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Asymptotic results for the regression function estimate on continuous time stationary and ergodic data
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Sultana Didi
Published/Copyright:
May 28, 2014
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
Received: 2012-5-28
Accepted: 2013-4-7
Published Online: 2014-5-28
Published in Print: 2014-6-28
©2014 Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- Asymptotic results for the regression function estimate on continuous time stationary and ergodic data
- A note on nonparametric estimation of bivariate tail dependence
- Prediction of regionalized car insurance risks based on control variates
- Stochastic orderings with respect to a capacity and an application to a financial optimization problem
Keywords for this article
Consistency;
continuous time processes;
ergodic data;
kernel estimator;
rate of convergence;
regression function
Articles in the same Issue
- Frontmatter
- Asymptotic results for the regression function estimate on continuous time stationary and ergodic data
- A note on nonparametric estimation of bivariate tail dependence
- Prediction of regionalized car insurance risks based on control variates
- Stochastic orderings with respect to a capacity and an application to a financial optimization problem
