Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes

Sultana Didi 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
Salim Bouzebda: LMAC (Laboratory of Applied Mathematics of Compiègne), Université de Technologie de Compiégne, 60200 Compiègne, France

Mathematics, 2022, vol. 10, issue 22, 1-37

Abstract: In this study, we look at the wavelet basis for the nonparametric estimation of density and regression functions for continuous functional stationary processes in Hilbert space. The mean integrated squared error for a small subset is established. We employ a martingale approach to obtain the asymptotic properties of these wavelet estimators. These findings are established under rather broad assumptions. All we assume about the data is that they are ergodic, but beyond that, we make no assumptions. In this paper, the mean integrated squared error findings in the independence or mixing setting were generalized to the ergodic setting. The theoretical results presented in this study are (or will be) valuable resources for various cutting-edge functional data analysis applications. Applications include conditional distribution, conditional quantile, entropy, and curve discrimination.

Keywords: multivariate regression estimation; multivariate density estimation; stationarity; ergodicity; rates of strong convergence; wavelet-based estimators; martingale differences; continuous time series (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 (1)

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