Large Sample Theory of Estimation in Biased Sampling Regression Models. I

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 $\sqrt n$ consistent, asymptotically Gaussian and are efficient locally, for example, if the error distribution is Gaussian. We support our asymptotics with a small simulation.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 $\sqrt n$ consistent, asymptotically Gaussian and are efficient locally, for example, if the error distribution is Gaussian. We support our asymptotics with a small simulation.

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Large Sample Theory of Estimation in Biased Sampling Regression Models. I

代码、数据与补充材料

有偏抽样回归模型估计的大样本理论（一）

原文摘要

同方向的基础文献

同方向的基础文献