Asymptotic results for the regression function estimate on continuous time stationary and ergodic data

Didi Sultana () and Louani Djamal ()
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Didi Sultana: LSTA, Université de Paris 6, 4, Place Jussieu, 75252 Paris, France
Louani Djamal: LSTA, Université de Paris 6, 4, Place Jussieu, 75252 Paris, France

Statistics & Risk Modeling, 2014, vol. 31, issue 2, 129-150

Abstract: This paper is devoted to the study of asymptotic properties of the regression function kernel estimate in the setting of continuous time stationary and ergodic data. More precisely, considering the Nadaraya–Watson type estimator, say m̂T(x), of the l-indexed regression function m(x) =𝔼 (l(Y)|X = x) built upon continuous time stationary and ergodic data (Xt, Yt)0≤t≤T, we establish its pointwise and uniform, over a dilative compact set, convergences with rates. Notice that the ergodic setting covers and completes various situations as compared to the mixing case and stands as more convenient to use in practice.

Keywords: Consistency; continuous time processes; ergodic data; kernel estimator; rate of convergence; regression function; Consistency; continuous time processes; ergodic data; kernel estimator; rate of convergence; regression function (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1515/strm-2012-1134

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