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Abstract:
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In this talk, I will investigate the predictive risk of possibly misspecified quantile regression models. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and I provide two relatively simple asymptotic characterizations of the associated bias, also called "expected optimism". The two characterizations help us to understand how the expected optimism depends on several factors such as the quantile level, the model misspecification bias, the model size, and the sampling variability. I discuss the implications of these results on risk estimation and model selection in quantile regression. I then propose uniformly consistent de-biased estimates for the expected optimism and the predictive risk. Our results hold for models of moderately growing size and linear, nonlinear and nonparametric quantile functions. Empirical evidence from the estimates is encouraging as it compares favorably with cross-validation.
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