摘要： Suppose that one can observe bivariate random variables (L,X) only when L≤X holds. Such data are called left-truncated data and found in many fields, such as experimental education and epidemiology. Recently, a method of fitting a parametric model on (L,X) has been considered, which can easily incorporate the dependent structure between the two variables. A primary concern for the parametric analysis is the goodness-of-fit for the imposed parametric forms. Due to the complexity of dependent truncation models, the traditional goodness-of-fit procedures, such as Kolmogorov–Smirnov type tests based on the Bootstrap approximation to null distribution, may not be computationally feasible. In this paper, we develop a computationally attractive and reliable algorithm for the goodness-of-fit test based on the asymptotic linear expression. By applying the multiplier central limit theorem to the asymptotic linear expression, we obtain an asymptotically valid goodness-of-fit test. Monte Carlo simulations show that the proposed test has correct type I error rates and desirable empirical power. It is also shown that the method significantly reduces the computational time compared with the commonly used parametric Bootstrap method. Analysis on law school data is provided for illustration. R codes for implementing the proposed procedure are available in the supplementary material. 出版者： Elsevier B.V 出版日期： 2012-07-01 出處： Computational Statistics & Data Analysis, 2012-07, Vol.56 (7), p.2237-2250 資源來源： ScienceDirect (Elsevier) Journals 版權： 2012 Elsevier B.V. 識別號： ISSN: 0167-9473 識別號： EISSN: 1872-7352 識別號： DOI: 10.1016/j.csda.2011.12.022
