Consistency results for the kernel density estimate on continuous time stationary and dependent data

Sultana Didi and Djamal Louani

Statistics & Probability Letters, 2013, vol. 83, issue 4, 1262-1270

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≥0, with an underlying density f. 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 σ-fields, we establish the almost sure pointwise and uniform consistencies with rates of the estimate fT of f built upon the part (Xt)0≤t≤T of the process X.

Keywords: Consistency; Continuous time; Density function; Kernel estimator; Rate of convergence (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2013.01.024

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