Wu Jingjing, Abedin Tasnima, Zhao Qiang
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4 Canada.
Clinical Research Unit and Translational Laboratories, Alberta Health Services, 1331 29 Street NW, Calgary, AB T2N 4N2 Canada.
Ann Inst Stat Math. 2023;75(1):39-70. doi: 10.1007/s10463-022-00835-5. Epub 2022 May 24.
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.
The online version contains supplementary material available at 10.1007/s10463-022-00835-5.
在这项工作中，我们研究了一个具有随机优势约束的双组分混合模型，该模型自然产生于许多基因研究。为了对随机优势进行建模，我们提出了密度比对数的半参数建模。更具体地说，当两个组分密度的比值的对数呈线性回归形式时，随机优势立即得到满足。对于由此产生的半参数混合模型，我们提出了两个估计量，最大经验似然估计量（MELE）和最小赫尔利距离估计量（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柯尔莫哥洛夫 - 斯米尔诺夫型检验。通过全面的蒙特卡罗模拟研究和实际数据分析，对这两个估计量和检验在效率和稳健性方面的有限样本性能进行了检验和比较。
在线版本包含可在10.1007/s10463 - 022 - 00835 - 5获取的补充材料。
