Testing composite hypotheses about discrete ergodic processes
Given a discrete-valued sample X 1 ,…, X n , we wish to decide whether it was generated by a distribution belonging to a family H 0 , or it was generated by a distribution belonging to a family H 1 . In this work we assume that all distributions are stationary ergodic and do not make any further ass...
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| Veröffentlicht in: | Test (Madrid, Spain) Spain), 2012-06, Vol.21 (2), p.317-329 |
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| creator | Ryabko, Daniil |
| description | Given a discrete-valued sample
X
1
,…,
X
n
, we wish to decide whether it was generated by a distribution belonging to a family
H
0
, or it was generated by a distribution belonging to a family
H
1
. In this work we assume that all distributions are stationary ergodic and do not make any further assumptions (in particular, no independence or mixing rate assumptions). We find some necessary and some sufficient conditions, formulated in terms of the topological properties of
H
0
and
H
1
, for the existence of a consistent test. For the case where
H
1
is the complement of
H
0
(to the set of all stationary ergodic processes), these necessary and sufficient conditions coincide, thereby providing a complete characterization of families of processes membership to which can be consistently tested, against their complement, based on sampling. This criterion includes as special cases several known and some new results on testing for membership to various parametric families, as well as testing identity, independence, and other hypotheses. |
| doi_str_mv | 10.1007/s11749-011-0245-3 |
| format | Article |
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X
1
,…,
X
n
, we wish to decide whether it was generated by a distribution belonging to a family
H
0
, or it was generated by a distribution belonging to a family
H
1
. In this work we assume that all distributions are stationary ergodic and do not make any further assumptions (in particular, no independence or mixing rate assumptions). We find some necessary and some sufficient conditions, formulated in terms of the topological properties of
H
0
and
H
1
, for the existence of a consistent test. For the case where
H
1
is the complement of
H
0
(to the set of all stationary ergodic processes), these necessary and sufficient conditions coincide, thereby providing a complete characterization of families of processes membership to which can be consistently tested, against their complement, based on sampling. This criterion includes as special cases several known and some new results on testing for membership to various parametric families, as well as testing identity, independence, and other hypotheses.</description><identifier>ISSN: 1133-0686</identifier><identifier>EISSN: 1863-8260</identifier><identifier>DOI: 10.1007/s11749-011-0245-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer-Verlag</publisher><subject>Analysis ; Economics ; Entropy ; Finance ; Hypotheses ; Hypothesis testing ; Insurance ; Management ; Markov analysis ; Mathematics ; Mathematics and Statistics ; Original Paper ; Probability ; Statistical Theory and Methods ; Statistics ; Statistics for Business ; Statistics Theory ; Studies</subject><ispartof>Test (Madrid, Spain), 2012-06, Vol.21 (2), p.317-329</ispartof><rights>Sociedad de Estadística e Investigación Operativa 2011</rights><rights>Sociedad de Estadística e Investigación Operativa 2012</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c383t-44385bd6418570c2a5fbb02a8402e555b1c988eae13ed08556610f622b5c611d3</citedby><cites>FETCH-LOGICAL-c383t-44385bd6418570c2a5fbb02a8402e555b1c988eae13ed08556610f622b5c611d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11749-011-0245-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11749-011-0245-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,41464,42533,51294</link.rule.ids><backlink>$$Uhttps://inria.hal.science/hal-00639477$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Ryabko, Daniil</creatorcontrib><title>Testing composite hypotheses about discrete ergodic processes</title><title>Test (Madrid, Spain)</title><addtitle>TEST</addtitle><description>Given a discrete-valued sample
X
1
,…,
X
n
, we wish to decide whether it was generated by a distribution belonging to a family
H
0
, or it was generated by a distribution belonging to a family
H
1
. In this work we assume that all distributions are stationary ergodic and do not make any further assumptions (in particular, no independence or mixing rate assumptions). We find some necessary and some sufficient conditions, formulated in terms of the topological properties of
H
0
and
H
1
, for the existence of a consistent test. For the case where
H
1
is the complement of
H
0
(to the set of all stationary ergodic processes), these necessary and sufficient conditions coincide, thereby providing a complete characterization of families of processes membership to which can be consistently tested, against their complement, based on sampling. This criterion includes as special cases several known and some new results on testing for membership to various parametric families, as well as testing identity, independence, and other hypotheses.</description><subject>Analysis</subject><subject>Economics</subject><subject>Entropy</subject><subject>Finance</subject><subject>Hypotheses</subject><subject>Hypothesis testing</subject><subject>Insurance</subject><subject>Management</subject><subject>Markov analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Probability</subject><subject>Statistical Theory and Methods</subject><subject>Statistics</subject><subject>Statistics for Business</subject><subject>Statistics 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X
1
,…,
X
n
, we wish to decide whether it was generated by a distribution belonging to a family
H
0
, or it was generated by a distribution belonging to a family
H
1
. In this work we assume that all distributions are stationary ergodic and do not make any further assumptions (in particular, no independence or mixing rate assumptions). We find some necessary and some sufficient conditions, formulated in terms of the topological properties of
H
0
and
H
1
, for the existence of a consistent test. For the case where
H
1
is the complement of
H
0
(to the set of all stationary ergodic processes), these necessary and sufficient conditions coincide, thereby providing a complete characterization of families of processes membership to which can be consistently tested, against their complement, based on sampling. This criterion includes as special cases several known and some new results on testing for membership to various parametric families, as well as testing identity, independence, and other hypotheses.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer-Verlag</pub><doi>10.1007/s11749-011-0245-3</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1133-0686 |
| ispartof | Test (Madrid, Spain), 2012-06, Vol.21 (2), p.317-329 |
| issn | 1133-0686 1863-8260 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_00639477v1 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Analysis Economics Entropy Finance Hypotheses Hypothesis testing Insurance Management Markov analysis Mathematics Mathematics and Statistics Original Paper Probability Statistical Theory and Methods Statistics Statistics for Business Statistics Theory Studies |
| title | Testing composite hypotheses about discrete ergodic processes |
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