Abstract Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample X 1 ,..., X n onto the first D eigenvectors of the Principal Component Analysis (PCA) associated with the empirical...

To overcome the curse of dimensionality, dimension reduction is important andnecessary for understanding the underlying phenomena in a variety of fields.Dimension reduction is the transformation of high-dimensional data into ameaningful representation in the low-dimensional space. It can be...

Quasi-Monte Carlo (QMC) methods are important numerical tools in the pricing and hedging of complex financial instruments. The effectiveness of QMC methods crucially depends on the discontinuity and the dimension of the problem. This paper shows how the two fundamental limitations can be...

We introduce a dimension reduction method for model-based clustering obtained from a finite mixture of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$t$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>t</mi> </mrow> </math> </EquationSource> </InlineEquation>-distributions. This approach is based on existing work on reducing dimensionality in the case of finite Gaussian mixtures. The method relies on identifying a reduced subspace of...</equationsource></equationsource></inlineequation>

In this paper, we study the estimation and variable selection of the sufficient dimension reduction space for survival data via a new combination of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$L_1$$</EquationSource> </InlineEquation> penalty and the refined outer product of gradient method (rOPG; Xia et al. in J R Stat Soc Ser B 64:363–410, <CitationRef CitationID="CR28">2002</CitationRef>), called SH-OPG...</citationref></equationsource></inlineequation>

We consider the treatment comparison problem in a general high-dimensional regression setting. In this article, we propose a nonparametric estimation approach based on partial sliced inverse regression (SIR) (Chiaromonte et al. in Ann Stat 30:475–497, <CitationRef CitationID="CR4">2002</CitationRef>) and an extension of partial inverse...</citationref>

Modelling covariance structures is known to suffer from the curse of dimensionality. In order to avoid this problem for forecasting, the authors propose a new factor multivariate stochastic volatility (fMSV) model for realized covariance measures that accommodates asymmetry and long memory....

In the common nonparametric regression model with high dimensional predictor several tests for the hypothesis of an additive regression are investigated. The corresponding test statistics are either based on the diiferences between a fit under the assumption of additivity and a fit in the...

The basic ideas of Desirability functions and indices are introduced and compared to other methods of multivariate optimisation. It is shown that gradient based techniques are not in general appropriate to perform the numerical optimisation for Desirability indices. The problems are shown for...