Semiparametric modelling of two-component mixtures with stochastic dominance

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Jingjing Wu, Tasnima Abedin, Qiang Zhao
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引用次数: 1

Abstract

In this work, we studied a two-component mixture model with stochastic dominance constraint, a model arising naturally from many genetic studies. To model the stochastic dominance, we proposed a semiparametric modelling of the log of density ratio. More specifically, when the log of the ratio of two component densities is in a linear regression form, the stochastic dominance is immediately satisfied. For the resulting semiparametric mixture model, we proposed two estimators, maximum empirical likelihood estimator (MELE) and minimum Hellinger distance estimator (MHDE), and investigated their asymptotic properties such as consistency and normality. In addition, to test the validity of the proposed semiparametric model, we developed Kolmogorov–Smirnov type tests based on the two estimators. The finite-sample performance, in terms of both efficiency and robustness, of the two estimators and the tests were examined and compared via both thorough Monte Carlo simulation studies and real data analysis.

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具有随机优势的双组分混合物的半参数建模
在这项工作中,我们研究了具有随机优势约束的双组分混合模型,这是许多遗传学研究中自然产生的模型。为了模拟随机优势,我们提出了密度比对数的半参数模型。更具体地说,当两分量密度之比的对数是线性回归形式时,立即满足随机优势。对于得到的半参数混合模型,我们提出了两个估计量,即最大经验似然估计量(MELE)和最小Hellinger距离估计量(MHDE),并研究了它们的渐近性质,如一致性和正态性。此外,为了检验所提出的半参数模型的有效性,我们基于这两个估计量开发了Kolmogorov-Smirnov型检验。通过彻底的蒙特卡罗模拟研究和实际数据分析,对两个估计器和测试的有限样本性能(效率和鲁棒性)进行了检查和比较。
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来源期刊
CiteScore
2.00
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
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