An Asymmetric Kernel Estimator of Density Function for Stationary Associated Sequences

Abstract

Here, we apply the smoothing technique proposed by Chaubey et al. (2007) for the empirical survival function studied in Bagai and Prakasa Rao (1991) for a sequence of stationary non-negative associated random variables.The derivative of this estimator in turn is used to propose a nonparametric density estimator. The asymptotic properties of the resulting estimators are studied and contrasted with some other competing estimators. A simulation study is carried out comparing the recent estimator based on the Poisson weights (Chaubey et al., 2011) showing that the two estimators have comparable finite sample global as well as local behavior.

Keywords:

• Associated sequence
• Asymmetric kernel estimator
• Strong consistency
• Survival function

Mathematics Subject Classification:

• 62G07
• 62G20

Acknowledgment

The research of the first author was partially supported from the author's Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. The authors are also grateful to two anonymous reviewers for their constructive comments.

Notes

I-Kernel, II-Poisson, III-Gamma, IV-Gamma Correction.

I-Kernel, II-Poisson, III-Gamma, IV-Gamma Correction.

I-Kernel, II-Poisson, III-Gamma, IV-Gamma Correction.

I-Kernel, II-Poisson, III-Gamma, IV-Gamma Correction.