ALNQD序列密度函数核估计的强相合性

吉林大学学报(理学版)

ALNQD序列密度函数核估计的强相合性

陆冬梅

长春理工大学光电信息学院, 长春 130022

收稿日期:2017-05-10 出版日期:2017-11-26 发布日期:2017-11-29
通讯作者: 陆冬梅 E-mail:loverpotato@163.com

Strong Consistency of Kernel Estimator of Density Function for ALNQD Sequence

LU Dongmei

College of Optical and Electronical Information, Changchun University of Science and Technology, Changchun 130022, China

Received:2017-05-10 Online:2017-11-26 Published:2017-11-29
Contact: LU Dongmei E-mail:loverpotato@163.com

摘要/Abstract

摘要： 设{X_n, n≥1}为一同分布的渐近线性负相依(ALNQD)序列, f_n(x)为密度函数f(x)基于样本X₁,…,X_n的核估计. 在适当的假设条件下, 利用ALNQD序列的矩不等式和Borel-Cantelli引理, 证明核密度估计的强相合性、一致强相合性及r阶相合性.

关键词: ALNQD序列, 核估计, (一致)强相合性, r阶相合性

Abstract: Let {X_n, n≥1} be an asymptotically linear negative quadrant dependent (ALNQD) sequence with the same distribution, and f_n(x) be the kernel estimator of the density function f(x) based on the sample X₁,…,X_n. Under some suitable assumptions, the author proved the strong consistency, the uniform strong consistency and the rorder consistency of the kernel density estimator by using the moment inequalities of ALNQD sequences and BorelCantelli lemma.

Key words: kernel estimator, (uniform) strong consistency, ALNQD sequence, rorder consistency

中图分类号:

O211.4

陆冬梅. ALNQD序列密度函数核估计的强相合性[J]. 吉林大学学报(理学版), 2017, 55(06): 1461-1464.

LU Dongmei. Strong Consistency of Kernel Estimator of Density Function for ALNQD Sequence[J]. Journal of Jilin University Science Edition, 2017, 55(06): 1461-1464.

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