LEADER 05520nam 2200649Ia 450 001 9910677848303321 005 20230421050557.0 010 $a1-283-27397-7 010 $a9786613273970 010 $a1-118-16486-5 010 $a1-118-16485-7 035 $a(CKB)2550000000054362 035 $a(EBL)818919 035 $a(SSID)ssj0000550645 035 $a(PQKBManifestationID)11379939 035 $a(PQKBTitleCode)TC0000550645 035 $a(PQKBWorkID)10509327 035 $a(PQKB)10614863 035 $a(MiAaPQ)EBC818919 035 $a(OCoLC)757511706 035 $a(EXLCZ)992550000000054362 100 $a19970610d1998 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStatistical tests in mixed linear models$b[electronic resource] /$fAndre? I. Khuri, Thomas Mathew, Bimal K. Sinha 210 $aNew York $cWiley$dc1998 215 $a1 online resource (378 p.) 225 1 $aWiley series in probability and statistics. Applied probability and statistics section 300 $aDescription based upon print version of record. 311 $a0-471-15653-1 320 $aIncludes bibliographical references (p. 335-343) and indexes. 327 $aStatistical Tests for Mixed Linear Models; Contents; Preface; 1. Nature of Exact and Optimum Tests in Mixed Linear Models; 1.1. Introduction; 1.2. Exact F-Tests; 1.3. Optimality of Tests; 1.3.1. Uniformly Most Powerful Similar and Uniformly Most Powerful Unbiased Tests; 1.3.2. Uniformly Most Powerful Invariant and Locally Most Powerful or Locally Best Invariant Tests; Appendix 1.1. Distribution of a Maximal Invariant T (x): Wijsman's Representation Theorem; Bibliography; 2. Balanced Random and Mixed Models; 2.1. Introduction; 2.2. Balanced Models - Notations and Definitions 327 $a2.3. Balanced Model Properties2.4. Balanced Mixed Models: Distribution Theory; 2.5. Derivation of Optimum Tests; 2.5.1. A Numerical Example; 2.6. Approximate and Exact Tests; 2.6.1. Satterthwaite's Approximation; 2.6.2. Exact Unbiased Tests of Bartlett-Scheffe? Type; Exercises; Bibliography; 3. Measures of Data Imbalance; 3.1. Introduction; 3.2. The Effects of Imbalance; 3.2.1. The Variance of ?2?; 3.2.2. The Probability of a Negative ?2?; 3.2.3. Power of the Test Concerning ?2?; 3.3. Measures of Imbalance for the One-Way Model; 3.3.1. The Effect of Imbalance on Var(?2?) 327 $a3.3.2. The Effect of Imbalance on the Test Concerning ?2?3.4. A General Procedure For Measuring Imbalance; 3.4.1. The One-Way Classification Model; 3.4.2. The Two-Way Classification Model; 3.4.3. The Three-Way Classification Model; 3.5. Special Types of Imbalance; 3.5.1. The Two-Fold Nested Classification Model; 3.5.2. A Model With a Mixture of Cross-Classified and Nested Effects; 3.6. A General Method for Determining the Effect of Imbalance; 3.6.1. Generation of Designs Having a Specified Degree of Imbalance for the One-Way Model; 3.6.2. An Example; 3.7. Summary 327 $aAppendix 3.1. Hirotsu's ApproximationExercises; Bibliography; 4. Unbalanced One-Way and Two-Way Random Models; 4.1. Introduction; 4.2. Unbalanced One-Way Random Models; 4.3. Two-Way Random Models; 4.3.1. Models Without Interaction: Exact Tests; 4.3.2. Models Without Interaction: Optimum Tests; 4.3.3. Models With Interaction: Exact Tests; 4.3.4. A Numerical Example; 4.4. Random Two-Fold Nested Models; 4.4.1. Testing H?(?) : ?2?(?) = 0; 4.4.2. Testing H? : ?2? = 0; Exercises; Bibliography; 5. Random Models with Unequal Cell Frequencies in the Last Stage; 5.1. Introduction 327 $a5.2. Unbalanced Random Models With Imbalance In The Last Stage Only-Notation5.3. Unbalanced Random Models With Imbalance In The Last Stage Only-Analysis; 5.3.1. Derivation of Exact Tests; 5.4. More on Exact Tests; 5.4.1. Power of the Exact Tests; 5.4.2. Sufficient Statistics Associated With the Exact Tests; 5.5. A Numerical Example; Exercises; Bibliography; 6. Tests in Unbalanced Mixed Models; 6.1. Introduction; 6.2. Mixed Models With Two Variance Components; 6.2.1. Test for H? : ?1 = ... = ??; 6.2.2. Optimum Test for H? : ?2? = 0 327 $a6.3. Mixed Two-Way Crossed-Classification Models With Interactions 330 $aAn advanced discussion of linear models with mixed or random effects. In recent years a breakthrough has occurred in our ability to draw inferences from exact and optimum tests of variance component models, generating much research activity that relies on linear models with mixed and random effects. This volume covers the most important research of the past decade as well as the latest developments in hypothesis testing. It compiles all currently available results in the area of exact and optimum tests for variance component models and offers the only comprehensive treatment for these 410 0$aWiley series in probability and statistics.$pApplied probability and statistics. 606 $aLinear models (Statistics) 606 $aStatistical hypothesis testing 615 0$aLinear models (Statistics) 615 0$aStatistical hypothesis testing. 676 $a519.5 700 $aKhuri$b Andre? I.$f1940-$0251821 701 $aMathew$b Thomas$f1955-$01341652 701 $aSinha$b Bimal K.$f1946-$0102097 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910677848303321 996 $aStatistical tests in mixed linear models$93069886 997 $aUNINA LEADER 01795nam 2200529 450 001 996479371303316 005 20231110224556.0 010 $a3-030-70578-1 035 $a(MiAaPQ)EBC7021275 035 $a(Au-PeEL)EBL7021275 035 $a(CKB)23976922500041 035 $aEBL7021275 035 $a(AU-PeEL)EBL7021275 035 $a(PPN)269150714 035 $a(EXLCZ)9923976922500041 100 $a20221226d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTesting statistical hypotheses /$fE. L. Lehmann and Joseph P. Romano 205 $a4th ed. 210 1$aCham, Switzerland :$cSpringer International Publishing,$d[2022] 210 4$d©2022 215 $a1 online resource (1016 pages) 225 1 $aSpringer Texts in Statistics 300 $aDescription based upon print version of record. 311 08$aPrint version: Lehmann, E. L. 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