Model testing for multivariate censored data

Abstract

In the fields like Astronomy and Ecology, the need for proper statistical analysis of data that are censored is being increasingly recognized. Such data occur when, due to noise or other factors, instruments fail to detect low luminosities of celestial objects, or low concentrations of certain pollutants. For multivariate censored data sets there are very few distribution free methods available and researchers in the various fields often impose an assumption on the joint distribution, such as multivariate normality, and carry out parametric inferences. Under censoring, however, such parametric inferences are asymptotically wrong if the imposed assumption is incorrect. In this paper we propose a class of goodness-of-fit procedures for testing assumptions about the multivariate distribution under random censoring. The test procedures generalize Pearson's goodness-of-fit test in the sense that they are based on the concept of observed-minus-expected frequencies. The theory of the test statistic, however, differs from that for the classical Pearson test due to the accommodation of censored data.