PREDICTIVE DENSITY ESTIMATION FOR MULTIPLE REGRESSION
PREDICTIVE DENSITY ESTIMATION FOR MULTIPLE REGRESSION
复制标题
多元回归的预测密度估计
作者：
E. George;Xinyi Xu
假设我们观察到X ~ Nm(a β,σ2I)，并希望估计未来y ~ Nn（Bβ,σ2I）的预测密度p（y|β）。利用Kullback-Leibler损失评估预测估计，我们开发并评估了该问题的贝叶斯方法。我们得到了“非信息”一致先验贝叶斯过程的极大性和优性的一般充分条件。我们将这些结果扩展到只有a中的预测因子子集被认为可能不相关的情况。然后我们考虑更现实的情况，其中存在模型不确定性，并且该子集是未知的。针对这种情况，我们建立了多个收缩预测估计量，并得到了一般的极小性和优势性条件。最后，给出了一个基于尺度调和先验的极大极小多重收缩预测估计的实例。我们感谢Larry Brown， Feng Liang， Linda Zhao和三位推荐人提出的有益建议。这项工作得到了美国国家科学基金会的各种资助，DMS-0605102是最近的。
Suppose we observe X ∼ Nm(Aβ,σ2I) and would like to estimate the predictive density p(y|β) of a future Y ∼ Nn(Bβ,σ2I). Evaluating predictive estimates by Kullback–Leibler loss, we develop and evaluate Bayes procedures for this problem. We obtain general sufficient conditions for minimaxity and dominance of the “noninformative” uniform prior Bayes procedure. We extend these results to situations where only a subset of the predictors in A is thought to be potentially irrelevant. We then consider the more realistic situation where there is model uncertainty and this subset is unknown. For this situation we develop multiple shrinkage predictive estimators and obtain general minimaxity and dominance conditions. Finally, we provide an explicit example of a minimax multiple shrinkage predictive estimator based on scaled harmonic priors.We acknowledge Larry Brown, Feng Liang, Linda Zhao, and three referees for their helpful suggestions. This work was supported by various NSF grants, DMS-0605102 the most recent.