m相依样本概率密度函数核估计的相合性

Consistency for the Kerneltype Density Estimator in the Case of m Dependent Samples

YU Zhuoxi¹,², DONG Zhishan¹,³, WANG Dehui¹

1. College of Mathematics, Jilin University, Changchun 130012, China;2. Department of Mathematics, Changchun Taxation College, Changchun 130117, China;3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China)

Received:2006-09-22 Revised:1900-01-01 Online:2007-07-26 Published:2007-07-26
Contact: WANG Dehui

Abstract

Abstract: Let ｛Xn,n≥1｝be a strict stationary sequence of mdependent random variables with probability density function f(x). Based on mdependent samples, the kernel estimator for f(x)is constructed, and with the application of the property of i.i.d.samples, the consistency in rorder mean, the pointwise strong consistencyand strong uniform consistency are shown under suitable conditions.

Key words: mdependent samples, density function, kernel est imator, property of consistency

CLC Number:

O212.7

YU Zhuoxi,, DONG Zhishan,, WANG Dehui. Consistency for the Kerneltype Density Estimator in the Case of m Dependent Samples[J].J4, 2007, 45(04): 507-510.

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Consistency for the Kerneltype Density Estimator in the Case of m Dependent Samples

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