A Pearson's Independence Test for Conditional Distribution Model Checking

A new goodness-of-fit test for continuous conditional distributions, based on the Pearson type test of independence, is proposed. The test exploits the fact that, under a correct specification, the conditional probability integral transform of the explained variable is independent of the explanatory variables. Unlike existing Pearson’s tests for conditional distributions, the test statistic proposed is distributed as a chi-square with known degrees of freedom when using general partitions that may depend on the sample. We propose alternative data grouping algorithms in multiple dimensions to construct partitions for constructing tests with different properties. The finite sample performance of the test is investigated by means of Monte Carlo simulations.

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