北京大学统计科学中心

北京大学数学科学学院概率统计系

北京大学数学科学学院金融数学系

拉斯维加斯9888商务统计与经济计量系

Title（标题）：EFFICIENT ESTIMATION OF CENSORED LINEAR REGRESSION MODEL

Speaker（汇报人）：Ms. Yuanyuan Lin (Ph.D candidate)

Department of Mathematics

Hong Kong University of Science & Technology, Hong Kong

Time（功夫）：2011年3月15日（周二）下午2:00-3:00

Place（地址）：北京大学理科一号楼1114教室

Abstract（提要）：In linear regression or accelerated failure time model, the method of efficient estimation, with or without censoring, has long been overlooked. The main reason is that complications arise from multiple roots of the efficient score and density estimation. In particular, when smoothing is involved, uncertainty in the choice of bandwidth is inevitable. Zeng and Lin (2007) provided a novel efficient estimation method for the accelerated failure time model by maximizing a kernelsmoothed profile likelihood function. This paper proposes a one-step efficient estimation method based on counting process martingale, which has several advantages: it avoids the multiple root problem, the initial estimator is easily available, and it is easy to implement numerically with a built-in inference procedure. The requirement on bandwidth is rather loose and less restrictive than that imposed in Zeng and Lin (2007). A simple and effective data-driven bandwidth selection method is provided. The resulting estimator is proved to be semiparametric efficient with the same asymptotic variance as the efficient estimator when the error distribution is assumed to be known up to a location shift. The asymptotic properties of the proposed method are justified and the asymptotic variance matrix of the regression coefficients is provided in a closed form. Numerical studies with supportive evidence are presented. Applications are illustrated with the well-known PBC data and the Colorado Plateau uranium miners data.