  This paper provides the theory about the convergence rate of the tilted
version of linear smoother. We study tilted linear smoother, a nonparametric
regression function estimator, 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 in the finite sample. The simulation study shows that
tilted Nadaraya-Watson and tilted local linear perform better than their
classical analogs in some conditions in terms of Mean Integrated Squared Error
(MISE). Finally, the performance of these estimators as well as the
conventional estimators were illustrated by curve fitting to COVID-19 data for
12 countries and a dose-response data set.
