Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time

Sultana Didi, Ahoud AL Harby and Salim Bouzebda ()
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Sultana Didi: Department of Statistics, College of Sciences, Qassim University, P.O. Box 6688, Buraydah 51452, Saudi Arabia
Ahoud AL Harby: Department of Mathematics, College of Sciences, Qassim University, P.O. Box 6688, Buraydah 51452, Saudi Arabia
Salim Bouzebda: LMAC (Laboratory of Applied Mathematics of Compiègne), Université de Technologie de Compiègne, 60200 Compiègne, France

Mathematics, 2022, vol. 10, issue 19, 1-33

Abstract: The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decomposition spaces is given. To obtain the asymptotic properties of wavelet density and regression estimators, the Martingale method is used. These results are obtained under some mild conditions on the model; aside from ergodicity, no other assumptions are imposed on the data. This paper extends the scope of some previous results for wavelet density and regression estimators by relaxing the independence or the mixing condition to the ergodicity. Potential applications include the conditional distribution, curve discrimination, and time series prediction from a continuous set of past values.

Keywords: multivariate regression estimation; multivariate density estimation; stationarity; ergodicity; rates of strong convergence; wavelet-based estimators; martingale differences; conditional distribution; curve discrimination (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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