TY - CHAP AB - Abstract For kernel-based estimators, smoothness conditions ensure that the asymptotic rate at which the bias goes to zero is determined by the kernel order. In a finite sample, the leading term in the expansion of the bias may provide a poor approximation. We explore the relation between smoothness and bias and provide estimators for the degree of the smoothness and the bias. We demonstrate the existence of a linear combination of estimators whose trace of the asymptotic mean-squared error is reduced relative to the individual estimator at the optimal bandwidth. We examine the finite-sample performance of a combined estimator that minimizes the trace of the MSE of a linear combination of individual kernel estimators for a multimodal density. The combined estimator provides a robust alternative to individual estimators that protects against uncertainty about the degree of smoothness. VL - 36 SN - 978-1-78560-786-8, 978-1-78560-787-5/0731-9053 DO - 10.1108/S0731-905320160000036025 UR - https://doi.org/10.1108/S0731-905320160000036025 AU - Kotlyarova Yulia AU - Schafgans Marcia M. A. AU - Zinde-Walsh Victoria PY - 2016 Y1 - 2016/01/01 TI - Smoothness: Bias and Efficiency of Nonparametric Kernel Estimators T2 - Essays in Honor of Aman Ullah T3 - Advances in Econometrics PB - Emerald Group Publishing Limited SP - 561 EP - 589 Y2 - 2024/03/28 ER -