Recent Advances in Statistics

Recent Advances in Statistics: Papers in Honor of Herman Chernoff on His Sixtieth Birthday is a collection of papers on statistics in honor of Herman Chernoff on the occasion of his 60th birthday. Topics covered range from sequential analysis (including designs) to optimization (including control theory), nonparametrics (including large sample theory), and statistical graphics.

Comprised of 27 chapters, this book begins with a discussion on optimal stopping of Brownian motion, followed by an analysis of sequential design of comparative clinical trials. A two-sample sequential test for shift with one sample size fixed in advance is then presented. Subsequent chapters focus on set-valued parameters and set-valued statistics; large deviations of the maximum likelihood estimate in the Markov chain case; the limiting behavior of multiple roots of the likelihood equation; and optimal uniform rate of convergence for nonparametric estimators of a density function and its derivatives. The book concludes by considering significance and confidence levels, closed regions and models, and discrete distributions.

This monograph should be of interest to students, researchers, and specialists in the fields of mathematics and statistics.

Contributors

Preface

Herman Chernoff: An Appreciation

I. Sequential Analysis Including Designs

Optimal Stopping of Brownian Motion: A Comparison Technique

Sequential Design of Comparative Clinical Trials

The Cramér-Rao Inequality Holds Almost Everywhere

A Two-Sample Sequential Test for Shift with One Sample Size Fixed in Advance

On Sequential Rank Tests

II. Optimization Including Control Theory

A Non-Homogeneous Markov Model of a Chain-Letter Scheme

Set-Valued Parameters and Set-Valued Statistics

Optimal Sequential Decisions in Problems Involving More than One Decision Maker

An Averaging Method for Stochastic Approximations with Discontinuous Dynamics, Constraints, and State Dependent Noise

Enlighted Approximations in Optimal Stopping

Survey of Classical and Bayesian Approaches to the Change-Point Problem: Fixed Sample and Sequential Procedures of Testing and Estimation

III. Nonparametrics Including Large Sample Theory

Large Deviations of the Maximum Likelihood Estimate in the Markov Chain Case

Bayesian Density Estimation by Mixtures of Normal Distribution

An Extension of a Theorem of H. Chernoff and E. L. Lehmann

The Limiting Behavior of Multiple Roots of the Likelihood Equation

On Some Recursive Residual Rank Tests for Change-Points

Optimal Uniform Rate of Convergence for Nonparametric Estimators of a Density Function and Its Derivatives

Ranks and Order Statistics

IV. Statistical Graphics

M and N Plots

Investigating the Space of Chernoff Faces

On Multivariate Display

V. Other Topics

Minimax Estimation of the Mean of a Normal Distribution Subject to Doing Well at a Point

Some New Dichotomous Regression Methods

The Application of Spline Functions to the Pharmacokinetic Analysis of Methotrexate Infused into Malignant Effusions

Selecting Representative Points in Normal Populations

Least Informative Distributions

Significance Levels, Confidence Levels, Closed Regions, Closed Models, and Discrete Distributions