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Title: Bias correction for local linear regression estimation using asymmetric kernels via the skewing method Authors:  Benedikt Funke - Technical University of Dortmund (Germany)
Masayuki Hirukawa - Ryukoku University (Japan) [presenting]
Abstract: The skewing method that has been originally proposed as a bias correction device is extended for local linear regression estimation using standard symmetric kernels to the cases of asymmetric kernels. The method is defined as a convex combination of three local linear estimators. It is demonstrated that the skewed estimator using asymmetric kernels with properly chosen weights can accelerate the bias convergence from $O(b)$ to $O(b^2)$ as $b->0$ under sufficient smoothness of the unknown regression curve while not inflating the variance in an order of magnitude, where b is the smoothing parameter and the regressor is assumed to have at least one boundary. As a consequence, the estimator has optimal pointwise convergence of $n^{4/9}$ when best implemented, where $n$ is the sample size. It is noteworthy that these properties are the same as those for a local cubic regression estimator. Finite-sample properties of the skewed estimator are assessed in comparison with local linear and local cubic estimators. An application of the skewed estimation to real data is also considered.