| m-WOD序列密度函数和失效率函数核估计的强相合性 |
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| 引用本文： | 关丽红,肖玉山,赵亚男.m-WOD序列密度函数和失效率函数核估计的强相合性[J].吉林大学学报(理学版),2019,57(4):833-838. |
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| 作者姓名： | 关丽红 肖玉山 赵亚男 |
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| 作者单位： | 长春大学理学院,长春,130022;长春大学理学院,长春,130022;长春大学理学院,长春,130022 |
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| 摘 要： | 设{Xn, n≥1}为一同分布的m 宽象限相依(m-WOD)序列, fn(x),rn(x)分别为密度函数f(x)基于样本X1,X2,…,Xn的核估计和失效率函数核估计. 在适当的假设条件下, 利用m-WOD序列的矩不等式和Borel Cantell 引理, 证明核密度估计及失效率函数核估计的强相合性和一致强相合性.
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| 关 键 词： | m-WOD序列 核估计 失效率函数 (一致)强相合性 |
| 收稿时间： | 2018-09-10 |
Strong Consistency of Kernel Estimator of Density Functionand Failure Rate Function for m-WOD Sequence#br# |
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| GUAN Lihong,XIAO Yushan,ZHAO Yanan.Strong Consistency of Kernel Estimator of Density Functionand Failure Rate Function for m-WOD Sequence#br#[J].Journal of Jilin University: Sci Ed,2019,57(4):833-838. |
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| Authors: | GUAN Lihong XIAO Yushan ZHAO Yanan |
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| Institution: | School of Science, Changchun University, Changchun 130022, China |
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| Abstract: | Let {Xn, n≥1} be an m-widely orthant dependence (m-WOD) sequence with the same distribution, fn(x) and rn(x) were the kernel estimators of the density function f(x) and the failure rate function based on the sample X1,X2,…,Xn, respectively. Under some suitable assumptions, we proved the strong consistency and the uniform strong consistency of the kernel density estimator and failure rate function kernel estimator by using the moment inequality for m-WOD sequence and Borel Cantelli lemma. |
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| Keywords: | m-WOD sequence kernel estimator failure rate function (uniform) strong consistency
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