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

• Published in: Mathematics (Basel) Vol. 10; no. 19; p. 3433
• Main Authors: DIDI, Sultana, AL HARBY, Ahoud AL, BOUZEBDA, Salim
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.10.2022; MDPI
• Subjects: Asymptotic methods; Asymptotic properties; Density; Discriminant analysis; Ergodic processes; ergodicity; Estimation theory; Estimators; Functional Analysis; Functionals; Hilbert space; Martingales; Mathematical functions; Mathematics; multivariate density estimation; multivariate regression estimation; Probability; Random variables; rates of strong convergence; Regression; Regression analysis; stationarity; Stationary processes; Statistics; Statistics Theory; Wavelet transforms; wavelet-based estimators; Saudi Arabia

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...