LARGE SAMPLE THEORY OF ESTIMATION IN BIASED SAMPLING REGRESSION-MODELS .1.

• 成果类型: Article
• 署名作者: BICKEL, PJ; RITOV, J
• 署名单位: Hebrew University of Jerusalem; Nokia Corporation; Nokia Bell Labs; AT&T; New York University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348121
• 发表日期: 1991
• 页码: 797-816
• 关键词: nonparametric-estimation; empirical distributions; truncated regression

摘要

Biased sampling regression models were introduced by Jewell, generalizing the truncated regression model studied by Bhattacharya, Chernoff and Yang. If the independent variable takes on only a finite number of values (as does the stratum variable), we show: 1. That if the slope of the underlying regression model is assumed known, then the nonparametric maximum likelihood estimates of the distribution of the independent and dependent variables (a) can be calculated from ordinary M estimates; (b) are asymptotically efficient. 2. How to construct M estimates of the slope which are always square-root n consistent, asymptotically Gaussian and are efficient locally, for example, if the error distribution is Gaussian. We support our asymptotics with a small simulation.