Tilted Nonparametric Regression Function Estimation

This paper provides the theory about the convergence rate of the tilted version of linear smoother. We study tilted linear smoother, a class of nonparametric regression function estimators, which is obtained by minimizing the distance to an infinite order flat-top trapezoidal kernel estimator. We prove that the proposed estimator achieves a high level of accuracy. Moreover, it preserves the attractive properties of the infinite order flat-top kernel estimator. We also present an extensive numerical study for analysing the performance of two members of the tilted linear smoother class named tilted Nadaraya-Watson and tilted local linear for finite samples. The simulation study shows that tilted Nadaraya-Watson and tilted local linear perform better than their classical analogs, under some specified conditions, in terms of Median Integrated Squared Error (MISE). Next, the performance of these estimators as well as the conventional estimators are illustrated by curve fitting to COVID-19 data for 12 countries and a dose-response data set. Finally, the R codes for obtaining various regression estimators mentioned above are given as an appendix.