Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives
Cressie and Read (J. Roy. Statist. Soc. B 46 (1984) 440–464) introduced the power divergence statistics, R a , as multinomial goodness-of-fit statistics. Each R a has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal alter...
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| Veröffentlicht in: | Journal of multivariate analysis 2004-11, Vol.91 (2), p.199-223 |
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| creator | Sekiya, Yuri Taneichi, Nobuhiro |
| description | Cressie and Read (J. Roy. Statist. Soc. B 46 (1984) 440–464) introduced the power divergence statistics,
R
a
, as multinomial goodness-of-fit statistics. Each
R
a
has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal alternative. Taneichi et al. (J. Multivariate Anal. 81 (2002) 335–359) derived an asymptotic approximation for the distribution of
R
a
under local alternatives. In this paper, using multivariate Edgeworth expansion for a continuous distribution, we show how the approximation based on the limiting normal distribution of
R
a
under nonlocal alternatives can be improved. We apply the expansion to the power approximation for
R
a
. The results of numerical investigation show that the proposed power approximation is very effective for the likelihood ratio test. |
| doi_str_mv | 10.1016/S0047-259X(03)00130-1 |
| format | Article |
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R
a
, as multinomial goodness-of-fit statistics. Each
R
a
has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal alternative. Taneichi et al. (J. Multivariate Anal. 81 (2002) 335–359) derived an asymptotic approximation for the distribution of
R
a
under local alternatives. In this paper, using multivariate Edgeworth expansion for a continuous distribution, we show how the approximation based on the limiting normal distribution of
R
a
under nonlocal alternatives can be improved. We apply the expansion to the power approximation for
R
a
. The results of numerical investigation show that the proposed power approximation is very effective for the likelihood ratio test.</description><identifier>ISSN: 0047-259X</identifier><identifier>EISSN: 1095-7243</identifier><identifier>DOI: 10.1016/S0047-259X(03)00130-1</identifier><identifier>CODEN: JMVAAI</identifier><language>eng</language><publisher>San Diego, CA: Elsevier Inc</publisher><subject>Approximation ; Distribution ; Distribution theory ; Exact sciences and technology ; Goodness-of-fit statistics ; Likelihood ratio test ; Limit theorems ; Mathematical models ; Mathematics ; Multinomial distribution ; Multinomial distribution Goodness-of-fit statistics Power approximation Likelihood ratio test Nonlocal alternative ; Multivariate analysis ; Nonlocal alternative ; Normal distribution ; Power approximation ; Probability and statistics ; Probability theory and stochastic processes ; Sciences and techniques of general use ; Statistical analysis ; Statistics ; Theory</subject><ispartof>Journal of multivariate analysis, 2004-11, Vol.91 (2), p.199-223</ispartof><rights>2003 Elsevier Inc.</rights><rights>2004 INIST-CNRS</rights><rights>Copyright Taylor & Francis Group Nov 2004</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c497t-de9e44067672964f168506c0942ccbdeb3146070c262de54df052625f6411bf73</citedby><cites>FETCH-LOGICAL-c497t-de9e44067672964f168506c0942ccbdeb3146070c262de54df052625f6411bf73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/S0047-259X(03)00130-1$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,3550,4008,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=16138245$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/eeejmvana/v_3a91_3ay_3a2004_3ai_3a2_3ap_3a199-223.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Sekiya, Yuri</creatorcontrib><creatorcontrib>Taneichi, Nobuhiro</creatorcontrib><title>Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives</title><title>Journal of multivariate analysis</title><description>Cressie and Read (J. Roy. Statist. Soc. B 46 (1984) 440–464) introduced the power divergence statistics,
R
a
, as multinomial goodness-of-fit statistics. Each
R
a
has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal alternative. Taneichi et al. (J. Multivariate Anal. 81 (2002) 335–359) derived an asymptotic approximation for the distribution of
R
a
under local alternatives. In this paper, using multivariate Edgeworth expansion for a continuous distribution, we show how the approximation based on the limiting normal distribution of
R
a
under nonlocal alternatives can be improved. We apply the expansion to the power approximation for
R
a
. The results of numerical investigation show that the proposed power approximation is very effective for the likelihood ratio test.</description><subject>Approximation</subject><subject>Distribution</subject><subject>Distribution theory</subject><subject>Exact sciences and technology</subject><subject>Goodness-of-fit statistics</subject><subject>Likelihood ratio test</subject><subject>Limit theorems</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Multinomial distribution</subject><subject>Multinomial distribution Goodness-of-fit statistics Power approximation Likelihood ratio test Nonlocal alternative</subject><subject>Multivariate analysis</subject><subject>Nonlocal alternative</subject><subject>Normal distribution</subject><subject>Power approximation</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Sciences and techniques of general use</subject><subject>Statistical analysis</subject><subject>Statistics</subject><subject>Theory</subject><issn>0047-259X</issn><issn>1095-7243</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqFkEuLFDEUhQtRsB39CUIQBF2U5lWprpXI4GNkwIUK7kI6uXHSVCVlkirsf-_tqWFcurjJTXLO5eRrmueMvmGUqbffKJV9y7vh5ysqXlPKBG3Zg2bH6NC1PZfiYbO7lzxunpRyRBHrerlrTlfTnNMKE8RKkidmxuOfMJkaUizEp0zqDRAXSs3hsGy3qJuWsYaYpmBG8islF6GUNvnWh0pKRXepwRayRAeZxBTHZFFpxgo54usK5WnzyJuxwLO7_aL58fHD98vP7fXXT1eX769bK4e-tg4GkJKqXvV8UNIzte-osnSQ3NqDg4NgUtGeWq64g046TztsO68kYwffi4vmxTYXP_Z7gVL1MS0YYiyas71SHEmgqNtENqdSMng9Z4SQT5pRfYasbyHrM0FNhb6FrBn6vmy-DDPYexMAHKfVRKNXLczAcDlhcZyBWzi3WDMWGwbNudA3dcJhL--SmoK0fDbRhvIviWJiz-U57LtNB4htDZB1sQGiBRcy2KpdCv-J_Rc9W6yE</recordid><startdate>20041101</startdate><enddate>20041101</enddate><creator>Sekiya, Yuri</creator><creator>Taneichi, Nobuhiro</creator><general>Elsevier Inc</general><general>Elsevier</general><general>Taylor & Francis LLC</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20041101</creationdate><title>Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives</title><author>Sekiya, Yuri ; Taneichi, Nobuhiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c497t-de9e44067672964f168506c0942ccbdeb3146070c262de54df052625f6411bf73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Approximation</topic><topic>Distribution</topic><topic>Distribution theory</topic><topic>Exact sciences and technology</topic><topic>Goodness-of-fit statistics</topic><topic>Likelihood ratio test</topic><topic>Limit theorems</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Multinomial distribution</topic><topic>Multinomial distribution Goodness-of-fit statistics Power approximation Likelihood ratio test Nonlocal alternative</topic><topic>Multivariate analysis</topic><topic>Nonlocal alternative</topic><topic>Normal distribution</topic><topic>Power approximation</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Sciences and techniques of general use</topic><topic>Statistical analysis</topic><topic>Statistics</topic><topic>Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sekiya, Yuri</creatorcontrib><creatorcontrib>Taneichi, Nobuhiro</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Journal of multivariate analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sekiya, Yuri</au><au>Taneichi, Nobuhiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives</atitle><jtitle>Journal of multivariate analysis</jtitle><date>2004-11-01</date><risdate>2004</risdate><volume>91</volume><issue>2</issue><spage>199</spage><epage>223</epage><pages>199-223</pages><issn>0047-259X</issn><eissn>1095-7243</eissn><coden>JMVAAI</coden><abstract>Cressie and Read (J. Roy. Statist. Soc. B 46 (1984) 440–464) introduced the power divergence statistics,
R
a
, as multinomial goodness-of-fit statistics. Each
R
a
has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal alternative. Taneichi et al. (J. Multivariate Anal. 81 (2002) 335–359) derived an asymptotic approximation for the distribution of
R
a
under local alternatives. In this paper, using multivariate Edgeworth expansion for a continuous distribution, we show how the approximation based on the limiting normal distribution of
R
a
under nonlocal alternatives can be improved. We apply the expansion to the power approximation for
R
a
. The results of numerical investigation show that the proposed power approximation is very effective for the likelihood ratio test.</abstract><cop>San Diego, CA</cop><pub>Elsevier Inc</pub><doi>10.1016/S0047-259X(03)00130-1</doi><tpages>25</tpages><oa>free_for_read</oa></addata></record> |
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| issn | 0047-259X 1095-7243 |
| language | eng |
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| source | RePEc; Elsevier ScienceDirect Journals Complete; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Approximation Distribution Distribution theory Exact sciences and technology Goodness-of-fit statistics Likelihood ratio test Limit theorems Mathematical models Mathematics Multinomial distribution Multinomial distribution Goodness-of-fit statistics Power approximation Likelihood ratio test Nonlocal alternative Multivariate analysis Nonlocal alternative Normal distribution Power approximation Probability and statistics Probability theory and stochastic processes Sciences and techniques of general use Statistical analysis Statistics Theory |
| title | Improvement of approximations for the distributions of multinomial goodness-of-fit statistics under nonlocal alternatives |
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