Since conventional cross–validation bandwidth selection methods don’t work for the case where the data considered are dependent time series, alternative bandwidth selection methods are needed. In recent years, Bayesian based global bandwidth selection methods have been proposed. Our experience shows that the use of a global bandwidth is however less suitable than using a localized bandwidth in ...

Many regression schemes deliver a point estimate only, but often it is useful or even essential to quantify the uncertainty inherent in a prediction. If a conditional density estimate is available, then prediction intervals can be derived from it. In this paper we compare three techniques for computing conditional density estimates using a class probability estimator, where this estimator is ap...

‎In this article‎, ‎we develop two nonparametric smoothing estimators for parameter of a time-variant parametric model‎. ‎This parameter can be from any parametric family or from any parametric or semi-parametric regression model‎. ‎Estimation is based on a two-step procedure‎, ‎in which we first get the raw estimate of the parameter at a set of disjoint time...

The argument of the log function is called the information potential. To make comparisons fair, for different kernels, we will use the estimator based on the empirical expectation of the Parzen density estimation. This estimator is given by the average of the summation of the elements of a matrix K whose elements are evaluation of the kernel k function between pairs of points (i, j) in the samp...

In this paper we derive rates of strong convergence for the kernel density estimator and for the Nadaraya-Watson estimator under the-mixing condition and under the condition of absolute regularity. A combination of an inequality of Bernstein type (Rio 1995) and an exponential inequality (cf. Fuk/Nagaev 1971) is the crucial tool for the proofs. Moreover, we consider the application of the main s...

We present two estimators for discrete non-Gaussian and nonstationary probability density estimation based on a dynamic Bayesian network (DBN). The first estimator is for offline computation and consists of a DBN whose transition distribution is represented in terms of kernel functions. The estimator parameters are the weights and shifts of the kernel functions. The parameters are determined th...

In this paper, we discuss some equivalences between two recently introduced statistical learning schemes, namely Mercer kernel methods and information theoretic methods. We show that Parzen window-based estimators for some information theoretic cost functions are also cost functions in a corresponding Mercer kernel space. The Mercer kernel is directly related to the Parzen window. Furthermore, ...

In this paper, we propose a new approach of boundary correction for kernel density estimation with the support $[0,1]$, in particular at right endpoints and derive theoretical properties estimator show that it asymptotically reduce order bias region, whereas variance remains unchanged. Our Monte Carlo simulations demonstrate good finite sample performance our proposed estimator. Two examples re...

Methods for improving the basic kernel density estimator include variable locations, variable bandwidths and variable weights. Typically these methods are implemented separately and via pilot estimation of variation functions derived from asymptotic considerations. The starting point here is a simple maximum likelihood procedure which allows (in its greatest generality) variation of all these q...

The nonparametric minimax estimation of an analytic density at a given point, under random censorship, is considered. Although the problem of estimating density is known to be irregular in a certain sense, we make some connections relating this problem to the problem of estimating smooth functionals. Under condition that the censoring is not too severe, we establish the exact limiting behavior ...