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.

ContributorsPrefaceHerman Chernoff: An AppreciationI. 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 TestsII. 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 EstimationIII. 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 StatisticsIV. Statistical Graphics M and N Plots Investigating the Space of Chernoff Faces On Multivariate DisplayV. 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