DECONVOLUTION-BASED SCORE TESTS IN MEASUREMENT ERROR MODELS

• 成果类型: Article
• 署名作者: STEFANSKI, LA; CARROLL, RJ
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176347979
• 发表日期: 1991
• 页码: 249-259
• 关键词: EMPIRICAL BAYES ESTIMATION; lebesgue-exponential families; rates; CONVERGENCE

摘要

Consider a generalized linear model with response Y and scalar predictor X. Instead of observing X, a surrogate W = X + Z is observed, where Z represents measurement error and is independent of X and Y. The efficient score test for the absence of association depends on m(w) = E(X\W = w) which is generally unknown. Assuming that the distribution of Z is known, asymptotically efficient tests are constructed using nonparametric estimators of m(w). Rates of convergence for the estimator of m(w) are established in the course of proving efficiency of the proposed test.