相关论文: Asymptotic Behavior of Principal Component Project…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
We analyze extremes of traffic flow profiles composed of traffic counts over a day. The data is essentially curves and determining which trajectory should be classified as extreme is not straight forward. To assess the extremes of the…
This work is concerned with the estimation of multidimensional regression and the asymptotic behaviour of the test involved in selecting models. The main problem with such models is that we need to know the covariance matrix of the noise to…
Max-stable distributions and processes are important models for extreme events and the assessment of tail risks. The full, multivariate likelihood of a parametric max-stable distribution is complicated and only recent advances enable its…
Asymptotic properties of three estimators of probability density function of sample maximum $f_{(m)}:=mfF^{m-1}$ are derived, where $m$ is a function of sample size $n$. One of the estimators is the parametrically fitted by the…
Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…
Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…
In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…
This paper develops a novel nonparametric significance test based on a tailored nonparametric-type projected weighting function that exhibits appealing theoretical and numerical properties. We derive the asymptotic properties of the…
The eigenvalue decomposition (EVD) parameters of the second order statistics are ubiquitous in statistical analysis and signal processing. Notably, the EVD of robust scatter $M$-estimators is a popular choice to perform robust probabilistic…
The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate,…
The research in this paper gives a systematic investigation on the asymptotic behaviours of four inverse probability weighting (IPW)-based estimators for conditional average treatment effect, with nonparametrically, semiparametrically,…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
Extreme-value copulas arise in the asymptotic theory for componentwise maxima of independent random samples. An extreme-value copula is determined by its Pickands dependence function, which is a function on the unit simplex subject to…
We analyze the extreme value dependence of independent, not necessarily identically distributed multivariate regularly varying random vectors. More specifically, we propose estimators of the spectral measure locally at some time point and…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
We consider nonparametric estimation of a regression curve when the data are observed with multiplicative distortion which depends on an observed confounding variable. We suggest several estimators, ranging from a relatively simple one that…
While there is considerable work on change point analysis in univariate time series, more and more data being collected comes from high dimensional multivariate settings. This paper introduces the asymptotic concept of high dimensional…
This paper investigates asymptotic properties of algorithms that can be viewed as robust analogues of the classical empirical risk minimization. These strategies are based on replacing the usual empirical average by a robust proxy of the…
In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…