Lecture Notes in Statistics : LECTURE NOTES IN STATISTICS - Hira L. Koul

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Lecture Notes in Statistics

By: Hira L. Koul

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Paperback | 1 June 2002 | Edition Number 2

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448 Pages

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23.39 x 15.6 x 2.31

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The role of the weak convergence technique via weighted empirical processes has proved to be very useful in advancing the development of the asymptotic theory of the so called robust inference procedures corresponding to non-smooth score functions from linear models to nonlinear dynamic models in the 1990's. This monograph is an ex- panded version of the monograph Weighted Empiricals and Linear Models, IMS Lecture Notes-Monograph, 21 published in 1992, that includes some aspects of this development. The new inclusions are as follows. Theorems 2. 2. 4 and 2. 2. 5 give an extension of the Theorem 2. 2. 3 (old Theorem 2. 2b. 1) to the unbounded random weights case. These results are found useful in Chapters 7 and 8 when dealing with ho- moscedastic and conditionally heteroscedastic autoregressive models, actively researched family of dynamic models in time series analysis in the 1990's. The weak convergence results pertaining to the partial sum process given in Theorems 2. 2. 6 . and 2. 2. 7 are found useful in fitting a parametric autoregressive model as is expounded in Section 7. 7 in some detail. Section 6. 6 discusses the related problem of fit- ting a regression model, using a certain partial sum process. Inboth sections a certain transform of the underlying process is shown to provide asymptotically distribution free tests. Other important changes are as follows. Theorem 7. 3.

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Non-Fiction Mathematics Probability & Statistics Medicine Medicine in General Applied Mathematics Nonlinear Science

Preface to the Second Edition
Preface to the First Edition
Notation and Conventions
Introduction	p. 1
Weighted Empirical Processes	p. 1
M-, R- and Scale Estimators	p. 2
M.D. Estimators & Goodness-of-fit Tests	p. 5
R.W.E. Processes and Dynamic Models	p. 10
Asymptotic Properties of W.E.P.'s	p. 15
Weak Convergence	p. 16
AUL of Residual W.E.P.'s	p. 50
Some Additional Results for W.E.P.'s	p. 64
Linear Rank and Signed Rank Statistics	p. 69
AUL of Linear Rank Statistics	p. 70
AUL of Linear Signed Rank Statistics	p. 83
Weak Convergence of Rank and Signed Rank W.E.P.'s	p. 89
M. R. and Some Scale Estimators	p. 99
M-Estimators	p. 101
Distributions of Some Scale Estimators	p. 112
R-Estimators	p. 121
Estimation of Q(f)	p. 128
Minimum Distance Estimators	p. 138
Definitions of M.D. Estimators	p. 140
Finite Sample Properties	p. 145
A General M. D. Estimator	p. 159
Asymptotic Uniform Quadraticity	p. 173
Distributions, Efficiency & Robustness	p. 201
Goodness-of-fit Tests in Regression	p. 229
The Supremum Distance Tests	p. 231
L[subscript 2]-Distance Tests	p. 247
Testing with Unknown Scale	p. 256
Testing for the Symmetry of the Errors	p. 258
Regression Model Fitting	p. 265
Autoregression	p. 294
AUL of W[subscript h] and F[subscript n]	p. 297
GM- and GR- Estimators	p. 311
Minimum Distance Estimation	p. 321
Autoregression Quantiles and Rank Scores	p. 333
Goodness-of-fit Testing for F	p. 340
Autoregressive Model Fitting	p. 341
Nonlinear Autoregression	p. 358
AR Models	p. 359
ARCH Models	p. 380
Appendix	p. 408
Appendix	p. 408
Bibliography	p. 414
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Lecture Notes in Statistics

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