Data-driven resistant kernel regression

Abstract

We investigate data-driven bandwidth selection within the confines of robust (resistant) kernel smoothing. While several approaches presently exist, they require user defined robustness parameters. We discuss identification issues within this setting and propose several tractable avenues to fully operationalise this approach. Simulations reveal that the proposed selection methods perform well relative to competing approaches and a small empirical example illustrates its usefulness.

Keywords:

• Kernel regression
• tuning parameter
• bandwidth selection

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 There we assume that ${\sigma }^2=1$ to remove scale effects from the calculation of R.

2 We caution users that the ratio between the corresponding minimised DDRCV and the minimised MASE should not be too large. For example, if the term $E{\rho }_{\mathrm{sl}}(\cdot ,c_{\mathrm{sl}})$ in the affine transformation of $\mathrm{MASE}(h,c_{\mathrm{sm}})$ is far larger than $\frac{E{\psi }_{\mathrm{sl}}^{\mathrm{\prime }}(\cdot ,c_{\mathrm{sl}})}{2}\mathrm{MASE}(h,c_{\mathrm{sm}})$ this may make it difficult to find (computationally) the optimal result.