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...

In this paper data-driven algorithms for fitting SEMIFAR models (Beran, 1999) are proposed. The algorithms combine the data-driven estimation of the nonparametric trend and maximum likelihood estimation of the parameters. For selecting the bandwidth, the proposal of Beran and Feng (1999) based...

This paper proposes a semiparametric approach by introducing a smooth scale function into the standard GARCH model so that conditional heteroskedasticity and scale change in a financial time series can be modelled simultaneously. An estimation procedure combining kernel estimation of the scale...

In this paper a modified double smoothing bandwidth selector, MDS, based on a new criterion, which combines the plug-in and the double smoothing ideas, is proposed. A self-complete iterative double smoothing rule (_IDS ) is introduced as a pilot method. The asymptotic properties of both_IDS...