Statistical Theory and Applications

ISBN-13: 9780387945910 / Angielski / Twarda / 1995 / 334 str.

H. N. Nagaraja; H. N. Nagaraja; Pranab K. Sen

Opis

Professor Herbert A. David of Iowa State University will be turning 70 on December 19, 1995. He is reaching this milestone in life with a very distinguished career as a statistician, educator and administrator. We are bringing out this volume in his honor to celebrate this occasion and to recognize his contributions to order statistics, biostatistics and design of experiments, among others; and to the statistical profession in general. With great admiration, respect and pleasure we dedicate this festschrift to Professor Herbert A. David, also known as Herb and H.A. among his friends, colleagues and students. When we began this project in Autumn 1993 and contacted potential contributors from the above group, the enthu siasm was phenomenal. The culmination of this collective endeavor is this volume that is being dedicated to him to celebrate his upcoming birthday. Several individuals have contributed in various capacities to the success ful completion of this project. We sincerely thank the authors of the papers appearing here. Without their dedicated work, we would just have this pref ace Many of them have served as (anonymous) referees as well. In addition, we are thankful to the following colleagues for their time and advice: John Bunge (Cornell), Z. Govindarajulu (Kentucky), John Klein (Medical U."

Spis treści

I General Distribution Theory and Inference.- 1 PIC: Power Divergence Information Criterion.- 1.1 Introduction.- 1.2 The Power Divergence Measures.- 1.3 Power-divergence Information Criterion (PIC).- 1.4 Count Data from the Framingham Study.- 1.5 Conclusions.- 1.6 References.- 2 Multivariate Student’s t and Its Applications.- 2.1 Introduction.- 2.2 A Multivariate Student t Distribution.- 2.2.1 Definition and Probability Integral.- 2.2.2 Computing the Probability Integral for p > 2.- 2.2.3 An Approximation for the Unequal pij Case.- 2.3 Applications of Multivariate t.- 2.3.1 Two-stage Indifference Zone Selection.- 2.3.2 Subset Selection.- 2.3.3 Treatments Versus Control Multiple Comparisons.- 2.3.4 Testing Multiple Contrasts.- 2.3.5 Multiple Comparisons with the “Best”.- 2.3.6 Additional Applications.- 2.4 References.- 3 Two Sets of Multivariate Bonferroni-type Inequalities.- 3.1 Introduction.- 3.2 The Results.- 3.3 Proofs.- 3.4 References.- 4 On the Proportion above Sample Mean for Symmetric Stable Laws.- 4.1 Introduction.- 4.2 The Result.- 4.3 A Partial Converse.- 4.4 Remarks and Extensions.- 4.5 References.- 5 The Relative Efficiency of Several Statistics Measuring Skewness.- 5.1 Introduction.- 5.2 Skewness Functional for X with Finite Support.- 5.3 Relative Efficiency of Skewness Estimators when X has Finite Support.- 5.4 Relative Efficiency of Skewness Estimators when X has Infinite Support.- 5.5 Summary.- 5.6 References.- 6 On a Class of Symmetric Nonnormal Distributions with a Kurtosis of Three.- 6.1 Introduction.- 6.2 Symmetric Mixtures with ?2 = 3.- 6.3 Examples.- 6.4 Limiting Distributions of the Extremes.- 6.5 Comments.- 6.6 References.- II Order Statistics — Distribution Theory.- 7 Moments of the Selection Differential from Exponential and Uniform Parents.- 7.1 Introduction.- 7.2 Moments of D from an Exponential Parent.- 7.3 Moments of D from a Uniform Parent.- 7.4 Asymptotes for the Moments of D.- 7.5 Convergence of the Moments: Exponential Parent.- 7.6 Convergence of the Moments: Uniform Parent.- 7.7 Tabular Analysis.- 7.7.1 Mean.- 7.7.2 Variance.- 7.7.3 Skewness.- 7.7.4 Kurtosis.- 7.8 Practical Implications.- 7.9 References.- 8 The Tallest Man in the World.- 8.1 Introduction.- 8.2 Some Useful Results on Branching Processes.- 8.3 The Tallest Man in the World.- 8.4 The Tallest Man in History.- 8.5 What Kind of Limit Laws can be Encountered?.- 8.6 References.- 9 Characterizing Distributions by Properties of Order Statistics — A Partial Review.- 9.1 Introduction.- 9.2 Independence of Linear Functions.- 9.3 Identical Distributions of Functions of Order Statistics.- 9.4 Moment Properties.- 9.5 Statistical Properties.- 9.6 Asymptotic Properties.- 9.7 References.- 10 Stochastic Ordering of the Number of Records.- 10.1 Introduction.- 10.2 The Results.- 10.2.1 Stochastic Ordering.- 10.2.2 Expectation of the Number of k-th Records.- 10.2.3 Integrated Likelihood Ratio Ordering.- 10.3 Proofs and an Example.- 10.4 References.- 11 Moments of Cauchy Order Statistics via Riemann Zeta Functions.- 11.1 Introduction.- 11.2 An Expression for the Mean.- 11.3 Expressions for Product Moments.- 11.4 References.- 12 Order Statistics of Bivariate Exponential Random Variables.- 12.1 Introduction.- 12.2 Freund, Marshall-Olkin, ?nd Raftery’s BVE Distributions.- 12.3 Joint Distributions.- 12.4 Marginal Distributions.- 12.4.1 Properties of T1.- 12.4.2 Properties of T2.- 12.5 Copula Functions.- 12.6 References.- III Order Statistics in Inference and Applications.- 13 Maximum Likelihood Estimation of the Laplace Parameters Based on Type-II Censored Samples.- 13.1 Introduction.- 13.2 Maximum Likelihood Estimators.- 13.3 Efficiency Relative to BLUE’s.- 13.4 References.- 14 The Impact of Order Statistics on Signal Processing.- 14.1 Introduction.- 14.2 Order Statistic Filters.- 14.2.1 Median and Rank-Order Filters.- 14.2.2 RO Filters.- 14.2.3 OS Filters.- 14.3 Generalizations.- 14.3.1 ? and Ll Filters.- 14.3.2 Permutation Filters.- 14.3.3 WMMR Filters.- 14.3.4 Stack Filters.- 14.3.5 Morphological Filters.- 14.4 Related Applications of Order Statistics.- 14.4.1 Edge Detection.- 14.4.2 Signal Enhancement and Restoration.- 14.5 Conclusions.- 14.6 References.- 15 A Nonlinear Ordered Rank Test to Detect Stochastic Ordering Between Two Distributions.- 15.1 Introduction.- 15.2 The Proposed Test.- 15.3 Simulation Study.- 15.4 Discussion.- 15.5 Asymptotic Properties.- 15.6 References.- 16 Estimation of Location and Scale Parameters of a Logistic Distribution Using a Ranked Set Sample.- 16.1 Introduction.- 16.2 Estimation of the Location Parameter.- 16.2.1 Best Linear Unbiased Estimator.- 16.2.2 Which Order Statistic?.- 16.3 Estimation of the Scale Parameter.- 16.4 Estimation of Quantiles.- 16.5 Proofs.- 16.6 References.- 17 Probability Models for an Employment Problem.- 17.1 Introduction.- 17.2 Definition of the Problem.- 17.2.1 Hiring Criteria.- 17.2.2 Notation.- 17.3 The Case of Couples and Single Applicants.- 17.3.1 Small Sample Results.- 17.3.2 Asymptotic Results.- 17.4 A Strategy for Couples.- 17.5 Conclusions.- 17.6 References.- IV Analysis of Variance and Experimental Design.- 18 On the Robustness of Bayes Estimators of the Variance Ratio in Balanced One-Way ANOVA Models with Covariates.- 18.1 Introduction.- 18.2 The Bayes Estimator and its Asymptotic Properties.- 18.3 Jackknifed Estimator of the Asymptotic Variance and Asymptotic Confidence Intervals.- 18.4 Simulation Results.- 18.5 References.- 19 Interchange Algorithms for Constructing Designs with Complex Blocking Structures.- 19.1 Historical Perspective.- 19.2 Optimality Criteria.- 19.3 Interchange Algorithms.- 19.4 Objective Functions.- 19.5 Discussion.- 19.6 References.- 20 Paired Comparisons for Multiple Characteristics: An ANOCOVA Approach.- 20.1 Introduction.- 20.2 ANOCOVAPC for Paired Characteristics.- 20.3 Probability Laws for Multiple Dichotomous Attributes.- 20.4 MANOCOVAPC Paired Comparisons Models and Analyses.- 20.5 Concluding Remarks.- 20.6 References.- V Biometry and Applications.- 21 On Assessing Multiple Equivalences with Reference to Bioequivalence.- 21.1 Introduction.- 21.2 Many-to-One Comparisons.- 21.3 Assessing Equivalence of k Formulations.- 21.4 Multiple Partial Equivalences.- 21.5 Example.- 21.6 References.- 22 Competing Risks.- 22.1 Introduction.- 22.2 Some Independent Competing Risk Results (After 1978).- 22.3 Non-identifiability Issues.- 22.4 Methods Assuming Informative Censoring (Dependent Competing Risks).- 22.5 Inference Using Estimable Quantities.- 22.6 Summary.- 22.7 References.- 23 Statistical Aspects of the Detection of Activation Effects in Cerebral Blood Flow and Metabolism by Positron Emission Tomography.- 23.1 Introduction: The Analysis of PET Data.- 23.2 The Activation Experiment and the Data.- 23.3 Activation Effects and a Simple Whole Brain Adjustment.- 23.4 Adjustment by the Analysis of Covariance.- 23.5 References.- 24 On Optimality of Q—Charts for Outliers in Statistical Process Control.- 24.1 Introduction.- 24.2 The Normal Mean Q-Chart.- 24.3 The Binomial Q-Chart.- 24.4 The Poisson Q-Chart.- 24.5 References.- VI Postscript.- 25 Herbert A. David.- 26 Conference Abstracts, Anecdotes, and Appreciation.

O autorze

H. N. NAGARAJA, PhD, is a professor in the Departments of Statistics and Internal Medicine at The Ohio State University. He coedited, along with P. K. Sen and D. F. Morrison, Statistical Theory and Applications: Papers in Honor of H. A. David, and coauthored, along with B. C. Arnold and N. Balakrishnan, Records.