2018/06/26 by Johannes Krebs, Krebs, Johannes T. N.
Computer Science · Environmental Science · Mathematics · #62F40 #62G09 #62M10 (Primary) #62M20 (Secondary) #62M30 #Bayesian Methods and Mixture Models #FOS: Mathematics #Soil Geostatistics and Mapping #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1806.10196
openalex publication_date 2018/06/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We consider the double functional nonparametric regression model\nY=r(X)+\ε, where the response variable Y is Hilbert space-valued and\nthe covariate X takes values in a pseudometric space. The data satisfy an\nergodicity criterion which dates back to Laib and Louani (2010) and are\narranged in a triangular array. So our model also applies to samples obtained\nfrom spatial processes, e.g., stationary random fields indexed by the regular\nlattice \ℤN for some N\∈\ℕ+. We consider a kernel\nestimator of the Nadaraya--Watson type for the regression operator r and\nstudy its limiting law which is a Gaussian operator on the Hilbert space.\nMoreover, we investigate both a naive and a wild bootstrap procedure in the\ndouble functional setting and demonstrate their asymptotic validity. This is\nquite useful as building confidence sets based on an asymptotic Gaussian\ndistribution is often difficult.\n