Relative error prediction via kernel regression smoothers

• Published in: Journal of statistical planning and inference Vol. 138; no. 10; pp. 2887 - 2898
• Main Authors: Jones, M.C., Park, Heungsun, Shin, Key-Il, Vines, S.K., Jeong, Seok-Oh
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.10.2008; New York,NY Elsevier Science; Amsterdam
• Subjects: Exact sciences and technology; General topics; Inference from stochastic processes; time series analysis; Linear inference, regression; Local linear regression; Mathematics; Mean squared relative error; Nadaraya–Watson estimator; Probability and statistics; Probability theory and stochastic processes; Ratio estimation; Sciences and techniques of general use; Statistics; Stochastic processes; Ratio estimation; Mean squared relative error; Local linear regression; Nadaraya–Watson estimator; Rank statistic; Conditional distribution; Error estimation; Bandwith selection; Prediction theory; Non parametric estimation; Stochastic process; Parametric method; Conditional expectation; Selection method; Linear regression; Prediction; Nonparametric regression; Statistical estimation; Statistical decision; Mean estimation; Two variables function; Kernel method; Statistical method; Kernels; Statistical regression; Response function; Selection problem; Simulation; Relative error; Filtering theory; Mean error; Expectation; Nadaraya-Watson estimator
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/j.jspi.2007.11.001

In this article, we introduce and study local constant and local linear nonparametric regression estimators when it is appropriate to assess performance in terms of mean squared relative error of prediction. We give asymptotic results for both boundary and non-boundary cases. These are special cases of more general asymptotic results that we provide concerning the estimation of the ratio of conditional expectations of two functions of the response variable. We also provide a good bandwidth selection method for the estimators. Examples of application, limited simulation results and discussion of related problems and approaches are also given.