We consider the problem of choosing two bandwidths simultaneously for estimating the difference of two functions at given points. When the asymptotic approximation of the mean squared error (AMSE) criterion is used, we show that minimisation problem is not well-defined when the sign of the...

Over the last four decades, several methods for selecting the smoothing parameter, generally called the bandwidth, have been introduced in kernel regression. They differ quite a bit, and although there already exist more selection methods than for any other regression smoother we can still see...