{"title":"正态混合模型和正态隐马尔可夫模型中最大似然估计的方差估计","authors":"M. Iqbal, A. Nishi, Yasuki Kikuchi, K. Nomakuchi","doi":"10.5183/JJSCS.1002001_183","DOIUrl":null,"url":null,"abstract":"In this article, we derive the observed information matrices for normal mixture models and normal hidden Markov models. We also describe the parametric bootstrap method for the said models. The matrices and the method mentioned above are used to estimate the variance of the maximum likelihood estimates (MLEs) obtained by the Expectation-Maximization (EM) algorithm. Finally, a numerical example is shown using a data set named \\faithful\" given in the free statistical software R.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"ESTIMATION OF THE VARIANCE FOR THE MAXIMUM LIKELIHOOD ESTIMATES IN NORMAL MIXTURE MODELS AND NORMAL HIDDEN MARKOV MODELS\",\"authors\":\"M. Iqbal, A. Nishi, Yasuki Kikuchi, K. Nomakuchi\",\"doi\":\"10.5183/JJSCS.1002001_183\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we derive the observed information matrices for normal mixture models and normal hidden Markov models. We also describe the parametric bootstrap method for the said models. The matrices and the method mentioned above are used to estimate the variance of the maximum likelihood estimates (MLEs) obtained by the Expectation-Maximization (EM) algorithm. Finally, a numerical example is shown using a data set named \\\\faithful\\\" given in the free statistical software R.\",\"PeriodicalId\":338719,\"journal\":{\"name\":\"Journal of the Japanese Society of Computational Statistics\",\"volume\":\"43 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2011-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Japanese Society of Computational Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5183/JJSCS.1002001_183\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Japanese Society of Computational Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5183/JJSCS.1002001_183","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ESTIMATION OF THE VARIANCE FOR THE MAXIMUM LIKELIHOOD ESTIMATES IN NORMAL MIXTURE MODELS AND NORMAL HIDDEN MARKOV MODELS
In this article, we derive the observed information matrices for normal mixture models and normal hidden Markov models. We also describe the parametric bootstrap method for the said models. The matrices and the method mentioned above are used to estimate the variance of the maximum likelihood estimates (MLEs) obtained by the Expectation-Maximization (EM) algorithm. Finally, a numerical example is shown using a data set named \faithful" given in the free statistical software R.
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