ON THE SMOOTHED PARAMETRIC ESTIMATION OF MIXING PROPORTION UNDER FIXED DESIGN REGRESSION MODEL

Ramakrishnaiah Y. S. (), Trivedi Manish () and Satish Konda ()
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Ramakrishnaiah Y. S.: Faculty of Statistics, Osmania University, in Hyderabad. India .
Trivedi Manish: Faculty of Statistics, School of Sciences, Indira Gandhi National Open University, in New Delhi. India .
Satish Konda: Faculty of Statistics, Aurora College, in Hyderabad. India .

Statistics in Transition New Series, 2019, vol. 20, issue 1, 87-102

Abstract: The present paper revisits an estimator proposed by Boes (1966) – James (1978), herein called BJ estimator, which was constructed for estimating mixing proportion in a mixed model based on independent and identically distributed (i.i.d.) random samples, and also proposes a completely new (smoothed) estimator for mixing proportion based on independent and not identically distributed (non-i.i.d.) random samples. The proposed estimator is nonparametric in true sense based on known “kernel function” as described in the introduction. We investigated the following results of the smoothed estimator under the non-i.i.d. set-up such as (a) its small sample behaviour is compared with the unsmoothed version (BJ estimator) based on their mean square errors by using Monte-Carlo simulation, and established the percentage gain in precision of smoothed estimator over its unsmoothed version measured in terms of their mean square error, (b) its large sample properties such as almost surely (a.s.) convergence and asymptotic normality of these estimators are established in the present work. These results are completely new in the literature not only under the case of i.i.d., but also generalises to non-i.i.d. set-up.

Keywords: mixture of distributions; mixing proportion; smoothed parametric estimation; fixed design regression model; mean square error; optimal band width; strong consistency; asymptotic normality. (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:stintr:v:20:y:2019:i:1:p:87-102:n:4

DOI: 10.21307/stattrans-2019-005

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