Statistical problems with nuisance parameters:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
1968
|
| Schriftenreihe: | Translations of mathematical monographs
20 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003555755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Aus dem Russ. übers. |
| Umfang: | IX, 258 S. |
Internformat
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| 100 | 1 | |a Linnik, Jurij V. |d 1915-1972 |e Verfasser |0 (DE-588)117715247 |4 aut | |
| 240 | 1 | 0 | |a Statističeskie zadači s mešajuščimi parametrami |
| 245 | 1 | 0 | |a Statistical problems with nuisance parameters |c by Ju. V. Linnik |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 1968 | |
| 300 | |a IX, 258 S. | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 20 | |
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Datensatz im Suchindex
| _version_ | 1819256819169624064 |
|---|---|
| adam_text | TABLE OF CONTENTS
Page
Preface iii
Preface to the American Edition v
Introduction 1
Chapter I. The multiple Laplace transformation, functions of several
complex variables, and analytic sheaves 7
¦§!• The multiple Laplace transformation 7
§2. Functions of several complex variables. Theorems yielding
bounds 10
§3. Ideals in rings of holomorphic functions. Analytic sheaves 17
Chapter II. Sufficient statistics and exponential families 23
§1. General information on sufficient statistics 23
§2. Examples of sufficient statistics 27
§3 Informational properties of sufficient statistics 32
§4. Sufficient statistics for a repeated sample. Exponential families 35
§5 Exponential families 41
§6. Sufficient statistics and unbiased estimates 45
Chapter III. Nuisance parameters. Tests with invariant power functions 49
§1. Nuisance parameters 49
§2. Tests with invariant power functions 51
§3 Some results dealing with tests with invariant power functions 53
§4. Stein s test 59
Chapter IV. Similar tests and statistics 63
§1. Similarity of tests and of statistics 63
§2. Neyman structures. Lehmann s and Scheffe s theorems 66
§3. Some methods of constructing similar zones 69
§4. Approximately similar zones 78
§5. Independent statistics 80
vii
viii
§6. Applications of a theorem of I . Cartan to the study of families
of statistics 83
Chapter V. Cotest ideals for exponential families 89
§1. Similar tests and cotest ideals 89
§2. Statement of the problem for incomplete exponential families 92
§3. Ideals of precotests 94
§4. Application of Cartan s theorems 97
§5 The behavior of smooth precotests 98
§6. Smoothing of precotests 101
§7. Formation of smooth precotests from a given one 104
§8. Formulation of the final results. Examples 106
Chapter VI. Wijsman s Z) method 117
§1. The D method and the conditions under which it can be applied 117
§2. Examples of application of the D method 119
Chapter VII. Unbiased estimates 125
§1. Unbiased estimates for incomplete exponential families depend¬
ing on sufficient statistics 125
§2. On the behavior of the variance of unbiased estimates 127
§3. A theorem of S. R. Rao on the inadmissibility of certain estimates 133
Chapter VIII. Analytical methods of studying unrandomized tests. Appli¬
cation to the Behrens Fisher problem 139
§1. Questions of existence of unrandomized similar tests for incom¬
plete exponential families 13^
§2. Statement of the problem of an unrandomized homogeneous similar
test in the Behrens Fisher problem 142
§3. Homogeneous Fisher Welch Wald tests 146
§4. Lemmas on tangency of a test boundary to a critic 151
§5 Completion of the proof of theorem 8.3 1 166
Chapter IX. Randomized homogeneous tests in the Behrens Fisher prob¬
lem. Characterization of tests of the Bartlett Scheffe type 167
§1. Nonexistence of null regular similar tests 167
§2. Bartlett Scheffe tests 178
§3 A homogeneous randomized test associated with Bartlett s test 181
§4. Characterization of tests of the Bartlett Scheffe type 183
ix
Chapter X. An unrandomized homogeneous similar test in the Behrens
Fisher problem 193
§1. Construction of an unrandomized test 193
§2. The Romanovskii Sudakov theorem 197
Chapter XI. The problem of many small samples 204
§1. Statement of the problem 204
§2. A. A. Petrov s investigations 205
Appendix 213
Supplement. New results in the theory of estimation and testing hypothe¬
ses for problems with nuisance parameters 217
§1. Invariant verification of functions which are polynomials in a
and l/ff2 for normal samples 217
§2. The description of all cotests for a class of exponential families
with polynomial relations 226
§3 Conditions of optimal unbiased estimation for incomplete exponen¬
tial families with polynomial relations 232
§4. The sample mean as the estimate of scale parameters 240
§5 Nonparametric approach to the estimation of location parameters 243
Bibliography to the Appendix 249
Bibliography 251
|
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| id | DE-604.BV005693085 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T08:36:51Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003555755 |
| oclc_num | 252361302 |
| open_access_boolean | |
| owner | DE-703 DE-739 DE-355 DE-BY-UBR DE-384 DE-20 DE-19 DE-BY-UBM DE-29T DE-83 DE-188 |
| owner_facet | DE-703 DE-739 DE-355 DE-BY-UBR DE-384 DE-20 DE-19 DE-BY-UBM DE-29T DE-83 DE-188 |
| physical | IX, 258 S. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spellingShingle | Linnik, Jurij V. 1915-1972 Statistical problems with nuisance parameters Translations of mathematical monographs Störparameter (DE-588)4183397-1 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4183397-1 (DE-588)4056995-0 |
| title | Statistical problems with nuisance parameters |
| title_alt | Statističeskie zadači s mešajuščimi parametrami |
| title_auth | Statistical problems with nuisance parameters |
| title_exact_search | Statistical problems with nuisance parameters |
| title_full | Statistical problems with nuisance parameters by Ju. V. Linnik |
| title_fullStr | Statistical problems with nuisance parameters by Ju. V. Linnik |
| title_full_unstemmed | Statistical problems with nuisance parameters by Ju. V. Linnik |
| title_short | Statistical problems with nuisance parameters |
| title_sort | statistical problems with nuisance parameters |
| topic | Störparameter (DE-588)4183397-1 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Störparameter Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003555755&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT linnikjurijv statisticeskiezadacismesajuscimiparametrami AT linnikjurijv statisticalproblemswithnuisanceparameters |