We consider the problem of uniform asymptotics in kernel functional estimation where the bandwidth can depend on the data. In a unified approach we investigate kernel estimates of the density and the hazard rate for uncensored and right-censored observations. The model allows for the fixed...

A monotone estimate of the conditional variance function in a heteroscedastic, nonpara- metric regression model is proposed. The method is based on the application of a kernel density estimate to an unconstrained estimate of the variance function and yields an esti- mate of the inverse variance...

Support Vector Machines (SVMs) have become a popular learning algorithm, in particular for large, high-dimensional classification problems. SVMs have been shown to give most accurate classification results in a variety of applications. Several methods have been proposed to obtain not only a...

Many robust statistical procedures have two drawbacks. Firstly, they are computer-intensive such that they can hardly be used for massive data sets. Secondly, robust confidence intervals for the estimated parameters or robust predictions according to the fitted models are often unknown. Here, we...

In the common Fourier regression model we determine the optimal designs for estimating the coefficients corresponding to the lower frequencies. An analytical solution is provided which is found by an alternative characterization of c-optimal designs. Several examples are provided and the...

We provide a set of probabilistic laws for range-based estimation of integrated variance of a continuous semi-martingale. To accomplish this, we exploit the properties of the price range as a volatility proxy and suggest a new method for non-parametric measurement of return variation. Assuming...

A new nonparametric estimate of a convex regression function is proposed and its stochastic properties are studied. The method starts with an unconstrained estimate of the derivative of the regression function, which is firstly isotonized and then integrated. We prove asymptotic normality of the...

Assume we have a dataset, Z say, from the joint distribution of random variables X and Y , and two further, independent datasets, X and Y, from the marginal distributions of X and Y , respectively. We wish to combine X, Y and Z, so as to construct an estimator of the joint density. This problem...

Recently, Dette, Neumeyer and Pilz (2005a) proposed a new monotone estimator for strictly increasing nonparametric regression functions and proved asymptotic normality. We explain two modifications of their method that can be used to obtain monotone versions of any nonparametric function...