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

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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability

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VOLUME 20 , ISSUE 1 (March 2019) > List of articles

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

Y. S. Ramakrishnaiah / Manish Trivedi / Konda Satish

Keywords : mixture of distributions, mixing proportion, smoothed parametric  estimation, fixed design regression model, mean square error, optimal band width, strong consistency, asymptotic normality

Citation Information : Statistics in Transition New Series. Volume 20, Issue 1, Pages 87-102, DOI: https://doi.org/10.21307/stattrans-2019-005

License : (CC BY-NC-ND 4.0)

Published Online: 27-May-2019

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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.

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