{"data":{"id":"10.6084/m9.figshare.c.2017265.v1","type":"dois","attributes":{"doi":"10.6084/m9.figshare.c.2017265.v1","prefix":"10.6084","suffix":"m9.figshare.c.2017265.v1","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Kasahara, Hiroyuki","nameType":"Personal","givenName":"Hiroyuki","familyName":"Kasahara","affiliation":[],"nameIdentifiers":[]},{"name":"Shimotsu, Katsumi","nameType":"Personal","givenName":"Katsumi","familyName":"Shimotsu","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Testing the Number of Components in Normal Mixture Regression Models"}],"publisher":"Figshare","container":{},"publicationYear":2015,"subjects":[{"subject":"Genetics"},{"subject":"FOS: Biological sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Biological sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Neuroscience"},{"subject":"Physiology"},{"subject":"39999 Chemical Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Chemical sciences","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Chemical sciences","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"19999 Mathematical Sciences not elsewhere classified","subjectScheme":"FOR"},{"subject":"FOS: Mathematics","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"FOS: Mathematics","subjectScheme":"Fields of Science and Technology (FOS)"},{"subject":"Mental Health"}],"contributors":[],"dates":[{"date":"2015-12-05","dateType":"Created"},{"date":"2016-04-29","dateType":"Updated"},{"date":"2015","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Collection","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[],"relatedItems":[],"sizes":[],"formats":[],"version":null,"rightsList":[{"rights":"CC-BY","rightsUri":"http://creativecommons.org/licenses/by/3.0/us"}],"descriptions":[{"description":"Testing the number of components in finite normal mixture models is a long-standing challenge because of its nonregularity. This article studies likelihood-based testing of the number of components in normal mixture regression models with heteroscedastic components. We construct a likelihood-based test of the null hypothesis of \u003ci\u003em\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e components against the alternative hypothesis of \u003ci\u003em\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e + 1 components for any \u003ci\u003em\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e. The null asymptotic distribution of the proposed modified EM test statistic is the maximum of \u003ci\u003em\u003c/i\u003e\u003csub\u003e0\u003c/sub\u003e random variables that can be easily simulated. The simulations show that the proposed test has very good finite sample size and power properties. Supplementary materials for this article are available online.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://figshare.com/collections/Testing_the_Number_of_Components_in_Normal_Mixture_Regression_Models/2017265/1","contentUrl":null,"metadataVersion":3,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"api","isActive":true,"state":"findable","reason":null,"viewCount":0,"viewsOverTime":[],"downloadCount":0,"downloadsOverTime":[],"referenceCo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