Weak and strong uniform consistency of a kernel error density estimator in nonparametric regression

被引：29

作者：

Cheng, FX ^{[1
]}

机构：

[1] Michigan State Univ, Dept Stat, E Lansing, MI 48824 USA

来源：

JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2004年 / 119卷 / 01期

关键词：

kernel density estimation; nonparametric residuals; empirical process;

D O I：

10.1016/S0378-3758(02)00417-2

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：

This paper considers the problem of estimating the kernel error density function in nonparametric regression models. Sufficient conditions are given under which the kernel error density estimator based on nonparametric residuals is uniformly weakly and strongly consistent. (C) 2002 Elsevier B.V. All rights reserved.

引用

页码：95 / 107

页数：13

共 19 条

[1]

[Anonymous], THEORY PROBABILITY I

[2]

[Anonymous], MULTIVARIATE ANAL

[3]

BOSQ D, 1996, NONPARAMETRIC STAT S

[4] Consistency of error density and distribution function estimators in nonparametric regression [J].

Cheng, F .

STATISTICS & PROBABILITY LETTERS, 2002, 59 (03) :257-270

[5] ASYMPTOTIC MINIMAX CHARACTER OF THE SAMPLE DISTRIBUTION FUNCTION AND OF THE CLASSICAL MULTINOMIAL ESTIMATOR [J].

DVORETZKY, A ;

KIEFER, J ;

WOLFOWITZ, J .

ANNALS OF MATHEMATICAL STATISTICS, 1956, 27 (03) :642-669

[6] STRONG UNIFORM CONSISTENCY RATES FOR ESTIMATORS OF CONDITIONAL FUNCTIONALS [J].

HARDLE, W ;

JANSSEN, P ;

SERFLING, R .

ANNALS OF STATISTICS, 1988, 16 (04) :1428-1449

[7] PROBABILITY-INEQUALITIES FOR SUMS OF BOUNDED RANDOM-VARIABLES [J].

HOEFFDING, W .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1963, 58 (301) :13-+

[8]

Kallenberg O., 1997, Foundations of modern probability

[9] WEAK-CONVERGENCE OF RANDOMLY WEIGHTED DEPENDENT RESIDUAL EMPIRICALS WITH APPLICATIONS TO AUTOREGRESSION [J].

KOUL, HL ;

OSSIANDER, M .

ANNALS OF STATISTICS, 1994, 22 (01) :540-562

[10]

Koul HL, 1996, ANN STAT, V24, P380

← 1 2 →