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...

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...

The analysis of high-dimensional data often begins with the identification of lower dimensional subspaces. Principal component analysis is a dimension reduction technique that identifies linear combinations of variables along which most variation occurs or which best “reconstruct” the...

The conventional Wilcoxon/Mann-Whitney test can be invalid for comparing treatment effects in the presence of missing values or in observational studies. This is because the missingness of the outcomes or the participation in the treatments may depend on certain pre-treatment variables. We...

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....

Factor construction methods are widely used to summarize a large panel of variables by means of a relatively small number of representative factors. We propose a novel factor construction procedure that enjoys the properties of robustness to outliers and of sparsity; that is, having relatively...

The daily average price of electricity represents the price of electricity to be delivered over the full next day and serves as a key reference price in the electricity market. It is an aggregate that equals the average of hourly prices for delivery during each of the 24 individual hours. This...

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...

We revisit cumulative slicing estimation (CUME; Zhu et al., 2010) from a different perspective to gain more insights, then refine its performance by incorporating the intra-slice covariances. We also prove that our new method, under some conditions, is more comprehensive than CUME.