Lan Wang
Professor
Department of Statistics
University of Minnesota
Minneapolis, Minnesota

Estimation and Inference of Quantile Regression Under Biased Sampling

Biased sampling occurs frequently in economics, epidemiology and medical studies either by design or due to data collecting mechanism. Failing to take into account the sampling bias usually leads to incorrect inference. We propose a unified estimation procedure and a computationally fast resampling method to make statistical inference for quantile regression with survival data under general biased sampling schemes, including but not limited to the length-biased sampling, the case-cohort design and variants thereof. We establish the uniform consistency and weak convergence of the proposed estimator  as a process of the quantile level. We also investigate more efficient estimation using the generalized method of moments and derive the asymptotic normality. We further propose a new resampling method for inference, which differs from alternative procedures in that it does not require to repeatedly solve estimating equations. It is proved that the resampling method consistently estimates the asymptotic covariance matrix. The unified framework proposed in this paper provides researchers and practitioners a convenient tool for analyzing data collected from various designs. Simulation studies and applications to real data sets are presented for illustration. (joint work with Gongjun Xu, Tony Sit and Chiung-Yu Huang)

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