On some non parametric estimators of the quantile density function for a stationary associated process
Article Type
Research Article
Publication Title
Communications in Statistics Theory and Methods
Abstract
In this article, we consider smooth estimators for the quantile density function (qdf) for a sequence (Formula presented.) of stationary non negative associated random variables with a common marginal distribution function. The qdf is given by (Formula presented.), (Formula presented.) representing the corresponding quantile function. The smooth estimators of (Formula presented.) considered here are adapted from those of (Formula presented.) considered in Chaubey, Dewan, and Li (2021). A few asymptotic properties of these estimators are established parallel to those in the i.i.d. case. A numerical study comparing the mean squared errors of various estimators indicates the advantages and a few limitations of various estimators. The smoothing parameter is selected based on the BCV and RLCV (a variation of likelihood cross-validation) criteria. It is concluded, based on the numerical studies, that the RLCV criterion may produce over-smoothing, hence BCV criterion may be preferable. The numerical studies also suggest that, overall, the estimator proposed by Soni, Dewan, and Jain (2012) seems to have some advantage over the other estimators considered in this article.
First Page
5553
Last Page
5573
DOI
10.1080/03610926.2023.2222922
Publication Date
1-1-2024
Recommended Citation
Chaubey, Yogendra P.; Dewan, Isha; and Li, Jun, "On some non parametric estimators of the quantile density function for a stationary associated process" (2024). Journal Articles. 4950.
https://digitalcommons.isical.ac.in/journal-articles/4950