2016/07/31 by Claire Lacour, Pascal Massart, Vincent Rivoirard · 1 citation
Computer Science · Engineering · Mathematics · #Artificial intelligence #Bayesian Methods and Mixture Models #Computer science #Engineering #Estimation #Estimator #Gaussian Processes and Bayesian Inference #Kernel (algebra) #Kernel density estimation #Kernel method #Mathematics #Multivariate kernel density estimation #Selection (genetic algorithm) #Statistical Methods and Inference #Statistics #Support vector machine #Variable kernel density estimation #math.ST #stat.TH
paper · pdf · doi:10.1007/s13171-017-0107-5
published as Sankhya A, Springer Verlag, 2017, 79 (2), pp.298 - 335
openalex publication_date 2017/06/12 · arxiv created 2017/10/18 · arxiv updated 2017/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Estimator selection has become a crucial issue in non parametric estimation. Two widely used methods are penalized empirical risk minimization (such as penalized log-likelihood estimation) or pairwise comparison (such as Lepski's method). Our aim in this paper is twofold. First we explain some general ideas about the calibration issue of estimator selection methods. We review some known results, putting the emphasis on the concept of minimal penalty which is helpful to design data-driven selection criteria. Secondly we present a new method for bandwidth selection within the framework of kernel density density estimation which is in some sense intermediate between these two main methods mentioned above. We provide some theoretical results which lead to some fully data-driven selection strategy.