Asymptotic theory of nonlinear regression:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer
1997
|
| Series: | Mathematics and its applications
389 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 327 S. |
| ISBN: | 0792343352 |
Staff View
MARC
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| 100 | 1 | |a Ivanov, Aleksandr V. |e Verfasser |0 (DE-588)128934492 |4 aut | |
| 245 | 1 | 0 | |a Asymptotic theory of nonlinear regression |c by Alexander V. Ivanov |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1997 | |
| 300 | |a VI, 327 S. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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Contents
Introduction 1
1 Consistency 5
1 Introductory Remarks 5
2 Large Deviations of the Least Squares Estimator in the Case of
Errors Having an Exponential Moment 9
3 Large Deviations of the Least Squares Estimator in the Case of
Errors with a Moment of Finite Order 25
4 The Differentiability of Regression Functions and the Consistency
of the the Least Squares Estimator 45
5 Strong Consistency 58
6 Taking the Logarithm of Non Linear Models 73
2 Approximation by a Normal Distribution 79
7 Stochastic Asymptotic Expansion of Least Squares Estimators . , 79
8 Asymptotic Normality of Least Squares Estimators: First Results . 92
9 Asymptotic Normality of Least Moduli Estimators 108
10 Asymptotic Expansion of the Distribution of Least Squares
Estimators 119
11 Calculation of First Polynomials of an Asymptotic Expansion of the
Distribution of a Least Squares Estimator 144
3 Asymptotic Expansions Related to the Least Squares
Estimator 155
12 Asymptotic Expansion of Least Squares Estimator Moments . 155
13 Asymptotic Expansions Related to the Estimator of the Variance
of Errors of Observation 168
14 Asymptotic Expansion of the Distribution of the Variance
Estimator of Observational Error in Gaussian Regression 188
15 Jack Knife and Cross Validation Methods of Estimation of the
Variance of Errors of Observation 196
16 Asymptotic Expansions of Distributions of Quadratic Functionals
of the Least Squares Estimator 207
v
vi CONTENTS
17 Comparison of Powers of a Class of Tests of Hypotheses on a
Non Linear Regression Parameter 229
4 Geometric Properties of Asymptotic Expansions 251
18 Certain Aspects of the Differential Geometry of Models of
Non Linear Regression 251
18.1 Embedded Riemannian Manifolds and Statistical
Connectedness 251
18.2 Statistical Curvature 254
18.3 Measures of the Non Linearity of Regression Models . 256
18.4 Statistical Invariants 267
18.5 Invariants of Non Linear Regression with a Scalar
Parameter 268
18.6 Invariants of Non Linear Regression with a Vector
Parameter 272
19 The Geometric Interpretation of Asymptotic Expansions 276
19.1 Geometry of the AE of the LSE Moments 276
19.2 The Geometry of AEs Associated with the Estimator of the
Variance a2 279
19.3 Geometry of AE of Distributions of Quadratic Functionals
of the LSE 281
19.4 Geometries of the Statistical Criteria for Testing Hypotheses
about Non Linear Regression Parameters 284
Appendix 289
I Subsidiary Facts 289
II List of Principal Notations 298
Commentary 303
Chapter 1 303
Chapter 2 304
Chapter 3 305
Chapter 4 306
Bibliography 309
Index 325 |
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| id | DE-604.BV011310527 |
| illustrated | Not Illustrated |
| indexdate | 2025-04-03T10:01:33Z |
| institution | BVB |
| isbn | 0792343352 |
| language | English |
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| physical | VI, 327 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Ivanov, Aleksandr V. Verfasser (DE-588)128934492 aut Asymptotic theory of nonlinear regression by Alexander V. Ivanov Dordrecht [u.a.] Kluwer 1997 VI, 327 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 389 Analyse de régression - Théorie asymptotique ram Niet-lineaire analyse gtt Regressieanalyse gtt Regression analysis -- Asymptotic theory Nonlinear theories Nichtlineare Regression (DE-588)4251077-6 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Nichtlineare Regression (DE-588)4251077-6 s Asymptotik (DE-588)4126634-1 s DE-604 Mathematics and its applications 389 (DE-604)BV008163334 389 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007597780&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ivanov, Aleksandr V. Asymptotic theory of nonlinear regression Mathematics and its applications Analyse de régression - Théorie asymptotique ram Niet-lineaire analyse gtt Regressieanalyse gtt Regression analysis -- Asymptotic theory Nonlinear theories Nichtlineare Regression (DE-588)4251077-6 gnd Asymptotik (DE-588)4126634-1 gnd |
| subject_GND | (DE-588)4251077-6 (DE-588)4126634-1 |
| title | Asymptotic theory of nonlinear regression |
| title_auth | Asymptotic theory of nonlinear regression |
| title_exact_search | Asymptotic theory of nonlinear regression |
| title_full | Asymptotic theory of nonlinear regression by Alexander V. Ivanov |
| title_fullStr | Asymptotic theory of nonlinear regression by Alexander V. Ivanov |
| title_full_unstemmed | Asymptotic theory of nonlinear regression by Alexander V. Ivanov |
| title_short | Asymptotic theory of nonlinear regression |
| title_sort | asymptotic theory of nonlinear regression |
| topic | Analyse de régression - Théorie asymptotique ram Niet-lineaire analyse gtt Regressieanalyse gtt Regression analysis -- Asymptotic theory Nonlinear theories Nichtlineare Regression (DE-588)4251077-6 gnd Asymptotik (DE-588)4126634-1 gnd |
| topic_facet | Analyse de régression - Théorie asymptotique Niet-lineaire analyse Regressieanalyse Regression analysis -- Asymptotic theory Nonlinear theories Nichtlineare Regression Asymptotik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007597780&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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