Statistical inference, by S. D. Silvey.

Por: Silvey, S. D. (Samuel David)Series Library of university mathematics; Penguin educationEditor: Harmondsworth, Penguin, 1970Descripción: 3-192 p. illus. 21 cmISBN: 0140800972Tema(s): Mathematical statisticsOtra clasificación: *CODIGO*
Contenidos:
Preface [11] --
1 Introduction [13] --
1.1 Preliminaries [13] --
1.2 The general inference problem [16] --
1.3 Estimation [18] --
1.4 Hypothesis testing [19] --
1.5 Decision theory 19 Examples 1 [19] --
2 Minimum-Variance Unbiased Estimation [21] --
2.1 The point estimation problem [21] --
22 ‘Good’ estimates [22] --
2.3 Sufficiency [25] --
24 The Rao-Blackwell theorem [28] --
25 Completeness [29] --
2.6 Completeness and M.V.U.E.s [33] --
2.7 Discussion [34] --
28 Efficiency of unbiased estimators [35] --
29 Fisher’s information [37] --
2.10 The Cramir- Rao lower bound [38] --
2.11 Efficiency [39] --
2.12 Generalization of the Cramir-Rao inequality [41] --
2.13 Concluding remarks [43] --
Examples 2 [44] --
3 The Method of Least Squares [46] --
3.1 Examples [46] --
3.2 Normal equations [47] --
3.3 Geometric interpretation [48] --
3.4 Identifiability [50] --
3.5 The Gauss-Markov theorem [51] --
3.6 Weighted least squares [54] --
3.7 Estimation of a2 [56] --
3.8 Variance of least-squares estimators [57] --
3.9 Normal theory [58] --
3.10 Least squares with side conditions [59] --
3.11 Discussion [64] --
Examples 3 [65] --
4 The Method of Maximum Likelihood [68] --
4.1 The likelihood function [68] --
4.2 Calculation of maximum-likelihood estimates [70] --
4.3 Optimal properties of maximum-likelihood estimators [73] --
4.4 Large-sample properties [74] --
4.5 Consistency [76] --
4.6 Large-sample efficiency [77] --
4.7 Restricted maximum-likelihood estimates [79] --
Examples 4 [84] --
5 Confidence Sets [87] --
5.1 Confidence interval [87] --
5.2 General definition of a confidence set [88] --
5.3 Construction of confidence sets [89] --
5.4 Optimal confidence sets 92 Examples 5 [92] --
6 Hypothesis Testing [94] --
6.1 The Neyman-Pearson theory [96] --
6.2 Simple hypotheses [97] --
6.3 Composite hypotheses [102] --
6.4 Unbiased and invariant tests [104] --
Examples 6 [106] --
7 The Likelihood-Ratio Test and Alternative ‘Large-Sample’ Equivalents of it [108] --
7.1 The likelihood-ratio test [108] --
7.2 The large-sample distribution of A [112] --
7.3 TheW-test [115] --
7.4 The test [118] --
Examples 7 [121] --
8 Sequential Tests [123] --
8.1 Definition of a sequential probability ratio test [124] --
8.2 Error probabilities and the constants A and B [125] --
8.3 Graphical procedure for an s.p.r. test [127] --
8.4 Composite hypotheses [129] --
8.5 Monotone likelihood ratio and the s.p.r. test [130] --
Examples 8 [136] --
9 Non-Parametric Methods [139] --
9.1 The Kolmogorov-Smirnov test [140] --
9.2 The x* goodness-of-fit test [142] --
9.3 The Wilcoxon test [143] --
9.4 Permutation tests [144] --
9.5 The use of a sufficient statistic for test construction [145] --
9.6 Randomization [148] --
Examples 9 [151] --
10 The Bayesian Approach [153] --
10.1 Prior distributions [153] --
10.2 Posterior distributions [154] --
10.3 Bayesian confidence intervals [155] --
10.4 Bayesian inference regarding hypotheses [156] --
10.5 Choosing a prior distribution [157] --
10.6 Improper prior distributions 158 Examples 10 [159] --
11 An Introduction to Decision Theory [161] --
11.1 The two-decision problem [161] --
11.2 Decision functions [162] --
11.3 The risk function [162] --
11.4 Minimax decision functions [165] --
11.5 Admissible decision functions [166] --
11.6 Bayes's solutions [166] --
11.7 A Bayes’s sequential decision problem 171 Examples 11 [175] --
Appendix A Some Matrix Results [177] --
Appendix B The Linear Hypothesis [180] --
References [189] --
Index [191] --
List(s) this item appears in: Últimas adquisiciones
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Libros Libros Instituto de Matemática, CONICET-UNS
Últimas adquisiciones 62 Si587s (Browse shelf) Available A-9362

Bibliografía: p. 189-190.

Preface [11] --
1 Introduction [13] --
1.1 Preliminaries [13] --
1.2 The general inference problem [16] --
1.3 Estimation [18] --
1.4 Hypothesis testing [19] --
1.5 Decision theory 19 Examples 1 [19] --
2 Minimum-Variance Unbiased Estimation [21] --
2.1 The point estimation problem [21] --
22 ‘Good’ estimates [22] --
2.3 Sufficiency [25] --
24 The Rao-Blackwell theorem [28] --
25 Completeness [29] --
2.6 Completeness and M.V.U.E.s [33] --
2.7 Discussion [34] --
28 Efficiency of unbiased estimators [35] --
29 Fisher’s information [37] --
2.10 The Cramir- Rao lower bound [38] --
2.11 Efficiency [39] --
2.12 Generalization of the Cramir-Rao inequality [41] --
2.13 Concluding remarks [43] --
Examples 2 [44] --
3 The Method of Least Squares [46] --
3.1 Examples [46] --
3.2 Normal equations [47] --
3.3 Geometric interpretation [48] --
3.4 Identifiability [50] --
3.5 The Gauss-Markov theorem [51] --
3.6 Weighted least squares [54] --
3.7 Estimation of a2 [56] --
3.8 Variance of least-squares estimators [57] --
3.9 Normal theory [58] --
3.10 Least squares with side conditions [59] --
3.11 Discussion [64] --
Examples 3 [65] --
4 The Method of Maximum Likelihood [68] --
4.1 The likelihood function [68] --
4.2 Calculation of maximum-likelihood estimates [70] --
4.3 Optimal properties of maximum-likelihood estimators [73] --
4.4 Large-sample properties [74] --
4.5 Consistency [76] --
4.6 Large-sample efficiency [77] --
4.7 Restricted maximum-likelihood estimates [79] --
Examples 4 [84] --
5 Confidence Sets [87] --
5.1 Confidence interval [87] --
5.2 General definition of a confidence set [88] --
5.3 Construction of confidence sets [89] --
5.4 Optimal confidence sets 92 Examples 5 [92] --
6 Hypothesis Testing [94] --
6.1 The Neyman-Pearson theory [96] --
6.2 Simple hypotheses [97] --
6.3 Composite hypotheses [102] --
6.4 Unbiased and invariant tests [104] --
Examples 6 [106] --
7 The Likelihood-Ratio Test and Alternative ‘Large-Sample’ Equivalents of it [108] --
7.1 The likelihood-ratio test [108] --
7.2 The large-sample distribution of A [112] --
7.3 TheW-test [115] --
7.4 The test [118] --
Examples 7 [121] --
8 Sequential Tests [123] --
8.1 Definition of a sequential probability ratio test [124] --
8.2 Error probabilities and the constants A and B [125] --
8.3 Graphical procedure for an s.p.r. test [127] --
8.4 Composite hypotheses [129] --
8.5 Monotone likelihood ratio and the s.p.r. test [130] --
Examples 8 [136] --
9 Non-Parametric Methods [139] --
9.1 The Kolmogorov-Smirnov test [140] --
9.2 The x* goodness-of-fit test [142] --
9.3 The Wilcoxon test [143] --
9.4 Permutation tests [144] --
9.5 The use of a sufficient statistic for test construction [145] --
9.6 Randomization [148] --
Examples 9 [151] --
10 The Bayesian Approach [153] --
10.1 Prior distributions [153] --
10.2 Posterior distributions [154] --
10.3 Bayesian confidence intervals [155] --
10.4 Bayesian inference regarding hypotheses [156] --
10.5 Choosing a prior distribution [157] --
10.6 Improper prior distributions 158 Examples 10 [159] --
11 An Introduction to Decision Theory [161] --
11.1 The two-decision problem [161] --
11.2 Decision functions [162] --
11.3 The risk function [162] --
11.4 Minimax decision functions [165] --
11.5 Admissible decision functions [166] --
11.6 Bayes's solutions [166] --
11.7 A Bayes’s sequential decision problem 171 Examples 11 [175] --
Appendix A Some Matrix Results [177] --
Appendix B The Linear Hypothesis [180] --
References [189] --
Index [191] --

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