A simple goodness-of-fit test for continuous conditional distributions

Abstract

This paper presents a pragmatic specification test for conditional continuous distributions with uncensored data.  We employ Monte Carlo (MC) experiments and the 2011 Medical Expenditure Panel Survey data to examine coverage and power to discern deviations from correct model specification in distribution and parameterization. We carry out MC experiments using 2000 runs for sample sizes 500 and 1000. The experiments show that the test has accurate coverage under correct specification, and that the test can discern deviations from correct specification in both the distributional family and parameterization. The power increases as sample size increases. The empirical example shows the test’s ability to identify specific distributions from other candidates using real cost data. Although the test can be used as a goodness-of-fit test for marginal distributions, it is particularly useful as an easy-to-use test for conditional continuous distributions, even those with one observation per pattern of explanatory variables.