In this article, we present new ideas concerning Non-Gaussian Component Analysis (NGCA). We use the structural assumption that a high-dimensional random vector X can be represented as a sum of two components - a lowdimensional signal S and a noise component N. We show that this assumption...

Let a high-dimensional random vector X can be represented as a sum of two components - a signal S, which belongs to some low-dimensional subspace S, and a noise component N. This paper presents a new approach for estimating the subspace S based on the ideas of the Non-Gaussian Component...

Most dimension reduction methods based on nonparametric smoothing are highly sensitive to outliers and to data coming from heavy-tailed distributions. We show that the recently proposed methods by Xia et al. (2002) can be made robust in such a way that preserves all advantages of the original...

Complex phenomena in environmental sciences can be conveniently represented by several inter-dependent random variables. In order to describe such situations, copula-based models have been studied during the last year. In this paper, we consider a novel family of bivariate copulas, called...

Normal distribution of the residuals is the traditional assumption in the classical multivariate time series models. Nevertheless it is not very often consistent with the real data. Copulae allows for an extension of the classical time series models to nonelliptically distributed residuals. In...

State price density (SPD) contains important information concerning market expectations. In existing literature, a constrained estimator of the SPD is found by nonlinear least squares in a suitable Sobolev space. We improve the behavior of this estimator by implementing a covariance structure...

State price densities (SPD) are an important element in applied quantitative finance. In a Black-Scholes model they are lognormal distributions with constant volatility parameter. In practice volatility changes and the distribution deviates from log-normality. We estimate SPDs using EUREX option...

Independent component analysis (ICA) is a modern factor analysis tool de- veloped in the last two decades. Given p-dimensional data, we search for that linear combination of data which creates (almost) independent components. Here copulae are used to model the p-dimensional data and then...

We propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression model. Asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence as univariate function estimation. For the...

This paper presents a new method for spatially adaptive local likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of themethod is given a sequence of local likelihood estimates (``weak´´...