Consistent estimates of the mode of the probability density function in nonparametric deconvolution problems

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• 作者：Rachdi ; Mustapha ; Sabre ; Rachid
• 关键词：Density ; Derivative estimation ; Kernel estimates ; Deconvolution problems ; Mode
• 刊名：Statistics and Probability Letters
• 出版年：2000
• 出版时间：April 1, 2000
• 年：2000
• 卷：47
• 期：2
• 页码：105-114
• 全文大小：111 K

文摘

We propose two estimates of the mode of the probability density function for nonparametric deconvolution problems. In fact, we observe Y=X+ξ, where ξ is a measurement error with a known distribution f_ξ, and we are interesting by estimating the mode of f_X the unknown probability density function of X, where Y₁,…,Y_n are n i.i.d given observations of Y. We study the asymptotic properties of these mode estimates and the asymptotic normality of the two mode estimates is also given.