Abstract Analysis of sufficient dimension reduction (SDR) is an important topic and has attracts our attention in decades. Several methods have been proposed based on simple settings. In applications, however, the ultrahigh-dimensional setting with p ≫ n and covariate measurement error usually appear in the dataset, and it is not trivial to adopt the conventional methods to handle this problem. In this paper, we consider the SDR with both the ultrahigh-dimensional setting and covariate measurement error incorporated simultaneously. The theoretical results of the proposed method are established.

中文翻译：

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具有协变量测量误差的超高维充分降维

摘要 充分降维（SDR）分析是一个重要的课题，几十年来一直引起我们的关注。已经基于简单的设置提出了几种方法。然而，在应用中，数据集中通常会出现p≫n的超高维设置和协变量测量误差，采用传统的方法来处理这个问题并非易事。在本文中，我们考虑了同时包含超高维设置和协变量测量误差的 SDR。建立了所提出方法的理论结果。