A unified treatment of direct and indirect estimation of a probability density and its derivatives

✍ Scribed by Belkacem Abdous; Stéphane Germain; Nadia Ghazzali

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 132 KB
• Volume: 56
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(01)00164-x

✦ Synopsis

This paper presents convolution-based estimates of a probability density and its derivatives. The proposed estimates can handle either contaminated data or not and they comprehend some classical estimates such that kernel, regularization estimates. By putting these direct and indirect estimation problems in the same framework, we clearly see how the estimates performances are a ected by contamination and by the order of the derivative to be estimated. Minimax optimal rates for the MISE criterion are proposed.