Selected Papers

ISBN-13: 9781493971336 / Angielski / Miękka / 2017 / 518 str.

Herbert Robbins; Tze Leung Lai; David Siegmund

Opis

Herbert Robbins is widely recognized as one of the most creative and original mathematical statisticians of our time. The purpose of this book is to reprint, on the occasion of his seventieth birthday, some of his most outstanding research. In making selections for reprinting we have tried to keep in mind three potential audiences: (1) the historian who would like to know Robbins' seminal role in stimulating a substantial proportion of current research in mathematical statistics; (2) the novice who would like a readable, conceptu- ally oriented introduction to these subjects; and (3) the expert who would like to have useful reference material in a single collection. In many cases the needs of the first two groups can be met simulta- neously. A distinguishing feature of Robbins' research is its daring original- ity, which literally creates new specialties for subsequent generations of statisticians to explore. Often these seminal papers are also models of exposition serving to introduce the reader, in the simplest possible context, to ideas that are important for contemporary research in the field. An example is the paper of Robbins and Monro which initiated the subject of stochastic approximation. We have also attempted to provide some useful guidance to the literature in various subjects by supplying additional references, particularly to books and survey articles, with some remarks about important developments in these areas.

Spis treści

One: Empirical Bayes Methodology and Compound Decision Theory.- [25] Asymptotically Subminimax Solutions of Compound Statistical Decision Problems.- [39] Asymptotic Solutions of the Compound Decision Problem for Two Completely Specified Distributions.- [41] An Empirical Bayes Approach to Statistics.- [59] The Empirical Bayes Approach to Statistical Decision Problems.- [103] Prediction and Estimation for the Compound Poisson Distribution.- [118] An Empirical Bayes Estimation Problem.- [123] Estimating Many Variances.- [124] Some Thoughts on Empirical Bayes Estimation.- Two: Sequential Experimentation and Analysis, A. Stochastic Approximation.- A. Stochastic Approximation.- [26] A Stochastic Approximation Method (with S. Monro).- [87] A Convergence Theorem for Non-Negative Almost Supermartingales and Some Applications (with D. Siegmund).- [107] Adaptive Design in Regression and Control (with T. L. Lai).- [113] Adaptive Design and Stochastic Approximation (with T. L. Lai).- B. Adaptive Allocation of Treatments in Sequential Experiments.- [28] Some Aspects of the Sequential Design of Experiments.- [42] A Sequential Decision Problem with a Finite Memory.- [129] Optimal Sequential Sampling From Two Populations (with T. L. Lai).- [89] Reducing the Number of Inferior Treatments in Clinical Trials (with B. Flehinger, T. Louis, and B. Singer).- [96] Sequential Tests Involving Two Populations (with D. Siegmund).- C. Sequential Estimation and Testing.- [44] Sequential Estimation of the Mean of a Normal Population.- [64] On the Asymptotic Theory of Fixed-Width Sequential Confidence Intervals for the Mean (with Y. S. Chow).- [68] Finding the Size of a Finite Population (with D. A. Darling).- [51] A Bayes Test of p ? ½ Versus p > ½ (with S. Moriguti).- [116] Sequential Medical Trials (with T. L. Lai, B. Levin, and D. Siegmund).- D. Power-One Tests and Related Boundary Crossing Probabilities.- [70] Iterated Logarithm Inequalities (with D. A. Darling).- [82] Statistical Methods Related to the Law of the Iterated Logarithm.- [83] Boundary Crossing Probabilities for the Wiener Process and Sample Sums (with D. Siegmund).- [91] A Class of Stopping Rules for Testing Parametric Hypotheses (with D. Siegmund).- [92] Statistical Tests of Power One and the Integral Representation of Solutions of Certain Partial Differential Equations (with D. Siegmund).- Three: Probability and Inference.- [7] On the Measure of a Random Set.- [12] Complete Convergence and the Law of Large Numbers (with P. L. Hsu).- [16] The Central Limit Theorem for Dependent Random Variables (with W. Hoeffding).- [21] Application of the Method of Mixtures to Quadratic Forms in Normal Variates (with E. J. G. Pitman).- [27] Minimum Variance Estimation Without Regularity Assumptions (with D. G. Chapman).- [30] Ergodic Property of the Brownian Motion Process (with G. Kallianpur).- [31] On the Equidistribution of Sums of Independent Random Variables.- [32] Ergodic Theory of Markov Chains Admitting an Infinite Invariant Measure (with T. E. Harris).- [38] A Remark on Stirling’s Formula.- [48] On Sums of Independent Random Variables with Infinite Moments and ‘Fair’ Games (with Y. S. Chow).- [49] A Martingale System Theorem and Applications (with Y. S. Chow).- [55] On Optimal Stopping Rules (with Y. S. Chow).- [61] Optimal Selection Based on Relative Rank—The ‘Secretary Problem’ (with Y. S. Chow, S. Moriguti, and S. M. Samuels).- [85] Optimal Stopping.- [63] Moments of Randomly Stopped Sums (with Y. S. Chow and H. Teicher).- [60] On the ‘Parking’ Problem (with A. Dvoretzky).- [75] Estimating the Total Probability of the Unobserved Outcomes of an Experiment.- [93] Mathematical Probability in Election Challenges (with M. O. Finkelstein).- [102] Maximally Dependent Random Variables (with T. L. Lai).- [110] Strong Consistency of Least Squares Estimates in Multiple Regression (with T. L. Lai and C. Z. Wei).- [125] A Note on the Underadjustment Phenomenon (with B. Levin).