LEADER 05526nam 22006734a 450 001 9910841121703321 005 20230828212950.0 010 $a1-280-44801-6 010 $a9786610448012 010 $a0-470-36055-0 010 $a0-471-77375-1 010 $a0-471-77374-3 035 $a(CKB)1000000000355586 035 $a(EBL)257208 035 $a(OCoLC)71522917 035 $a(SSID)ssj0000258240 035 $a(PQKBManifestationID)11194633 035 $a(PQKBTitleCode)TC0000258240 035 $a(PQKBWorkID)10255213 035 $a(PQKB)11004198 035 $a(MiAaPQ)EBC257208 035 $a(EXLCZ)991000000000355586 100 $a20050622d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTheory of preliminary test and Stein-type estimation with applications$b[electronic resource] /$fA.K. Md. Ehsanes Saleh 210 $aHoboken, NJ $cWiley-Interscience$dc2006 215 $a1 online resource (656 p.) 225 1 $aWiley Series in Probability and Statistics ;$vv.517 300 $aDescription based upon print version of record. 311 $a0-471-56375-7 320 $aIncludes bibliographical references (p. 601-612) and indexes. 327 $aTheory 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 Models 327 $a1.4.5 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 Theorems 327 $a2.8 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 functions 327 $a3.2.1 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 Efficiencies 327 $a3.3.3 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 Estimation 327 $a3.5.1 Graph of the relative efficiency of SE and PTE for different values of a 330 $aTheory of Preliminary Test and Stein-Type Estimation with Applications provides a com-prehensive account of the theory and methods of estimation in a variety of standard models used in applied statistical inference. It is an in-depth introduction to the estimation theory for graduate students, practitioners, and researchers in various fields, such as statistics, engineering, social sciences, and medical sciences. Coverage of the material is designed as a first step in improving the estimates before applying full Bayesian methodology, while problems at the end of each chapter enlarge the scope 410 0$aWiley Series in Probability and Statistics 606 $aParameter estimation 606 $aRegression analysis 606 $aBayesian statistical decision theory 615 0$aParameter estimation. 615 0$aRegression analysis. 615 0$aBayesian statistical decision theory. 676 $a519.5/44 676 $a519.544 700 $aSaleh$b A. K. Md. Ehsanes$0150888 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910841121703321 996 $aTheory of preliminary test and Stein-type estimation with applications$9245973 997 $aUNINA