Regression analysis with response-biased sampling
主 题: Regression analysis with response-biased sampling
报告人: YAO, Yuan (Hong Kong Baptist University)
时 间: 2014-06-20 14:00-15:00
地 点: 理科一号楼 1114（主持人：姚远）
Response-biased sampling, in which samples are drawn from a population according to the values of the response variable, is common in biomedical, epidemiological, economic and social studies. Thiswork proposes to use transformation models for regression analysis with response-biased sampling. With unknown error distribution, the transformation models are broad enough to cover linear regression models, the Cox's model and the proportional oddsmodel as special cases. We prove that the maximum rank correlation estimation is valid for response-biased sampling and establish its consistency and asymptotic normality. Unlike the inverse probability methods, the proposed method of estimation does not involve the sampling probabilities, which are often difficult to obtain in practice. Without the need of estimating the unknown transformation function or the error distribution, the proposed method is numerically easy to implement with the Nelder-Mead simplex algorithm, which does not require convexity or continuity. We propose an inference procedureusing random weighting to avoid the complication of density estimation when using the plug-in rule for variance estimation. Numerical studies with supportive evidence are presented. Applications are illustrated with the Forbes Global 2000 data.
