MEASUREMENT ERROR REGRESSION WITH UNKNOWN LINK - DIMENSION REDUCTION AND DATA VISUALIZATION

• 成果类型: Article
• 署名作者: CARROLL, RJ; LI, KC
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.2307/2290641
• 发表日期: 1992
• 页码: 1040-1050
• 关键词: projection pursuit; score tests; models; binary

摘要

A general nonlinear regression problem is considered with measurement error in the predictors. We assume that the response is related to an unknown linear combination of a multidimensional predictor through an unknown link function. Instead of observing the predictor, we instead observe a surrogate with the property that its expectation is linearly related to the true predictor with constant variance. We identify an important transformation of the surrogate variable. Using this transformed variable, we show that if one proceeds with the usual analysis ignoring measurement error, then both ordinary least squares and sliced inverse regression yield estimates which consistently estimate the true regression parameter, up to a constant of proportionality. We derive the asymptotic distribution of the estimates. A simulation study is conducted applying sliced inverse regression in this context.