2016/11/07 by Alessio Sancetta, Sancetta, Alessio
Computer Science · Mathematics · #62G10 #62G20 #62G5 #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1611.02199
openalex publication_date 2016/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A framework for estimation and hypothesis testing of functional restrictions\nagainst general alternatives is proposed. The parameter space is a reproducing\nkernel Hilbert space (RKHS). The null hypothesis does not necessarily define a\nparametric model. The test allows us to deal with infinite dimensional nuisance\nparameters. The methodology is based on a moment equation similar in spirit to\nthe construction of the efficient score in semiparametric statistics. The\nfeasible version of such moment equation requires to consistently estimate\nprojections in the space of RKHS and it is shown that this is possible using\nthe proposed approach. This allows us to derive some tractable asymptotic\ntheory and critical values by fast simulation. Simulation results show that the\nfinite sample performance of the test is consistent with the asymptotics and\nthat ignoring the effect of nuisance parameters highly distorts the size of the\ntests.\n