A Log-Linear Model for a Poisson Process Change Point
Many methods have been proposed for modelling nonhomogeneous Poisson processes, including change point models and log-linear models. In this paper, we use likelihood ratio tests to choose which of these models are necessary. Of particular interest is the test for the presence of a change point, for...
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| Veröffentlicht in: | The Annals of statistics 1992-09, Vol.20 (3), p.1391-1411 |
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| creator | Loader, Clive R. |
| description | Many methods have been proposed for modelling nonhomogeneous Poisson processes, including change point models and log-linear models. In this paper, we use likelihood ratio tests to choose which of these models are necessary. Of particular interest is the test for the presence of a change point, for which standard asymptotic theory is not valid. Large deviation methods are applied to approximate the significance level, and power approximations are given. Confidence regions for the change point and other parameters in the model are also derived. A British coal mining accident data set is used to illustrate the methodology. |
| doi_str_mv | 10.1214/aos/1176348774 |
| format | Article |
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A British coal mining accident data set is used to illustrate the methodology.</description><subject>60G55</subject><subject>62F03</subject><subject>62M99</subject><subject>Accidents</subject><subject>Approximation</subject><subject>Boundary crossing</subject><subject>change points</subject><subject>Coal mining</subject><subject>Exact sciences and technology</subject><subject>Inference from stochastic processes; time series analysis</subject><subject>log-linear model</subject><subject>Mathematics</subject><subject>Maximum likelihood estimation</subject><subject>Maximum likelihood estimators</subject><subject>non-nested hypothesis</subject><subject>Parametric models</subject><subject>Poisson process</subject><subject>Probability and statistics</subject><subject>Ratio test</subject><subject>Sciences and techniques of general use</subject><subject>Significance level</subject><subject>Statistics</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1992</creationdate><recordtype>article</recordtype><recordid>eNplULtOwzAUtRBIlMLKxOCBNe31M8lGFfGSguhA58h1rkuqEFd2GPh7UiUqA9PRPfc8pEPILYMF40wujY9LxlItZJam8ozMONNZkuVan5MZQA6JElpekqsY9wCgcilmRK1o6XdJ2XRoAn3zNbbU-UANXfsmRt_RdfAWY6TFp-l2eKS7_ppcONNGvJlwTjZPjx_FS1K-P78WqzKxQqo-MTlIBM4zLrbSOctqy2uFMNwsA4NWO4OADO1AMOWktjq3W8GBS8GtFnPyMOYegt-j7fHbtk1dHULzZcJP5U1TFZtyYicYZqj-ZhgiFmOEDT7GgO7kZlAdd_tvuJ86TbSmdcF0toknl1TpIGOD7G6U7WPvw-nNueTAUvELeLB1uA</recordid><startdate>19920901</startdate><enddate>19920901</enddate><creator>Loader, Clive R.</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19920901</creationdate><title>A Log-Linear Model for a Poisson Process Change Point</title><author>Loader, Clive R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c345t-a904e022823b4ffc1dc2d5e0823180aec6fae0e1ec23115f46c69cb3202432c63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1992</creationdate><topic>60G55</topic><topic>62F03</topic><topic>62M99</topic><topic>Accidents</topic><topic>Approximation</topic><topic>Boundary crossing</topic><topic>change points</topic><topic>Coal mining</topic><topic>Exact sciences and technology</topic><topic>Inference from stochastic processes; time series analysis</topic><topic>log-linear model</topic><topic>Mathematics</topic><topic>Maximum likelihood estimation</topic><topic>Maximum likelihood estimators</topic><topic>non-nested hypothesis</topic><topic>Parametric models</topic><topic>Poisson process</topic><topic>Probability and statistics</topic><topic>Ratio test</topic><topic>Sciences and techniques of general use</topic><topic>Significance level</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Loader, Clive R.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Loader, Clive R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Log-Linear Model for a Poisson Process Change Point</atitle><jtitle>The Annals of statistics</jtitle><date>1992-09-01</date><risdate>1992</risdate><volume>20</volume><issue>3</issue><spage>1391</spage><epage>1411</epage><pages>1391-1411</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><coden>ASTSC7</coden><abstract>Many methods have been proposed for modelling nonhomogeneous Poisson processes, including change point models and log-linear models. 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| ispartof | The Annals of statistics, 1992-09, Vol.20 (3), p.1391-1411 |
| issn | 0090-5364 2168-8966 |
| language | eng |
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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Project Euclid Complete |
| subjects | 60G55 62F03 62M99 Accidents Approximation Boundary crossing change points Coal mining Exact sciences and technology Inference from stochastic processes time series analysis log-linear model Mathematics Maximum likelihood estimation Maximum likelihood estimators non-nested hypothesis Parametric models Poisson process Probability and statistics Ratio test Sciences and techniques of general use Significance level Statistics |
| title | A Log-Linear Model for a Poisson Process Change Point |
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