Reweighting estimators for the transformation models with length-biased sampling data and missing covariates

Length-biased sampling data are commonly observed in cross-sectional surveys and epidemiological cohort studies. Due to study design or accident, some components of the covariate vector are often missing. This article considers the statistical inference for the transformation models with length-biased sampling data and missing covariates. The reweighting estimating procedures are proposed for the unknown regression parameters when the selection probability is known, estimated non parametrically, or estimated parametrically. The large sample properties of the resulting estimators are studied. Simulation studies are presented to demonstrate the utility and efficiency of the proposed methods.