ADAPTIVE DENSITY ESTIMATION FOR GENERAL ARCH MODELS

Adaptive density estimation for general ARCH models

Adaptive Estimation in Arch Models

We construct efficient estimators of the identifiable parameters in a regression model when the errors follow a stationary parametric ARCH(P) process. We do not assume a functional form for the conditional density of the errors, but do require that it be symmetric about zero. The estimators of the mean parameters are adaptive in the sense of Bickel [2]. The ARCH parameters are not jointly ident...

Adaptive Laguerre density estimation for mixed Poisson models

In this paper, we consider the observation of n i.i.d. mixed Poisson processes with random intensity having an unknown density f on R. For fixed observation time T , we propose a nonparametric adaptive strategy to estimate f . We use an appropriate Laguerre basis to build adaptive projection estimators. Non-asymptotic upper bounds of the L-integrated risk are obtained and a lower bound is provi...

Adaptive Dantzig density estimation

This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Candès and Tao’s approach, we propose an l1-minimization under an adaptive Dantzig constraint coming from sharp concentration inequalities. This allows to consider a wide class of dictionaries. Under local or global coher...

Adaptive mixture density estimation

A~trac t -A recursive, nonparametric method is developed for performing density estimation derived from mixture models, kernel estimation and stochastic approximation. The asymptotic performance of the method, dubbed "adaptive mixtures" (Priebe and Marchette, Pattern Recognition 24, 1197-1209 (1991)) for its data-driven development of a mixture model approximation to the true density, is invest...