by Julia Polak, Maxwell L. King, and Xibin Zhang
Abstract:
In order to make the kernel estimator of the conditional density easier to apply, we derive a reference rule for bandwidth selection. The proposed bandwidths result from the minimization of an approximated
weighted integrated mean square error function. In contrast to the usual simple assumption of normally or uniformly distributed data, we assume that the y given x and the x are both skew t distributed (with includes the normal, the skew normal and the Student's t distributions as a special cases). Moreover, we allow distribution parameters to change as a linear function of the conditional values. This very flexible framework allows us to capture variations in the skewness and kurtosis of the conditional density as well as the change in its location and scale as a function of the conditioning variables. We illustrate the improvement in the conditional density estimator accuracy when we choose the bandwidths under the skew t distribution assumption instead of the normality assumption on simulated data.
Keywords: Bandwidth selection, Conditional density, Kernel smoothing, Skew t distribution.