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9789810218751

Group Invariance in Statistical Inference

by Giri, Narayan C.
  • ISBN13:

    9789810218751

  • ISBN10:

    9810218753

  • eBook ISBN(s):

    9789812831705

  • Format: Hardcover
  • Copyright: 1997-05-01
  • Publisher: WORLD SCIENTIFIC PUB CO INC
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Table of Contents

Chapter 0. GROUP INVARIANCE
1(6)
0.0. Introduction
1(2)
0.1. Examples
3(4)
Chapter 1. MATRICES, GROUPS AND JACOBIANS
7(9)
1.0. Introduction
7(1)
1.1. Matrices
7(3)
1.1.1. Characteristic Roots and Vectors
8(1)
1.1.2. Factorization of Matrices
9(1)
1.1.3. Partitioned Matrices
9(1)
1.2. Groups
10(2)
1.3. Homomorphism, Isomorphism and Direct Product
12(1)
1.4. Topological Transitive Groups
12(1)
1.5. Jacobians
13(20)
Chapter 2. INVARIANCE
16(33)
2.0. Introduction
16(1)
2.1. Invariance of Distributions
16(9)
2.1.1. Transformation of Variable in Abstract Integral
22(3)
2.2. Invariance of Testing Problems
25(1)
2.3. Invariance of Statistical Tests and Maximal Invariant
26(2)
2.4. Some Examples of Maximal Invariants
28(3)
2.5. Distribution of Maximal Invariant
31(2)
2.5.1. Existence of an Invariant Probability Measure on O(p) (Group of p x p Othogonal Matrices)
33(1)
2.6. Applications
33(3)
2.7. The Distribution of a Maximal Invariant in the General Case
36(1)
2.8. An Important Multivariate Distribution
37(7)
2.9. Almost Invariance, Sufficiency and Invariance
44(1)
2.10. Invariance, Type D and E Regions
45(4)
Chapter 3. EQUIVARIANT ESTIMATION IN CURVED MODELS
49(19)
3.1. Best Equivariant Estimation of with Known
50(3)
3.1.1. Maximum Likelihood Estimators
53(1)
3.2. A Particular Case
53(7)
3.2.1. An Application
58(1)
3.2.2. Maximum Likelihood Estimator
58(2)
3.3. Best Equivariant Estimation in Curved Covariance Models
60(8)
3.3.1. Characterization of Equivariant Estimators of
61(2)
3.3.2. Characterization of Equivariant Estimators of
63(5)
Chapter 4. SOME BEST INVARIANT TESTS IN MULTINORMALS
68(23)
4.0. Introduction
68(1)
4.1. Tests of Mean Vector
68(7)
4.2. The Classification Problem (Two Populations)
75(7)
4.3. Tests of Multiple Correlation
82(3)
4.4. Tests of Multiple Correlation with Partial Information
85(6)
Chapter 5. SOME MINIMAX TESTS IN MULTINORMALES
91(46)
5.0. Introduction
91(2)
5.1. Locally Minimax Tests
93(13)
5.2. Asymptotically Minimax Tests
106(5)
5.3. Minimax Tests
111(26)
5.3.1. Hotelling's T2 Test
112(12)
5.3.2. R2-Test
124(11)
5.3.3. E-Minimax Test (Linnik, 1966)
135(2)
Chapter 6. LOCALLY MINIMAX TESTS IN SYMMETRICAL DISTRIBUTIONS
137(25)
6.0. Introduction
137(1)
6.1. Elliptically Symmetric Distributions
137(3)
6.2. Locally Minimax Tests in Ep ( , )
140(3)
6.3. Examples
143(19)
Chapter 7. TYPE D AND E REGIONS
162

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