2018/02/02 by Alexander Giessing, Xuming He, Giessing, Alexander +1
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Risk and Portfolio Optimization #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1802.00555
openalex publication_date 2018/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple (asymptotic) characterizations of the associated bias, also called expected optimism. We propose estimates for the expected optimism and the predictive risk, and establish their uniform consistency under mild conditions. Our results hold for models of moderately growing size and allow the quantile function to be incorrectly specified. Empirical evidence from our estimates is encouraging as it compares favorably with cross-validation.