2018/12/11 by Alejandro Cholaquidis, Cholaquidis, Alejandro, Ricardo Fraiman +5
Computer Science · Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Face and Expression Recognition #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1812.04343
openalex publication_date 2018/12/11 · arxiv created 2018/12/21 · arxiv updated 2018/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Non-linear aggregation strategies have recently been proposed in response to the problem of how to combine, in a non-linear way, estimators of the regression function (see for instance \citebiau:16), classification rules (see \citech:16), among others. Although there are several linear strategies to aggregate density estimators, most of them are hard to compute (even in moderate dimensions). Our approach aims to overcome this problem by estimating the density at a point x using not just sample points close to x but in a neighborhood of the (estimated) level set f(x). We show, both theoretically and through a simulation study, that the mean squared error of our proposal is smaller than that of the aggregated densities. A Central Limit Theorem is also proven.