Prakasa Rao / Birnbaum / Lukacs Nonparametric Functional Estimation

1. Auflage 2014
ISBN: 978-1-4832-6923-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 538 Seiten, Web PDF

Nonparametric Functional Estimation is a compendium of papers, written by experts, in the area of nonparametric functional estimation. This book attempts to be exhaustive in nature and is written both for specialists in the area as well as for students of statistics taking courses at the postgraduate level. The main emphasis throughout the book is on the discussion of several methods of estimation and on the study of their large sample properties. Chapters are devoted to topics on estimation of density and related functions, the application of density estimation to classification problems, and the different facets of estimation of distribution functions. Statisticians and students of statistics and engineering will find the text very useful.

Autoren/Hrsg.

Prakasa Rao, B. L. S.

Birnbaum, Z. W.

Lukacs, E.

Inhaltsverzeichnis

1;Front Cover;1
2;Nonparametric Functional Estimation;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;12
7;List of Notation;14
8;Chapter 1. Estimation of Functionals;16
8.1;1.0. Introduction;16
8.2;1.1. Estimability of Functionals;17
8.3;1.2. Necessary and Sufficient Conditions for the Existence of Unbiased Estimators of Functionals;30
8.4;1.3. Asymptotic Efficiency of Estimators of Functionals;34
8.5;Bibliographical Notes;39
8.6;Problems;39
9;Chapter 2. Density Estimation (Univariate Case);42
9.1;2.0. Introduction;42
9.2;2.1. The Method of Kernels;48
9.3;2.2. The Method of Orthogonal Series;86
9.4;2.3. The Method of Histograms with Fixed Partition;107
9.5;2.4. The Method of Histograms with Random Partition;116
9.6;2.5. The Method of Histosplines;129
9.7;2.6. The Method of Penalty Functions;137
9.8;2.7. The Method of Fourier Inversion;147
9.9;2.8. The Method of Delta Sequences;151
9.10;2.9. A Bayesian Approach;158
9.11;2.10. Comparison of Different Methods;160
9.12;2.11. Optimal Density Estimation;162
9.13;2.12. Invariant Density Estimation;165
9.14;Bibliographical Notes;166
9.15;Problems;167
10;Chapter 3. Density Estimation (Multivariate Case);189
10.1;3.0. Introduction;189
10.2;3.1. The Method of Kernels;195
10.3;3.2. The Method of Nearest Neighbors;215
10.4;3.3. The Method of Orthogonal Series;229
10.5;3.4. The Method of Delta Sequences;233
10.6;3.5. The Method of Stochastic Approximation;239
10.7;3.6. Further Topics;240
10.8;Bibliographical Notes;241
10.9;Problems;242
11;Chapter 4. Estimation of Functionals Related to Density;252
11.1;4.0. Introduction;252
11.2;4.1. Estimation of Derivatives of a Density;252
11.3;4.2. Estimation of Regression Function;254
11.4;4.3. Estimation of Failure Rate;273
11.5;4.4. Estimation of Functionals of Density and Its Derivatives;281
11.6;4.5. Estimation of Mode;288
11.7;4.6. Further Topics;301
11.8;Bibliographical Notes;302
11.9;Problems;303
12;Chapter 5. Sequential and Recursive Estimation;319
12.1;5.0. Introduction;319
12.2;5.1. Recursive Estimation;320
12.3;5.2. Sequential Estimation;323
12.4;Bibliographical Notes;327
12.5;Problems;327
13;Chapter 6. Estimation for Stochastic Processes;334
13.1;6.1. Discrete Time Stationary Markov Processes;334
13.2;6.2. Discrete Time Stationary .-Mixing Processes;340
13.3;6.3. Continuous Time Stationary Markov Processes;342
13.4;6.4. Diffusion Processes;349
13.5;Bibliographical Notes;352
13.6;Problems;352
14;Chapter 7. Estimation under Order Restrictions;367
14.1;7.0. Introduction;367
14.2;7.1. Estimation of Unimodal Density;368
14.3;7.2. Estimation for Distributions with Monotone Failure Rates;375
14.4;7.3. Further Topics;377
14.5;Bibliographical Notes;381
14.6;Problems;381
15;Chapter 8. Nonparametric Discrimination;388
15.1;8.0. Introduction;388
15.2;8.1. Bayes Risk Consistency;391
15.3;8.2. Nearest Neighbor Rules;397
15.4;8.3. Histogram Method for Classification;400
15.5;Bibliographical Notes;402
15.6;Problems;402
16;Chapter 9. Estimation of a Distribution Function;407
16.1;9.0. Introduction;407
16.2;9.1. Estimation by the Method of Rao–Blackwellization;409
16.3;9.2. Estimation by the Method of Kernels;412
16.4;9.3. Estimation by the Method of Stochastic Approximation;416
16.5;9.4. Estimation of a Distribution Function from Incomplete Observations (Univariate Case);418
16.6;9.5. Estimation in the Competing Risks Problem;431
16.7;9.6. Estimation of a Distribution Function from Incomplete Observations (Bivariate Case);437
16.8;Bibliographical Notes;447
16.9;Problems;448
17;Chapter 10. Estimation of a Mixing Distribution;452
17.1;10.0. Introduction;452
17.2;10.1. Estimation for Finite Mixtures;455
17.3;10.2. Estimation for Arbitrary Mixtures;459
17.4;Bibliographical Notes;462
17.5;Problems;462
18;Chapter 11. Bayes Estimation;465
18.1;11.0. Introduction;465
18.2;11.1. Estimation of a Distribution Function;474
18.3;11.2. Estimation of a Distribution Function from Incomplete Data;479
18.4;11.3. Estimation of a Symmetric Distribution Function;485
18.5;11.4. Estimation of a Functional of a Distribution Function;488
18.6;Bibliographical Notes;491
18.7;Problems;491
19;References;498
20;Author Index;528
21;Subject Index;534