Abstract

In order to incorporate group information for different groups, we extend the partial envelopes (Su and Cook, Statistica Sinica 23:213–30, 2011) to the groupwise partial envelopes which can improve the efficiency of parameter estimation and enlarge the scope of partial envelope model. It maintains the potential of the original partial envelope methods to increase efficiency and allows for both different regression coefficients and different error structures for diverse groups. Further, we demonstrate the maximum likelihood estimation under the groupwise partial envelope model. Meanwhile, we give asymptotic distribution and theoretical properties. At last, simulation studies are carried out to compare our proposed groupwise partial envelope model with the other three methods, including the standard model, the partial envelope model and the separate partial envelope model. From the simulation results and real data analysis, we can see that the performance of the groupwise partial envelope estimators is much better than that of the standard model estimators, the partial envelope estimators and the separate partial envelope estimators.

摘要

为了融合不同群体的群体信息，我们将部分包络（Su and Cook, Statistica Sinica 23:213–30, 2011）扩展到分组部分包络，这可以提高参数估计的效率并扩大部分包络模型的范围。它保持了原始部分包络方法提高效率的潜力，并允许不同组使用不同的回归系数和不同的误差结构。此外，我们演示了分组部分包络模型下的最大似然估计。同时给出了渐近分布及其理论性质。最后，进行了仿真研究，将我们提出的分组部分包络模型与其他三种方法进行比较，包括标准模型、部分包络线模型和单独的部分包络线模型。从仿真结果和实际数据分析可以看出，分组部分包络估计器的性能远优于标准模型估计器、部分包络估计器和单独部分包络估计器。