Strong Consistency Rate for the Kernel Mode Estimator Under Strong Mixing Hypothesis and Left Truncation

被引：8

作者：

Ould-Said, Elias ^{[1
]}

Tatachak, Abdelkader ^{[2
]}

机构：

[1] Univ Littoral Cote dOpale, LMPA J Liouville, F-62228 Calais, France

[2] USTHB, Fac Math, Dept Probabilites & Stat, El Alia, Algeria

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2009年 / 38卷 / 08期

关键词：

Kernel estimator; Lynden-Bell estimator; Mode; Random left truncation; Rate of convergence; Strong consistency; Strong mixing; PRODUCT-LIMIT ESTIMATOR; CONDITIONAL MODE; NONPARAMETRIC-ESTIMATION; ASYMPTOTIC PROPERTIES; DENSITY-ESTIMATION; PROBABILITY; PREDICTION; DEVIATIONS; NORMALITY;

D O I：

10.1080/03610920802379169

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let (YN)N1 be a sequence of copies of a random variable of interest Y. In this article, we study the kernel estimator, say [image omitted], of the mode of Y when Y is subject to the random left truncation. While based on n (nN) actual observations fulfilling the well-known -mixing condition, we establish the strong consistency with a rate of the proposed estimator [image omitted].

引用

页码：1154 / 1169

页数：16

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