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.

Inhalt

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