Relative error prediction: Strong uniform consistency for censoring time series model

• Published in: Communications in statistics. Theory and methods Vol. 52; no. 11; pp. 3709 - 3729
• Main Authors: Bouhadjera, Feriel, Elias, Ould Saïd, Mohamed Riad, Remita
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03.06.2023; Taylor & Francis Ltd
• Subjects: Censored data; Consistency; Errors; Kernel estimate; Mathematics; Outliers (statistics); regression function; relative error; Statistics; strong mixing; uniform almost sure consistency; Censored data; uniform almost sure consistency; Kernel estimate; relative error; regression function; strong mixing
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2021.1979584

This article considers an adaptive method based on the relative error criteria to estimate the regression operator by a kernel smoothing. It is assumed that the variable of interest is subject to random right censoring and that the observations are from a stationary α-mixing process. The uniform almost sure consistency over a compact set with rate where we highlighted the covariance term is established. The simulation study indicates that the proposed approach has better performance in the presence of high level censoring and outliers in data to an existing classical method based on the least squares. An experiment prediction shows the quality of the relative error predictor.