Asymptotic theory for robust principal components
Journal of Multivariate Analysis
Robust forecasting of mortality and fertility rates: A functional data approach
Computational Statistics & Data Analysis
Depth-based inference for functional data
Computational Statistics & Data Analysis
Robust estimation and classification for functional data via projection-based depth notions
Computational Statistics
A functional analysis of NOx levels: location and scale estimation and outlier detection
Computational Statistics
On depth measures and dual statistics. A methodology for dealing with general data
Journal of Multivariate Analysis
| Hi-index | 0.00 |
A new projection-based definition of quantiles in a multivariate setting is proposed. This approach extends in a natural way to infinite-dimensional Hilbert spaces. The directional quantiles we define are shown to satisfy desirable properties of equivariance and, from an interpretation point of view, the resulting quantile contours provide valuable information when plotting them. Sample quantiles estimating the corresponding population quantiles are defined and consistency results are obtained. The new concept of principal quantile directions, closely related in some situations to principal component analysis, is found specially attractive for reducing the dimensionality and visualizing important features of functional data. Asymptotic properties of the empirical version of principal quantile directions are also obtained. Based on these ideas, a simple definition of robust principal components for finite and infinite-dimensional spaces is also proposed. The presented methodology is illustrated with examples throughout the paper.