响应变量缺失下可伸缩的模型平均估计

Scalable Model Averaging Estimation with Missing Responses

摘要: 当响应变量缺失时，本文研究了线性模型的可伸缩的模型平均估计问题。基于逆概率加权方法和奇异值分解对原模型进行转换，所构建的模型平均估计最多只需要选择p个候选模型的权重。利用Jackknife准则选择权重，且权重之和不必限制为1。在一定的条件下证明了所提方法在实现最小二次损失意义下是渐近最优的，并通过数值模拟进一步验证了所提方法在预测效率和计算成本方面的优良性。

Abstract: In this paper, a scalable model averaging method is developed for the linear regression models with response missing. By using inverse probability weighted method and the singular value decomposition to transform the original models, this method enables us to find the optimal weights by considering at most p candidate models. The weights can be selected by Jackknife criterion, and the sum of weights is not necessarily restricted to one. Under some mild conditions, it is shown that the proposed method is asymptotically optimal in the sense of achieving the lowest possible squared error. Some simulation studies are conducted to illustrate the superiority of the proposed method in terms of both predictive efficiency and computational cost.