Approximation theorems of mathematical statistics / Robert J. Serfling.

Por: Serfling, Robert J. (Robert Joseph)Series Wiley series in probability and mathematical statisticsEditor: New York : Wiley, c1980Descripción: xiv, 371 p. ; 24 cmISBN: 0471024031 :Tema(s): Mathematical statistics | Limit theorems (Probability theory)Otra clasificación: *CODIGO* Recursos en línea: Publisher description | Table of Contents
Contenidos:
1 Preliminary Tools and Foundations [1] --
1.1 Preliminary Notation and Definitions, [1] --
1.2 Modes of Convergence of a Sequence of Random Variables, [6] --
1.3 Relationships Among the Modes of Convergence, [9] --
1.4 Convergence of Moments; Uniform Integrability, [13] --
1.5 Further Discussion of Convergence in Distribution, [16] --
1.6 Operations on Sequences to Produce Specified Convergence Properties, [22] --
1.7 Convergence Properties of Transformed Sequences, [24] --
1.8 Basic Probability Limit Theorems: The WLLN and SLLN, [26] --
1.9 Basic Probability Limit Theorems: The CLT, [28] --
1.10 Basic Probability Limit Theorems: The LIL, [35] --
1.11 Stochastic Process Formulation of the CLT, [37] --
1.12 Taylor’s Theorem; Differentials, [43] --
1.13 Conditions for Determination of a Distribution by Its Moments, [45] --
1.14 Conditions for Existence of Moments of a Distribution, [46] --
1.15 Asymptotic Aspects of Statistical Inference Procedures, [47] --
l.P Problems, [52] --
2 The Basic Sample Statistics [55] --
2.1 The Sample Distribution Function, [56] --
2.2 The Sample Moments, [66] --
2.3 The Sample Quantiles, [74] --
2.4 The Order Statistics, [87] --
2.5 Asymptotic Representation Theory for Sample Quantiles, Order Statistics, and Sample Distribution Functions, [91] --
2.6 Confidence Intervals for Quantiles, [102] --
2.7 Asymptotic Multivariate Normality of Cell Frequency Vectors, [107] --
2.8 Stochastic Processes Associated with a Sample, [109] --
2.P Problems, [113] --
3 Transformations of Given Statistics [117] --
3.1 Functions of Asymptotically Normal Statistics: Univariate Case, [118] --
3.2 Examples and Applications, [120] --
3.3 Functions of Asymptotically Normal Vectors, [122] --
3.4 Further Examples and Applications, [125] --
3.5 Quadratic Forms in Asymptotically Multivariate Normal Vectors, [128] --
3.6 Functions of Order Statistics, [134] --
3.P Problems, [136] --
4 Asymptotic Theory in Parametric Inference [138] --
4.1 Asymptotic Optimality in Estimation, [138] --
4.2 Estimation by the Method of Maximum Likelihood, [143] --
4.3 Other Approaches toward Estimation, [150] --
4.4 Hypothesis Testing by Likelihood Methods, [151] --
4.5 Estimation via Product-Multinomial Data, [160] --
4.6 Hypothesis Testing via Product-Multinomial Data, [165] --
4.P Problems, [169] --
5 U-Statistics [171] --
5.1 Basic Description of U-Statistics, [172] --
5.2 The Variance and Other Moments of a U-Statistic, [181] --
5.3 The Projection of a U-Statistic on the Basic Observations, [187] --
5.4 Almost Sure Behavior of [/-Statistics, [190] --
5.5 Asymptotic Distribution Theory of U-Statistics, [192] --
5.6 Probability Inequalities and Deviation Probabilities for U-Statistics, [199] --
5.7 Complements, [203] --
5.P Problems, [207] --
6 Von Mises Differentiable Statistical Functions [210] --
6.1 Statistics Considered as Functions of the Sample Distribution Function, [211] --
6.2 Reduction to a Differential Approximation, [214] --
6.3 Methodology for Analysis of the Differential Approximation, [221] --
6.4 Asymptotic Properties of Differentiable Statistical Functions, [225] --
6.5 Examples, [231] --
6.6 Complements, [238] --
6.P Problems, [241] --
7 M-Estimates [243] --
7.1 Basic Formulation and Examples, [243] --
7.2 Asymptotic Properties of M-Estimates, [248] --
7.3 Complements, [257] --
7.P Problems, [260] --
8 L-Estimates [262] --
8.1 Basic Formulation and Examples, [262] --
8.2 Asymptotic Properties of R-Estimates, [271] --
8.P Problems, [290] --
9 R-Estimates [262] --
9.1 Basic Formulation and Examples, [292] --
9.2 Asymptotic Normality of Simple Linear Rank Statistics, [295] --
9.3 Complements, [311] --
9.P Problems, [312] --
10 Asymptotic Relative Efficiency [314] --
10.1 Approaches toward Comparison of Test Procedures, [314] --
10.2 The Pitman Approach, [316] --
10.3 The Chemoff Index, [325] --
10.4 Bahadur’s “Stochastic Comparison,” [332] --
10.5 The Hodges-Lehmann Asymptotic Relative Efficiency, [341] --
10.6 Hoeffding’s Investigation (Multinomial Distributions), [342] --
10.7 The Rubin-Sethuraman “Bayes Risk” Efficiency, [347] --
10.P Problems, [348] --
Appendix [351] --
References [353] --
Author Index [365] --
Subject Index [369] --
List(s) this item appears in: Últimas adquisiciones
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Libros Libros Instituto de Matemática, CONICET-UNS
Últimas adquisiciones 62 Se483 (Browse shelf) Available A-9370

Includes indexes.

Bibliografía: p. 353-363.

1 Preliminary Tools and Foundations [1] --
1.1 Preliminary Notation and Definitions, [1] --
1.2 Modes of Convergence of a Sequence of Random Variables, [6] --
1.3 Relationships Among the Modes of Convergence, [9] --
1.4 Convergence of Moments; Uniform Integrability, [13] --
1.5 Further Discussion of Convergence in Distribution, [16] --
1.6 Operations on Sequences to Produce Specified Convergence Properties, [22] --
1.7 Convergence Properties of Transformed Sequences, [24] --
1.8 Basic Probability Limit Theorems: The WLLN and SLLN, [26] --
1.9 Basic Probability Limit Theorems: The CLT, [28] --
1.10 Basic Probability Limit Theorems: The LIL, [35] --
1.11 Stochastic Process Formulation of the CLT, [37] --
1.12 Taylor’s Theorem; Differentials, [43] --
1.13 Conditions for Determination of a Distribution by Its Moments, [45] --
1.14 Conditions for Existence of Moments of a Distribution, [46] --
1.15 Asymptotic Aspects of Statistical Inference Procedures, [47] --
l.P Problems, [52] --
2 The Basic Sample Statistics [55] --
2.1 The Sample Distribution Function, [56] --
2.2 The Sample Moments, [66] --
2.3 The Sample Quantiles, [74] --
2.4 The Order Statistics, [87] --
2.5 Asymptotic Representation Theory for Sample Quantiles, Order Statistics, and Sample Distribution Functions, [91] --
2.6 Confidence Intervals for Quantiles, [102] --
2.7 Asymptotic Multivariate Normality of Cell Frequency Vectors, [107] --
2.8 Stochastic Processes Associated with a Sample, [109] --
2.P Problems, [113] --
3 Transformations of Given Statistics [117] --
3.1 Functions of Asymptotically Normal Statistics: Univariate Case, [118] --
3.2 Examples and Applications, [120] --
3.3 Functions of Asymptotically Normal Vectors, [122] --
3.4 Further Examples and Applications, [125] --
3.5 Quadratic Forms in Asymptotically Multivariate Normal Vectors, [128] --
3.6 Functions of Order Statistics, [134] --
3.P Problems, [136] --
4 Asymptotic Theory in Parametric Inference [138] --
4.1 Asymptotic Optimality in Estimation, [138] --
4.2 Estimation by the Method of Maximum Likelihood, [143] --
4.3 Other Approaches toward Estimation, [150] --
4.4 Hypothesis Testing by Likelihood Methods, [151] --
4.5 Estimation via Product-Multinomial Data, [160] --
4.6 Hypothesis Testing via Product-Multinomial Data, [165] --
4.P Problems, [169] --
5 U-Statistics [171] --
5.1 Basic Description of U-Statistics, [172] --
5.2 The Variance and Other Moments of a U-Statistic, [181] --
5.3 The Projection of a U-Statistic on the Basic Observations, [187] --
5.4 Almost Sure Behavior of [/-Statistics, [190] --
5.5 Asymptotic Distribution Theory of U-Statistics, [192] --
5.6 Probability Inequalities and Deviation Probabilities for U-Statistics, [199] --
5.7 Complements, [203] --
5.P Problems, [207] --
6 Von Mises Differentiable Statistical Functions [210] --
6.1 Statistics Considered as Functions of the Sample Distribution Function, [211] --
6.2 Reduction to a Differential Approximation, [214] --
6.3 Methodology for Analysis of the Differential Approximation, [221] --
6.4 Asymptotic Properties of Differentiable Statistical Functions, [225] --
6.5 Examples, [231] --
6.6 Complements, [238] --
6.P Problems, [241] --
7 M-Estimates [243] --
7.1 Basic Formulation and Examples, [243] --
7.2 Asymptotic Properties of M-Estimates, [248] --
7.3 Complements, [257] --
7.P Problems, [260] --
8 L-Estimates [262] --
8.1 Basic Formulation and Examples, [262] --
8.2 Asymptotic Properties of R-Estimates, [271] --
8.P Problems, [290] --
9 R-Estimates [262] --
9.1 Basic Formulation and Examples, [292] --
9.2 Asymptotic Normality of Simple Linear Rank Statistics, [295] --
9.3 Complements, [311] --
9.P Problems, [312] --
10 Asymptotic Relative Efficiency [314] --
10.1 Approaches toward Comparison of Test Procedures, [314] --
10.2 The Pitman Approach, [316] --
10.3 The Chemoff Index, [325] --
10.4 Bahadur’s “Stochastic Comparison,” [332] --
10.5 The Hodges-Lehmann Asymptotic Relative Efficiency, [341] --
10.6 Hoeffding’s Investigation (Multinomial Distributions), [342] --
10.7 The Rubin-Sethuraman “Bayes Risk” Efficiency, [347] --
10.P Problems, [348] --
Appendix [351] --
References [353] --
Author Index [365] --
Subject Index [369] --

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