Trapezoidal rule and sampling designs for the nonparametric estimation of the regression function in models with correlated errors. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Benelmadani, D.; Benhenni, K.; Louhichi, S.
• Is Part Of: Statistics. Volume 54:Issue 1(2020)
• Page Start: 59
• Page End: 96
• Publication Date: 2020-01-02
• Subjects: Nonparametric regression -- optimal design -- autocovariance function -- trapezoidal rule -- asymptotic normality; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2020.1715409
• Languages: English
• ISSNs: 0233-1888

Abstract

ABSTRACT: The problem of estimating the regression function in a fixed design models with correlated observations is considered. Such observations are obtained from several experimental units, each of them forms a time series. Based on the trapezoidal rule, we propose a simple kernel estimator and we derive the asymptotic expression of its integrated mean squared error IMSE and its asymptotic normality. The problems of the optimal bandwidth and the optimal design with respect to the asymptotic IMSE are also investigated. Finally, a simulation study is conducted to study the performance of the new estimator and to compare it with the classical estimator of Gasser and Müller in a finite sample set. In addition, we study the robustness of the optimal design with respect to the misspecification of the autocovariance function.