Title: Bias correction for local linear regression estimation using asymmetric kernels via the skewing method
Authors: Masayuki Hirukawa - Ryukoku University (Japan) [presenting]
Abstract: The aim is to extend the skewing method that has been originally proposed as a bias correction device for local linear regression estimation using standard symmetric kernels to the cases of asymmetric kernels. The method is defined as a convex combination of two or three local linear estimators. It is demonstrated that as with symmetric kernels, the skewed regression estimator using asymmetric kernels with properly chosen weights can accelerate the bias convergence under sufficient smoothness of the unknown regression curve while not inflating the variance in order of magnitude. Orders of magnitude in the bias and variance convergences are the same as those for a local cubic estimator. A remarkable difference between the cases of symmetric and asymmetric kernels can be found in the form of weights. While the weights are constant regardless of the position of the design point for symmetric kernels, they vary with the design point for asymmetric kernels. Finite-sample performance of the skewed regression estimator is examined via Monte Carlo simulations in comparison with a local cubic smoother, and an empirical application is considered.