Recursive Kernel Density Estimation for Time Series

• Published in: IEEE transactions on information theory Vol. 66; no. 10; pp. 6378 - 6388
• Main Authors: Aboubacar, Amir, El Machkouri, Mohamed
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Asymptotic normality; Bandwidth; Continuity (mathematics); density function; Density functional theory; Estimation; Estimators; Kernel; Mathematical analysis; Probability density function; Probability density functions; quadratic mean error; Random variables; Recursive estimation; recursive kernel estimators; strong mixing
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2020.3014797

We consider the recursive estimation of the probability density function of continuous random variables from a strongly mixing random sample. We revisit here earlier research on this subject by considering a more general class of recursive estimators, including the usual ones. We derive the quadratic mean error of the considered class of estimators. Moreover, we establish a central limit theorem by using Lindeberg's method resulting in a simplification of the existing assumptions on the sequence of smooth parameters and the mixing coefficient. This is the main contribution of this paper. Finally, the feasibility of the proposed estimator is illustrated throughout an empirical study.