05526nam 22006734a 450 991084112170332120230828212950.01-280-44801-697866104480120-470-36055-00-471-77375-10-471-77374-3(CKB)1000000000355586(EBL)257208(OCoLC)71522917(SSID)ssj0000258240(PQKBManifestationID)11194633(PQKBTitleCode)TC0000258240(PQKBWorkID)10255213(PQKB)11004198(MiAaPQ)EBC257208(EXLCZ)99100000000035558620050622d2006 uy 0engur|n|---|||||txtccrTheory of preliminary test and Stein-type estimation with applications[electronic resource] /A.K. Md. Ehsanes SalehHoboken, NJ Wiley-Intersciencec20061 online resource (656 p.)Wiley Series in Probability and Statistics ;v.517Description based upon print version of record.0-471-56375-7 Includes bibliographical references (p. 601-612) and indexes.Theory of Preliminary Test and Stein-Type Estimation with Applications; Contents; List of Figures; List of Figures; List of Tables; List of Tables; Preface; 1 Introduction; 1.1.1 Batting averages of 18 players; 1.1 Display of predicted batting averages based on Stein's formula; 1.1 Objective of This Book; 1.2 Statistical Decision Principle; 1.3 Quadratic Loss Function; 1.4 Some Statistical Models with Preliminaries; 1.4.1 Mean and Simple Linear Models; 1.4.2 One-Sample Multivariate Model; 1.4.3 ANOVA Models; 1.4.4 Parallelism Models1.4.5 Multiple Regression Model and General Linear Hypothesis1.4.6 Simple Multivariate Linear Model; 1.4.7 Discrete Data Models; 1.5 Organization of the Book; 1.6 Conclusions; 1.7 Problems; 2 Preliminaries; 2.1 Normal Distribution; 2.2 Chi-square Distribution and Properties; 2.3 Some Results from Multivariate Normal Theory; 2.4 Beta Distribution and Applications; 2.5 Discrete Distributions; 2.5.1 Binomial Distribution; 2.5.2 Multinomial Distribution; 2.6 Matrix Results; 2.7 Large Sample Theory; 2.7.1 Four Types of Convergence; 2.7.2 Law of Large Numbers; 2.7.3 Central Limit Theorems2.8 Nonparametric Theory: Preliminaries2.8.1 Order-Statistics, Ranks, and Sign Statistics; 2.8.2 Linear rank-statistics (LRS); 2.8.3 Rank Estimators of the Parameters of Various Models; 2.9 Problems; 3 Preliminary Test Estimation; 3.1 Simple Linear Model, Estimators, and Tests; 3.1.1 Simple Linear Model; 3.1.2 Estimation of the Intercept and Slope Parameter; 3.1.3 Test for the Slope Parameter; 3.2 PTE of the Intercept Parameter; 3.2.1 UE, RE and PTE of the Intercept Parameter; 3.2.2 Bias and MSE Expressions; 3.2.3 Comparison of bias and mse functions3.2.1 Graph of quadratic bias functions of the estimators3.2.4 Optimum Level of Significance of Preliminary Test; 3.2.2 Graph of MRE(tn; tn) and MRE(tPTn; tn); 3.2.1 Maximum and Minimum Guaranteed Efficiencies for n = 8; 3.2.2 Maximum and Minimum Guaranteed Efficiencies for n = 12 and x2/Q = 0.1(0.2)0.9; 3.3 Two-Sample Problem and Pooling of Means; 3.3.1 Model; 3.3.2 Estimation and Test of the Difference between Two Means; 3.3.3 Bias and mse Expression of the Three Estimators of a Mean; 3.3.1 Maximum and Minimum Guaranteed Efficiencies; 3.3.2 Maximum and Minimum Guaranteed Efficiencies3.3.3 Maximum and Minimum Guaranteed Efficiencies3.4 One-Sample Problem: Estimation of Mean; 3.4.1 Model; 3.4.2 Unrestricted, Restricted, and Preliminary Test Estimators; 3.3.1 Graph of MRE (m1; m1) and MRE(mPT1; m1); 3.4.3 Bias, mse, and Analysis of Efficiency; 3.5 An Alternative Approach; 3.5.1 Introduction; 3.4.1 Minimum and Maximum Efficiency of PTE; 3.5.2 One-Sample Problem; 3.5.3 Comparison of PTE, tPTn and SE tSn; 3.5.1 Maximum and Minimum Efficiencies of SE and Efficiency of PTE at D0 for Selected a; 3.5.4 Simple Linear Model and Shrinkage Estimation3.5.1 Graph of the relative efficiency of SE and PTE for different values of aTheory of Preliminary Test and Stein-Type Estimation with Applications provides a com-prehensive account of the theory and methods of estimation in a variety of standard models used in applied statistical inference. It is an in-depth introduction to the estimation theory for graduate students, practitioners, and researchers in various fields, such as statistics, engineering, social sciences, and medical sciences. Coverage of the material is designed as a first step in improving the estimates before applying full Bayesian methodology, while problems at the end of each chapter enlarge the scope Wiley Series in Probability and StatisticsParameter estimationRegression analysisBayesian statistical decision theoryParameter estimation.Regression analysis.Bayesian statistical decision theory.519.5/44519.544Saleh A. K. Md. Ehsanes150888MiAaPQMiAaPQMiAaPQBOOK9910841121703321Theory of preliminary test and Stein-type estimation with applications245973UNINA