Linearized maximum rank correlation estimation of doubly truncated data

Truncated data frequently arise in many areas such as economics, astronomical studies, and survival analysis, and the existence of truncation makes statistical inference more difficult due to the incomplete information. In this paper, we propose a linearized maximum rank correlation estimation of doubly truncated data under a single-index model. Unlike the existing methods, the proposed estimation has a closed-form expression and does not need knowledge of the unknown link function or the error distribution, which makes it more appealing in theory and computation. The proposed estimators are shown to be consistent and asymptotically normal, and an extensive simulation study is conducted and indicates that the proposed method works well in various situations. The method is further demonstrated by applying it to an AIDS study.