Model Validation under Heteroskedastic Measurement Error Models

Metro Toronto Convention Centre 

Astronomers often deal with data where the covariates and the dependent variable are measured with heteroskedastic, non-Gaussian errors. While techniques have been developed for estimating regression parameters for data with heteroskedasticity and measurement errors, most methods lack procedures for model validation such as checking structural assumptions. We develop a model validation test, using ideas from conformal prediction, that is invariant to heteroskedasticity and measurement errors. We empirically demonstrate that this new test gives finite-sample control over type 1 error probabilities under a variety of assumptions on the measurement errors in the observed data, while other prediction intervals do not. We further demonstrate how our conformal prediction approach can be used for testing structural assumptions of proposed models from the literature relating planet mass and planet radius.