Polish Statistical Association

Central Statistical Office of Poland

**Subject:** Economics, Statistics & Probability

**ISSN:** 1234-7655

**eISSN:** 2450-0291

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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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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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