Nonparametric Inference for an Inverse-Probability-Weighted Estimator with Doubly Truncated Data

Efron and Petrosian (1999 Efron, B., Petrosian, V. (1999). Nonparametric methods for doubly truncated data. Journal of the American Statistical Association 94:824–834.Taylor &; Francis Online], Web of Science ®] , Google Scholar]) formulated the problem of double truncation and proposed nonparametric methods on testing and estimation. An alternative estimation method was proposed by Shen (2010a Shen, P.S. (2010a). Nonparametric analysis of doubly truncated data. Annals of the Institute of Statistical Mathematics 62:835–853.Crossref], Web of Science ®] , Google Scholar]), utilizing the inverse-probability-weighting technique. One aim of this paper was to assess the computational complexity of the existing estimation methods. Through a simulation study, we found that these two estimation methods have the same level of computational efficiency. The other aim was to study the noniterative IPW estimator under the condition that truncation variables are independent. The IPW estimator and the interval estimation was proved satisfactory in the simulation study.