Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1152174 | Statistics & Probability Letters | 2013 | 9 Pages |
Abstract
The aim of this paper is to study the consistency of the kernel density estimator pertaining to a continuous time stationary process X=(Xt)t≥0X=(Xt)t≥0, with an underlying density ff. More precisely, in a rather general dependency setting, where we use a martingale difference device and a technique based on a sequence of projections on σσ-fields, we establish the almost sure pointwise and uniform consistencies with rates of the estimate fTfT of ff built upon the part (Xt)0≤t≤T(Xt)0≤t≤T of the process XX.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Sultana Didi, Djamal Louani,