Fixed design regression for time series: Asymptotic normality

• Published in: Journal of multivariate analysis Vol. 40; no. 2; pp. 262 - 291
• Main Authors: Roussas, George G., Tran, Lanh T., Ioannides, D.A.
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.02.1992; Elsevier
• Series: Journal of Multivariate Analysis
• Subjects: asymptotic normality; bounded case; Exact sciences and technology; fixed design; Mathematics; Nonparametric inference; Probability and statistics; regression; regression fixed design weights asymptotic normality strict stationarity strong mixing bounded case unbounded case; Sciences and techniques of general use; Statistics; strict stationarity; strong mixing; unbounded case; weights; 62G05; 62J02; 62M10; asymptotic normality; fixed design; unbounded case; regression; 62E20; bounded case; weights; strict stationarity; strong mixing; Regression function; Non parametric estimation; Stationary process; Weighting; Asymptotic normality; Time series
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/0047-259X(92)90026-C

Consider the fixed regression model with general weights, and suppose that the error random variables are coming from a strictly stationary stochastic process, satisfying the strong mixing condition. The asymptotic normality of the proposed estimate is established under weak conditions. The applicability of the results obtained is demonstrated by way of two existing estimates, the Gasser-Müller estimate and that of Priestley and Chao. The asymptotic normality of these estimates is further illustrated by means of a concrete example from the class of autoregressive processes.