihood estimates and their asymptotic distribution are obtained for the transition probabilities in a Markov chain of arbitrary order when there are repeated observations of the chain. Likelihood ratio tests and $\chi^2$-tests of the form used in contingency tables are obtained for testing the following hypotheses: (a) that the transition probabilities of a first order chain are constant, (b) that in case the transition probabilities are constant, they are specified numbers, and (c) that the process is a $u$th order Markov chain against the alternative it is $r$th but not $u$th order. In case $u = 0$ and $r = 1$, case (c) results in tests of the null hypothesis that observations at successive time points are statistically independent against the alternate hypothesis that observations are from a first order Markov chain. Tests of several other hypotheses are also considered. The statistical analysis in the case of a single observation of a long chain is also discussed. There is some discussion of the relation between likelihood ratio criteria and $\chi^2$-tests of the form used in contingency tables.

Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations

Abstract: A method is given for estimating the coefficients of a single equation in a complete system of linear stochastic equations (see expression (2.1)), provided that a number of the coefficients of the selected equation are known to be zero. Under the assumption of the knowledge of all variables in the system and the assumption that the disturbances in the equations of the system are normally distributed, point estimates are derived from the regressions of the jointly dependent variables on the predetermined variables (Theorem 1). The vector of the estimates of the coefficients of the jointly dependent variables is the characteristic vector of a matrix involving the regression coefficients and the estimate of the covariance matrix of the residuals from the regression functions. The vector corresponding to the smallest characteristic root is taken. An efficient method of computing these estimates is given in section 7. The asymptotic theory of these estimates is given in a following paper [2]. When the predetermined variables can be considered as fixed, confidence regions for the coefficients can be obtained on the basis of small sample theory (Theorem 3). A statistical test for the hypothesis of over-identification of the single equation can be based on the characteristic root associated with the vector of point estimates (Theorem 2) or on the expression for the small sample confidence region (Theorem 4). This hypothesis is equivalent to the hypothesis that the coefficients assumed to be zero actually are zero. The asymptotic distribution of the criterion is shown in a following paper [2] to be that of $\chi^2$.

Asymptotic theory for principal component analysis

Abstract: : The asymptotic distribution of the characteristic roots and (normalized) vectors of a sample covariance matrix is given when the observations are from a multivariate normal distribution whose covariance matrix has characteristic roots of arbitrary multiplicity. The elements of each characteristic vector are the coefficients of a principal component (with sum of squares of coefficients being unity), and the corresponding characteristic root is the variance of the principal component. Tests of hypotheses of equality of population roots are treated, and confidence intervals for assumed equal roots are given; these are useful in assessing the importance of principal components. A similar study for correlation matrices is considered. (Author)

Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives

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...

A new look at the statistical model identification

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.

Econometric Analysis of Cross Section and Panel Data

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.

Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations.

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.

Statistical Principles in Experimental Design

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