Non parametric sequential estimation of the probability density function by orthogonal series

被引:2
作者
Lagha, Karima [1 ]
Adjabi, Smail [1 ]
机构
[1] Univ Bejaia, Lab LAMOS, Bejaia 06000, Algeria
关键词
Non parametric estimation; orthogonal function; probability density; random sample size;
D O I
10.1080/03610926.2015.1115075
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
We present in this work an orthogonal series density estimator based on random number of observations N-t. We give its statistical properties (bias, variance, mean square error, and mean square integrated error) and some asymptotic properties. We consider that N-t is independent of the observations and as t . We show that Kronmal-Tarter method for choosing the smoothing parameter is still valid in the case where the sample size is random. A detailed study with cosine basis is presented. The estimator obtained is a probability density, asymptotically unbiased and consistent. A simulation is used in order to study the behavior of the density estimator and shows that the estimator is performant.
引用
收藏
页码:5941 / 5955
页数:15
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