NECESSARY AND SUFFICIENT CONDITIONS FOR THE ASYMPTOTIC NORMALITY OF PERTURBED SAMPLE QUANTILES

被引：14

作者：

RALESCU, SS

SUN, S

机构：

[1] CUNY QUEENS COLL,DEPT MATH,FLUSHING,NY 11367

[2] INDIANA UNIV,DEPT MATH,BLOOMINGTON,IN 47401

[3] JAMES MADISON UNIV,DEPT MATH,HARRISONBURG,VA 22807

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 1993年 / 35卷 / 01期

关键词：

PERTURBED SAMPLE QUANTILE; KERNEL ESTIMATE; BANDWIDTH; ASYMPTOTIC NORMALITY;

D O I：

10.1016/0378-3758(93)90067-G

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 deal with perturbed sample quantiles based on a kernel k and a sequence of window-width a(n) > 0. Under minimal assumptions on the underlying cumulative distribution and the kernel k, necessary and sufficient conditions for the central limit theorem to hold for these quantiles are found for the sequence {a(n)}. Our results (i) generalize the central limit theorem of Nadaraya (1964), and (ii) extend results of Chanda (1975) and Falk (1985). Several applications are included.

引用

页码：55 / 64

页数：10

共 24 条

[1] A NOTE ON THE ESTIMATION OF A DISTRIBUTION FUNCTION AND QUANTILES BY A KERNEL-METHOD [J].