Electronic Journal of Statistics

CDF and survival function estimation with infinite-order kernels

Arthur Berg and Dimitris Politis

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Abstract

A reduced-bias nonparametric estimator of the cumulative distribution function (CDF) and the survival function is proposed using infinite-order kernels. Fourier transform theory on generalized functions is utilized to obtain the improved bias estimates. The new estimators are analyzed in terms of their relative deficiency to the empirical distribution function and Kaplan-Meier estimator, and even improvements in terms of asymptotic relative efficiency (ARE) are present under specified assumptions on the data. The deficiency analysis introduces a deficiency rate which provides a continuum between the classical deficiency analysis and an efficiency analysis. Additionally, an automatic bandwidth selection algorithm, specially tailored to the infinite-order kernels, is incorporated into the estimators. In small sample sizes these estimators can significantly improve the estimation of the CDF and survival function as is illustrated through the deficiency analysis and computer simulations.

Article information

Source
Electron. J. Statist., Volume 3 (2009), 1436-1454.

Dates
First available in Project Euclid: 24 December 2009

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1261671304

Digital Object Identifier
doi:10.1214/09-EJS396

Mathematical Reviews number (MathSciNet)
MR2578832

Zentralblatt MATH identifier
1326.62073

Subjects
Primary: 62G05: Estimation 62N02: Estimation 62N02: Estimation
Secondary: 62P10: Applications to biology and medical sciences

Keywords
Bandwidth cumulative distribution function deficiency infinite-order kernels nonparametric estimation survival function

Citation

Berg, Arthur; Politis, Dimitris. CDF and survival function estimation with infinite-order kernels. Electron. J. Statist. 3 (2009), 1436--1454. doi:10.1214/09-EJS396. https://projecteuclid.org/euclid.ejs/1261671304


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