{"title":"基于尺度拉普拉斯变换反演的非参数密度估计","authors":"Fairouz Elmagbri, Robert M. Mnatsakanov","doi":"10.1016/j.trmi.2018.09.003","DOIUrl":null,"url":null,"abstract":"<div><p>New nonparametric procedure for estimating the probability density function of a positive random variable is suggested. Asymptotic expressions of the bias term and Mean Squared Error are derived. By means of graphical illustrations and evaluating the Average of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-errors we conducted comparisons of the finite sample performance of proposed estimate with the one based on kernel density method.</p></div>","PeriodicalId":43623,"journal":{"name":"Transactions of A Razmadze Mathematical Institute","volume":"172 3","pages":"Pages 440-447"},"PeriodicalIF":0.3000,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.trmi.2018.09.003","citationCount":"2","resultStr":"{\"title\":\"Nonparametric density estimation based on the scaled Laplace transform inversion\",\"authors\":\"Fairouz Elmagbri, Robert M. Mnatsakanov\",\"doi\":\"10.1016/j.trmi.2018.09.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>New nonparametric procedure for estimating the probability density function of a positive random variable is suggested. Asymptotic expressions of the bias term and Mean Squared Error are derived. By means of graphical illustrations and evaluating the Average of <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-errors we conducted comparisons of the finite sample performance of proposed estimate with the one based on kernel density method.</p></div>\",\"PeriodicalId\":43623,\"journal\":{\"name\":\"Transactions of A Razmadze Mathematical Institute\",\"volume\":\"172 3\",\"pages\":\"Pages 440-447\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2018-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.trmi.2018.09.003\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of A Razmadze Mathematical Institute\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2346809218300898\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of A Razmadze Mathematical Institute","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2346809218300898","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Nonparametric density estimation based on the scaled Laplace transform inversion
New nonparametric procedure for estimating the probability density function of a positive random variable is suggested. Asymptotic expressions of the bias term and Mean Squared Error are derived. By means of graphical illustrations and evaluating the Average of -errors we conducted comparisons of the finite sample performance of proposed estimate with the one based on kernel density method.
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