NONPARAMETRIC BINARY REGRESSION - A BAYESIAN-APPROACH

• 成果类型: Article
• 署名作者: DIACONIS, P; FREEDMAN, DA
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176349413
• 发表日期: 1993
• 页码: 2108-2137
• 关键词: cross-validation; Consistency; approximation; likelihood; estimators; variables

摘要

The performance of Bayes estimates are studied, under an assumption of conditional exchangeability. More exactly, for each subject in a data set, let xi be a vector of binary covariates and let eta be a binary response variable, with P{eta = 1\xi} = f(xi). Here, f is an unknown function to be estimated from the data; the subjects are independent, and satisfy a natural ''balance'' condition. Define a prior distribution on f as SIGMA(k)omega(k)pi(k)/SIGMA(k)omega(k), where pi(k) is uniform on the set of f which only depend on the first k covariates and omega(k) > 0 for infinitely many k. Bayes estimates are consistent at all f if omega(k) decreases rapidly as k increase. Otherwise, the estimates are inconsistent at f = 1/2.