Minimax Estimation of the Mixing Proportion of Two Known Distributions

Houwelingen, J.C. van; Vries, L.

doi:10.1080/01621459.1987.10478433

Journal of the American Statistical Association

1987

DOI: 10.1080/01621459.1987.10478433

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Minimax Estimation of the Mixing Proportion of Two Known Distributions

J.C. van Houwelingen

L. Vries

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Cited by 4 publications

References 5 publications

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A Semiparametric Approach to Hazard Estimation with Randomly Censored Observations

Kouassi

Singh

1997

Journal of the American Statistical Association

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One method for estimating the hazard function is to use a parametric estimator, provided that the underlying distribution of the data can be assumed to belong to some well known family of distributions depending on an unknown, possibly vector-valued parameter. Another approach is to use nonparametric estimators, such as Cox's proportional hazard models, kernel hazard estimators, and so on. However, nonparametric estimators are less efficient than suitably chosen parametric models. But, regardless of how suitable a parametric model may be, because of errors associated with data collection, it is impossible to determine with certainty whether the observed data are actually generated by the postulated model. Consequently, instead of using exclusively a parametric or a nonparametric estimator, we propose to fit a weighted average of both. The weight is estimated by minimizing the mean square error of the combination. The main point is that we expect the proposed model to assign more weight to the estimator that best fits the data. Indeed, we show that when the parametric model holds, the proposed hazard estimator converges to the true hazard function at the same rate as the parametric hazard estimator; otherwise, it converges at the same rate as the nonparametric estimator.

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A Semiparametric Approach to Hazard Estimation with Randomly Censored Observations

Kouassi

Singh

1997

Journal of the American Statistical Association

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Some recent research in the analysis of mixture distributions

Titterington

1990

Statistics

101

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On Smoothed MWSD Estimation of Mixing Proportion

Konda¹,

Mehra

Y.S.

2021

Pak.j.stat.oper.res.

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The problem considered in the present paper is estimation of mixing proportions of mixtures of two (known) distributions by using the minimum weighted square distance (MWSD) method. The two classes of smoothed and unsmoothed parametric estimators of mixing proportion proposed in a sense of MWSD due to Wolfowitz(1953) in a mixture model F(x)=p (x)+(1-p) (x) based on three independent and identically distributed random samples of sizes n and , =1,2 from the mixture and two component populations. Comparisons are made based on their derived mean square errors (MSE). The superiority of smoothed estimator over unsmoothed one is established theoretically and also conducting Monte-Carlo study in sense of minimum mean square error criterion. Large sample properties such as rates of a.s. convergence and asymptotic normality of these estimators are also established. The results thus established here are completely new in the literature.

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Minimax Estimation of the Mixing Proportion of Two Known Distributions

Cited by 4 publications

References 5 publications

A Semiparametric Approach to Hazard Estimation with Randomly Censored Observations

A Semiparametric Approach to Hazard Estimation with Randomly Censored Observations

Some recent research in the analysis of mixture distributions

On Smoothed MWSD Estimation of Mixing Proportion

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