2015/06/15 by Lucien Birgé, Birgé, Lucien, Nelo Magalhães +3
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1506.04692
openalex publication_date 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a general V-fold cross-validation type method based on robust tests, which is an extension of the hold-out defined by Birgé [7, Section 9]. We give some theoretical results showing that, under some weak assumptions on the considered statistical procedures, our selected estimator satisfies an oracle type inequality. We also introduce a fast algorithm that implements our method. Moreover we show in our simulations that this V-fold performs generally well for estimating a density for different sample sizes, and can handle well-known problems, such as binwidth selection for histograms or bandwidth selection for kernels. We finally provide a comparison with other classical V-fold methods and study empirically the influence of the value of V on the risk.