Recent Advances in Statistics

Recent Advances in Statistics

Papers in Honor of Herman Chernoff on His Sixtieth Birthday

1st Edition - January 28, 1983

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  • Editors: M. Haseeb Rizvi, Jagdish S. Rustagi, David Siegmund
  • eBook ISBN: 9781483266602

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Description

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.

Table of Contents


  • 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

Product details

  • No. of pages: 626
  • Language: English
  • Copyright: © Academic Press 1983
  • Published: January 28, 1983
  • Imprint: Academic Press
  • eBook ISBN: 9781483266602

About the Editors

M. Haseeb Rizvi

Jagdish S. Rustagi

David Siegmund

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