Boundary Crossing of Brownian Motion: Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
New York, NY
Springer New York
1986
|
| Schriftenreihe: | Lecture Notes in Statistics
40 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-1-4615-6569-7 |
| Beschreibung: | This is a research report about my work on sequential statistic~ during 1980 - 1984. Two themes are treated which are closely related to each other and to the law of the iterated logarithm:· I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries. In the first chapter I discuss the tangent approximation for Brownianmotion as a global approximation device. This is an extension of Strassen' s approach to t'he law of the iterated logarithm which connects results of fluctuation theory of Brownian motion with classical methods of sequential statistics. In the second chapter I make use of these connections and derive optimal properties of tests of power one and repeated significance tests for the simpiest model of sequential statistics, the Brownian motion with unknown drift. To both topics:there under1ies an asymptotic approach which is closely linked to large deviation theory: the stopping boundaries recede to infinity. This is a well-known approach in sequential stötistics which is extensively discussed in Siegmund's recent book ·Sequential Analysis". This approach also leads to some new insights about the law of the iterated logarithm (LIL). Although the LIL has been studied for nearly seventy years the belief is still common that it applies only for large sampIe sizes which can never be obser ved in practice |
| Umfang: | 1 Online-Ressource (V, 143 p) |
| ISBN: | 9781461565697 9780387964331 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4615-6569-7 |
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| 245 | 1 | 0 | |a Boundary Crossing of Brownian Motion |b Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis |c by Hans Rudolf Lerche |
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| 500 | |a This is a research report about my work on sequential statistic~ during 1980 - 1984. Two themes are treated which are closely related to each other and to the law of the iterated logarithm:· I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries. In the first chapter I discuss the tangent approximation for Brownianmotion as a global approximation device. This is an extension of Strassen' s approach to t'he law of the iterated logarithm which connects results of fluctuation theory of Brownian motion with classical methods of sequential statistics. In the second chapter I make use of these connections and derive optimal properties of tests of power one and repeated significance tests for the simpiest model of sequential statistics, the Brownian motion with unknown drift. To both topics:there under1ies an asymptotic approach which is closely linked to large deviation theory: the stopping boundaries recede to infinity. This is a well-known approach in sequential stötistics which is extensively discussed in Siegmund's recent book ·Sequential Analysis". This approach also leads to some new insights about the law of the iterated logarithm (LIL). Although the LIL has been studied for nearly seventy years the belief is still common that it applies only for large sampIe sizes which can never be obser ved in practice | ||
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Datensatz im Suchindex
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| id | DE-604.BV042420926 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:43Z |
| institution | BVB |
| isbn | 9781461565697 9780387964331 |
| issn | 0930-0325 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856343 |
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| physical | 1 Online-Ressource (V, 143 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Springer New York |
| record_format | marc |
| series2 | Lecture Notes in Statistics |
| spellingShingle | Lerche, Hans Rudolf Boundary Crossing of Brownian Motion Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis Statistics Statistics, general Statistik Gesetz vom iterierten Logarithmus (DE-588)4128315-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Sequentialanalyse (DE-588)4128461-6 gnd Sequenzieller Test (DE-588)4139128-7 gnd Randwertproblem (DE-588)4048395-2 gnd |
| subject_GND | (DE-588)4128315-6 (DE-588)4128328-4 (DE-588)4128461-6 (DE-588)4139128-7 (DE-588)4048395-2 |
| title | Boundary Crossing of Brownian Motion Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis |
| title_auth | Boundary Crossing of Brownian Motion Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis |
| title_exact_search | Boundary Crossing of Brownian Motion Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis |
| title_full | Boundary Crossing of Brownian Motion Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis by Hans Rudolf Lerche |
| title_fullStr | Boundary Crossing of Brownian Motion Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis by Hans Rudolf Lerche |
| title_full_unstemmed | Boundary Crossing of Brownian Motion Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis by Hans Rudolf Lerche |
| title_short | Boundary Crossing of Brownian Motion |
| title_sort | boundary crossing of brownian motion its relation to the law of the iterated logarithm and to sequential analysis |
| title_sub | Its Relation to the Law of the Iterated Logarithm and to Sequential Analysis |
| topic | Statistics Statistics, general Statistik Gesetz vom iterierten Logarithmus (DE-588)4128315-6 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Sequentialanalyse (DE-588)4128461-6 gnd Sequenzieller Test (DE-588)4139128-7 gnd Randwertproblem (DE-588)4048395-2 gnd |
| topic_facet | Statistics Statistics, general Statistik Gesetz vom iterierten Logarithmus Brownsche Bewegung Sequentialanalyse Sequenzieller Test Randwertproblem |
| url | https://doi.org/10.1007/978-1-4615-6569-7 |
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