Presmoothed estimation of the density function with truncated and censored data

被引：4

作者：

Jacome, M. A. ^{[1
]}

Iglesias-Perez, M. C. ^{[2
]}

机构：

[1] Univ A Coruna, Fac Ciencias, Dept Matemat, La Coruna 15071, Spain

[2] Univ Vigo, EU Ing Tecn Forestal, Dept Estadist & Invest Operat, Pontevedra 36005, Spain

来源：

STATISTICS | 2010年 / 44卷 / 03期

关键词：

almost sure representation; kernel-type density estimator; LTRC data; presmoothing; survival analysis; PRODUCT-LIMIT ESTIMATOR; STRONG REPRESENTATION; BANDWIDTH SELECTION; SURVIVAL FUNCTION; KAPLAN-MEIER; LAW;

D O I：

10.1080/02331880903043231

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：

A new kernel-type density estimator is presented in the context of left truncated and right censored data. This estimator is obtained by the convolution of a kernel with an estimator of the distribution function based on presmoothing ideas. Asymptotic properties, including an i.i.d. representation, consistency, asymptotic normality and mean integrated squared error expressions, are given. The practical performance of this estimator is illustrated in a simulation study and used to analyse the lifetime density in a real data example.

引用

页码：217 / 234

页数：18

共 32 条

[1]

Andersen P. K., 1993, Statistical Models Based on Counting Processes.Springer Series in Statistics

[2]

[Anonymous], 2005, Statistical Methodology, DOI DOI 10.1016/J.STAMET.2005.04.001

[3] ON THE LAW OF THE ITERATED LOGARITHM FOR CANONICAL U-STATISTICS AND PROCESSES [J].

ARCONES, MA ;

GINE, E .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1995, 58 (02) :217-245

[4] BOOTSTRAPPING THE MEAN INTEGRATED SQUARED ERROR [J].

CAO, R .

JOURNAL OF MULTIVARIATE ANALYSIS, 1993, 45 (01) :137-160

[5] Presmoothed Kaplan-Meier and Nelson-Aalen estimators [J].

Cao, R ;

López-De-Ullibarri, I ;

Janssen, P ;

Veraverbeke, N .

JOURNAL OF NONPARAMETRIC STATISTICS, 2005, 17 (01) :31-56

[6] Presmoothed kernel density estimator for censored data [J].

Cao, R ;

Jácome, MA .

JOURNAL OF NONPARAMETRIC STATISTICS, 2004, 16 (1-2) :289-309

[7] A COMPARATIVE-STUDY OF SEVERAL SMOOTHING METHODS IN DENSITY-ESTIMATION [J].

CAO, R ;

CUEVAS, A ;

MANTEIGA, WG .

COMPUTATIONAL STATISTICS & DATA ANALYSIS, 1994, 17 (02) :153-176

[8] The strong law under semiparametric random censorship models [J].

Dikta, G .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 2000, 83 (01) :1-10

[9] On semiparametric random censorship models [J].

Dikta, G .

JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 1998, 66 (02) :253-279

[10] STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR FOR TRUNCATED AND CENSORED-DATA WITH APPLICATIONS [J].

GIJBELS, I ;

WANG, JL .

JOURNAL OF MULTIVARIATE ANALYSIS, 1993, 47 (02) :210-229

← 1 2 3 4 →