Abstract:This article introduces a Pearson-type goodness-of-fit test for the parametric specification of conditional distribution models with continuous responses. Under correct specification, the Rosenblatt transform is uniformly distributed on $[0,1]$ conditionally on the explanatory variables. The test exploits this characterization by cross-classifying the transformed observations and the explanatory variables according to partitions of $[0,1]$ and their support, respectively. The resulting Pearson statistic has a chi-squared limiting distribution with known degrees of freedom, and this result remains valid for the class of data-dependent partitions considered. Monte Carlo simulations indicate accurate size control and favorable power relative to existing bootstrap-based tests, particularly in high-dimensional settings.
From: Julius Vainora [view email]
[v1]
Sun, 2 Oct 2022 20:52:15 UTC (37 KB)
[v2]
Fri, 10 Feb 2023 14:09:52 UTC (41 KB)
[v3]
Sun, 7 May 2023 00:02:27 UTC (36 KB)
[v4]
Fri, 22 Sep 2023 14:36:11 UTC (28 KB)
[v5]
Tue, 18 Aug 2026 19:26:57 UTC (42 KB)
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