Related papers: Assessing extrema of empirical principal component…
Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in…
The process generates substantial amounts of data with highly complex structures, leading to the development of numerous nonlinear statistical methods. However, most of these methods rely on computations involving large-scale dense kernel…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…
Analysis of stochastic models of networks is quite important in light of the huge influx of network data in social, information and bio sciences, but a proper statistical analysis of features of different stochastic models of networks is…
We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…
Simultaneous occurrences of extreme events need not imply symmetric or reciprocal tail dependence. However, most existing measures of extremal dependence are inherently symmetric and hence often fail to capture directional influence in tail…
Bootstrapping can produce confidence levels for hypotheses about quadratic regression models - such as whether the U-shape is inverted, and the location of optima. The method has several advantages over conventional methods: it provides…
A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the…
Bootstrap methods for estimating the long-run covariance of stationary functional time series are considered. We introduce a versatile bootstrap method that relies on functional principal component analysis, where principal component scores…
We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finite-order ARMA approximations in the state space representation,…
This paper aims to construct a valid and efficient confidence interval for the extrema of parameters under privacy protection. The usual statistical inference on the extrema of parameters often suffers from the selection bias issue, and the…
In experimental causal inference, we distinguish between two sources of uncertainty: design uncertainty, due to the treatment assignment mechanism, and sampling uncertainty, when the sample is drawn from a super-population. This distinction…
Principal component analysis is a ubiquitous tool in exploratory data analysis. It is widely used by applied scientists for visualization and interpretability purposes. We raise an important issue (the curse of isotropy) about the…
This paper presents a novel approach to functional principal component analysis (FPCA) in Bayes spaces in the setting where densities are the object of analysis, but only few individual samples from each density are observed. We use the…
The extremal dependence structure of a regularly varying random vector Xis fully described by its limiting spectral measure. In this paper, we investigate how torecover characteristics of the measure, such as extremal coefficients, from the…
The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…
This paper establishes bounds on the predictive performance of empirical risk minimization for principal component regression. Our analysis is nonparametric, in the sense that the relation between the prediction target and the predictors is…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…
We consider the problem of describing excursion sets of a real-valued function $f$, i.e. the set of inputs where $f$ is above a fixed threshold. Such regions are hard to visualize if the input space dimension, $d$, is higher than 2. For a…