Local linear regression with reciprocal inverse Gaussian kernel

Abstract

In this paper, we propose a local linear estimator for the regression model $$Y=m(X)+\varepsilon $$ based on the reciprocal inverse Gaussian kernel when the design variable is supported on $$(0,\infty )$$ . The conditional mean-squared error of the proposed estimator is derived, and its asymptotic properties are thoroughly investigated, including the asymptotic normality and the uniform almost sure convergence. The finite sample performance of the proposed estimator is evaluated via simulation studies and a real data application. A comparison study with other existing estimation methods is also made, and the pros and cons of the proposed estimator are discussed.