Nonparametric tests for and against likelihood ratio ordering in the two-sample problem
We derive nonparametric procedures for testing for and against likelihood ratio ordering in the two-population setting with continuous distributions. We account for this ordering by examining the least concave majorant of the ordinal dominance curve formed from the nonparametric maximum likelihood e...
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| Veröffentlicht in: | Biometrika 2005-03, Vol.92 (1), p.159-171 |
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| container_title | Biometrika |
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| creator | Carolan, Christopher A. Tebbs, Joshua M. |
| description | We derive nonparametric procedures for testing for and against likelihood ratio ordering in the two-population setting with continuous distributions. We account for this ordering by examining the least concave majorant of the ordinal dominance curve formed from the nonparametric maximum likelihood estimators of the continuous distribution functions F and G. In particular, we focus on testing equality of F and G versus likelihood ratio ordering and testing for a violation of likelihood ratio ordering. For both testing problems, we propose area-based and sup-norm-based test statistics, derive appropriate limiting distributions, and provide simulation results that characterise the performance of our procedures. We illustrate our methods using data from a controlled experiment involving the effects of radiation on mice. |
| doi_str_mv | 10.1093/biomet/92.1.159 |
| format | Article |
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We account for this ordering by examining the least concave majorant of the ordinal dominance curve formed from the nonparametric maximum likelihood estimators of the continuous distribution functions F and G. In particular, we focus on testing equality of F and G versus likelihood ratio ordering and testing for a violation of likelihood ratio ordering. For both testing problems, we propose area-based and sup-norm-based test statistics, derive appropriate limiting distributions, and provide simulation results that characterise the performance of our procedures. We illustrate our methods using data from a controlled experiment involving the effects of radiation on mice.</description><subject>Applications</subject><subject>Applied statistics</subject><subject>Biology, psychology, social sciences</subject><subject>Brownian bridge</subject><subject>Concavity</subject><subject>Critical values</subject><subject>Data sampling</subject><subject>Distribution functions</subject><subject>Distribution theory</subject><subject>Exact sciences and technology</subject><subject>Isotonic regression</subject><subject>Kolmogorov–Smirnov</subject><subject>Least concave majorant</subject><subject>Local uniform ordering</subject><subject>Mann–Whitney</subject><subject>Mathematics</subject><subject>Nonparametric inference</subject><subject>Nonparametric tests</subject><subject>Order-restricted inference</subject><subject>Ordinal dominance curve</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Ratios</subject><subject>Sciences and techniques of general use</subject><subject>Statistical theories</subject><subject>Statistics</subject><subject>Stochastic ordering</subject><issn>0006-3444</issn><issn>1464-3510</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2005</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNpFkM1v1DAQxSMEEkvLmROShcQxux5_JT6iCihV6YcEKurFmk2crrdJnNpeoP89XmW1HJ5G1vu9mfEUxTugS6Car9bODzatNFvCEqR-USxAKFFyCfRlsaCUqpILIV4Xb2Lc7p9KqkVxd-XHCQPmaHANSTamSDofCI4twQd0Y0ykd4-2dxvvWxIwOU98aG1w4wNxI0kbS9IfX0Ycpt6SKfh1b4fT4lWHfbRvD_Wk-Pnl84-z8_Ly-uu3s0-XZSOYTGXNkHVWdy3FuqkBbY3YSsYqaAEl1lyuRa0R67VCYBKA1jU2yHTDhe205ifFh7lvnvu0y9ubrd-FMY80jILS-fdVhlYz1AQfY7CdmYIbMDwboGZ_PDMfz2hmwOTj5cTFnAh2ss0R97vpQP42HDPN8TmLUSpzcVmQNe2r1AYqMJs05GYfDztibLDvAo6Ni_93UEowDSpz72duG5MPR59RIQAqnv1y9l1M9u_Rx_BoVMUrac5_3Zv7G_n97vbmwgj-D_01o80</recordid><startdate>20050301</startdate><enddate>20050301</enddate><creator>Carolan, Christopher A.</creator><creator>Tebbs, Joshua M.</creator><general>Oxford University Press</general><general>Biometrika Trust, University College London</general><general>Oxford University Press for Biometrika Trust</general><general>Oxford Publishing Limited (England)</general><scope>BSCLL</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7QO</scope><scope>8FD</scope><scope>FR3</scope><scope>P64</scope></search><sort><creationdate>20050301</creationdate><title>Nonparametric tests for and against likelihood ratio ordering in the two-sample problem</title><author>Carolan, Christopher A. ; Tebbs, Joshua M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c425t-82a2fe9fd0a8c81ae8aad52271d1a5a835b489aa8b6a12511088aca29c34ef993</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2005</creationdate><topic>Applications</topic><topic>Applied statistics</topic><topic>Biology, psychology, social sciences</topic><topic>Brownian bridge</topic><topic>Concavity</topic><topic>Critical values</topic><topic>Data sampling</topic><topic>Distribution functions</topic><topic>Distribution theory</topic><topic>Exact sciences and technology</topic><topic>Isotonic regression</topic><topic>Kolmogorov–Smirnov</topic><topic>Least concave majorant</topic><topic>Local uniform ordering</topic><topic>Mann–Whitney</topic><topic>Mathematics</topic><topic>Nonparametric inference</topic><topic>Nonparametric tests</topic><topic>Order-restricted inference</topic><topic>Ordinal dominance curve</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Ratios</topic><topic>Sciences and techniques of general use</topic><topic>Statistical theories</topic><topic>Statistics</topic><topic>Stochastic ordering</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Carolan, Christopher A.</creatorcontrib><creatorcontrib>Tebbs, Joshua M.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>Biotechnology Research Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Biotechnology and BioEngineering Abstracts</collection><jtitle>Biometrika</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Carolan, Christopher A.</au><au>Tebbs, Joshua M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonparametric tests for and against likelihood ratio ordering in the two-sample problem</atitle><jtitle>Biometrika</jtitle><addtitle>Biometrika</addtitle><date>2005-03-01</date><risdate>2005</risdate><volume>92</volume><issue>1</issue><spage>159</spage><epage>171</epage><pages>159-171</pages><issn>0006-3444</issn><eissn>1464-3510</eissn><coden>BIOKAX</coden><abstract>We derive nonparametric procedures for testing for and against likelihood ratio ordering in the two-population setting with continuous distributions. We account for this ordering by examining the least concave majorant of the ordinal dominance curve formed from the nonparametric maximum likelihood estimators of the continuous distribution functions F and G. In particular, we focus on testing equality of F and G versus likelihood ratio ordering and testing for a violation of likelihood ratio ordering. For both testing problems, we propose area-based and sup-norm-based test statistics, derive appropriate limiting distributions, and provide simulation results that characterise the performance of our procedures. We illustrate our methods using data from a controlled experiment involving the effects of radiation on mice.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/biomet/92.1.159</doi><tpages>13</tpages></addata></record> |
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| ispartof | Biometrika, 2005-03, Vol.92 (1), p.159-171 |
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| language | eng |
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| source | RePEc; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Oxford University Press Journals All Titles (1996-Current) |
| subjects | Applications Applied statistics Biology, psychology, social sciences Brownian bridge Concavity Critical values Data sampling Distribution functions Distribution theory Exact sciences and technology Isotonic regression Kolmogorov–Smirnov Least concave majorant Local uniform ordering Mann–Whitney Mathematics Nonparametric inference Nonparametric tests Order-restricted inference Ordinal dominance curve Probability and statistics Probability theory and stochastic processes Ratios Sciences and techniques of general use Statistical theories Statistics Stochastic ordering |
| title | Nonparametric tests for and against likelihood ratio ordering in the two-sample problem |
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