A Simple Estimator of Error Correlation in Non-parametric Regression Models

• Published in: Scandinavian journal of statistics Vol. 33; no. 3; pp. 451 - 462
• Main Authors: PARK, BYEONG U., LEE, YOUNG KYUNG, KIM, TAE YOON, PARK, CHEOLYONG
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.09.2006; Blackwell Publishers; Blackwell; Danish Society for Theoretical Statistics
• Series: Scandinavian Journal of Statistics
• Subjects: bandwidth selection; bimodal kernel; correlated errors; Correlations; Error rates; Estimating techniques; Estimation bias; Estimators; Exact sciences and technology; Human error; kernel regression; Linear inference, regression; Logical proofs; Mathematical models; Mathematics; Modeling; Nonparametric inference; Probability and statistics; Regression analysis; residuals; Sciences and techniques of general use; Statistical methods; Statistical theories; Statistical variance; Statistics; Studies; Estimation error; Error estimation; Prior distribution; Bandwith selection; Nonparametric regression; Non parametric estimation; correlated errors; Bimodal kernel; residuals; Statistical method; Residue; Correlated error; bandwidth selection; kernel regression
• ISSN: 0303-6898; 1467-9469
• DOI: 10.1111/j.1467-9469.2006.00506.x

It is well known that major strength of non-parametric regression function estimation breaks down when correlated errors exist in the data. Positively (negatively) correlated errors tend to produce undersmoothing (oversmoothing). Several remedies have been proposed in the context of bandwidth selection problem, but they are hard to implement without prior knowledge of error correlations. In this paper we propose a simple estimator of error correlation which is ready to implement and reports a reasonably good performance.