| ¡@¡@Under the random truncation model, both the target variable X and the truncation variable T are observable only when X ? T. The distribution function F of X is estimated by the product-limit estimator, which is the maximum likelihood estimate (MLE). However, assuming the distribution function of T, the product-limit estimator is no longer the MLE and a corresponding MLE of F referred as the semiparametric estimator is obtained. This semiparametric estimator is more efficient than the product limit estimator when parametric information of the truncation distribution. To use this more efficient estimator, the parametric assumption has to be validated. In this article, we propose a chi-sqaure test to test the goodness of fit under random truncation. Both the simple and composite null hypotheses are considered. The size and power of the chi-square test are evaluated for small and moderate sample sizes using Monte Carlo simulations. The proposed chi-square test is found to maintain the size of the test in all the cases studied. A real life data is also presented. |