Boundary performance of the beta kernel estimators

被引:19
作者
Zhang, Shunpu [1 ]
Karunamuni, Rohana J. [2 ]
机构
[1] Univ Nebraska, Dept Stat, Lincoln, NE 68583 USA
[2] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
基金
加拿大自然科学与工程研究理事会;
关键词
nonparametric density estimation; boundary problem; beta kernel estimator; reflection estimator; boundary kernel estimator; DENSITY-ESTIMATION; TRANSFORMATIONS; BIAS;
D O I
10.1080/10485250903124984
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
The beta kernel estimators are shown in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131-145] to be non-negative and have less severe boundary problems than the conventional kernel estimator. Numerical results in Chen [S.X. Chen, Beta kernel estimators for density functions, Comput. Statist. Data Anal. 31 (1999), pp. 131-145] further show that beta kernel estimators have better finite sample performance than some of the widely used boundary corrected estimators. However, our study finds that the numerical comparisons of Chen are confounded with the choice of the bandwidths and the quantities being compared. In this paper, we show that the performances of the beta kernel estimators are very similar to that of the reflection estimator, which does not have the boundary problem only for densities exhibiting a shoulder at the endpoints of the support. For densities not exhibiting a shoulder, we show that the beta kernel estimators have a serious boundary problem and their performances at the boundary are inferior to that of the well-known boundary kernel estimator.
引用
收藏
页码:81 / 104
页数:24
相关论文
共 29 条
[1]  
[Anonymous], 1994, Kernel smoothing
[2]   Consistency of the beta kernel density function estimator [J].
Bouezmarni, T ;
Rolin, JM .
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE, 2003, 31 (01) :89-98
[3]   Beta kernel estimators for density functions [J].
Chen, SX .
COMPUTATIONAL STATISTICS & DATA ANALYSIS, 1999, 31 (02) :131-145
[4]  
Chen SX, 2000, STAT SINICA, V10, P73
[5]  
Cheng MY, 1997, ANN STAT, V25, P1691
[6]  
CLINE DBH, 1991, STATISTICS-ABINGDON, V22, P69, DOI DOI 10.1080/02331889108802286
[7]  
Cowling A, 1996, J ROY STAT SOC B, V58, P551
[8]  
Devroye L., 1985, Nonparametric density estimation: the L 1 view
[9]   Central limit theorem for asymmetric kernel functionals [J].
Fernandes, M ;
Monteiro, PK .
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 2005, 57 (03) :425-442
[10]  
GASSER T, 1985, J ROY STAT SOC B MET, V47, P238