BOOTSTRAP SIMULTANEOUS ERROR BARS FOR NONPARAMETRIC REGRESSION

被引:185
作者
HARDLE, W
MARRON, JS
机构
[1] UNIV BONN,FAK RECHTS & STAATSWISSENSCH,W-5300 BONN 1,GERMANY
[2] CATHOLIC UNIV LOUVAIN,B-1348 LOUVAIN,BELGIUM
关键词
BOOTSTRAP; ERROR BARS; KERNEL SMOOTHING; NONPARAMETRIC REGRESSION; VARIABILITY BOUND;
D O I
10.1214/aos/1176348120
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
Simultaneous error bars are constructed for nonparametric kernel estimates of regression functions. The method is based on the bootstrap, where resampling is done from a suitably estimated residual distribution. The error bars are seen to give asymptotically correct coverage probabilities uniformly over any number of gridpoints. Applications to an economic problem are given and comparison to both pointwise and Bonferroni-type bars is presented through a simulation study.
引用
收藏
页码:778 / 796
页数:19
相关论文
共 25 条
[1]  
[Anonymous], 1991, INTRO PROBABILITY TH
[2]   SOME ASYMPTOTIC THEORY FOR THE BOOTSTRAP [J].
BICKEL, PJ ;
FREEDMAN, DA .
ANNALS OF STATISTICS, 1981, 9 (06) :1196-1217
[3]  
BIERENS HJ, 1987, 198744 FREE U TECHN
[4]  
Billingsley P., 1986, CONVERGENCE PROBABIL
[5]   NONPARAMETRIC-ESTIMATION OF REGRESSION - BIBLIOGRAPHICAL SURVEY [J].
COLLOMB, G .
INTERNATIONAL STATISTICAL REVIEW, 1981, 49 (01) :75-93
[6]  
Cox D.R., 1989, ANAL BINARY DATA, V32
[7]  
DIKTA G, 1988, APPROXIMATION NEARES
[8]  
Eubank R.L., 1988, SPLINE SMOOTHING NON
[9]  
GASSER T, 1984, SCAND J STAT, V11, P171
[10]   ON CONFIDENCE BANDS IN NONPARAMETRIC DENSITY-ESTIMATION AND REGRESSION [J].
HALL, P ;
TITTERINGTON, DM .
JOURNAL OF MULTIVARIATE ANALYSIS, 1988, 27 (01) :228-254