Misspecification testing in a class of conditional distributional models
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Date
2011-01-18
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Abstract
We propose a specification test for a wide range of parametric models for conditional
distribution function of an outcome variable given a vector of covariates.
The test is based on the Cramer-von Mises distance between an unrestricted estimate
of the joint distribution function of the data, and an restricted estimate that
imposes the structure implied by the model. The procedure is straightforward to
implement, is consistent against fixed alternatives, has non-trivial power against
local deviations from the null hypothesis of order n^(-1/2), and does not require the
choice of smoothing parameters. We also provide an empirical application using
data on wages in the US.
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Keywords
Bootstrap, Cramer-von Mises Distance, Distributional Regression, Quantile Regression