Adaptive orthogonal series density estimation for small samples

被引：10

作者：

Efromovich, S ^{[1
]}

机构：

[1] UNIV NEW MEXICO, DEPT MATH & STAT, ALBUQUERQUE, NM 87131 USA

来源：

COMPUTATIONAL STATISTICS & DATA ANALYSIS | 1996年 / 22卷 / 06期

基金：

美国国家科学基金会;

关键词：

adaptation; density; MISE; nonparametric; orthogonal series; small sample;

D O I：

10.1016/0167-9473(96)00012-6

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Adaptive nonnegative orthogonal series estimators are investigated for the case of small sample sizes. The estimators are analyzed via intensive Monte Carlo study and oracle inequalities when an estimator is compared with optimal pseudo-estimators (''oracles'') based on an underlying (estimated) density. The results are favorable to a modified asymptotically efficient estimator. The paper also sheds light on that how to employ results of asymptotic theory for the practically important case of small sample sizes.

引用

页码：599 / 617

页数：19

共 21 条

[1]

CHENTSOV N, 1972, STAT DECISION RULES

[2]

CONOHO D, 1992, NEW MINIMAX THEOREMS

[3] THE SELECTION OF TERMS IN AN ORTHOGONAL SERIES DENSITY ESTIMATOR [J].

DIGGLE, PJ ;

HALL, P .

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 1986, 81 (393) :230-233

[4]

DONOHO D, 1993, ADAPTING UNKNOWN SMO

[5] MINIMAX RISK OVER HYPERRECTANGLES, AND IMPLICATIONS [J].

DONOHO, DL ;

LIU, RC ;

MACGIBBON, B .

ANNALS OF STATISTICS, 1990, 18 (03) :1416-1437

[6]

DONOHO DL, 1995, J ROY STAT SOC B MET, V57, P301

[7] NONPARAMETRIC-ESTIMATION OF A DENSITY OF UNKNOWN SMOOTHNESS [J].

EFROIMOVICH, SY .

THEORY OF PROBABILITY AND ITS APPLICATIONS, 1986, 30 (03) :557-568

[8]

EFROIMOVICH SY, 1982, PROBL PEREDACHI INF, V18, P19

[9]

FELDMAN I, 1989, MINIMAX RISK ESTIMAT

[10]

Gyorfi L., 1985, The L 1 View

← 1 2 3 →