Related papers: Robust Functional Data Analysis for Discretely Obs…

We introduce flexible robust functional regression models, using various heavy-tailed processes, including a Student $t$-process. We propose efficient algorithms in estimating parameters for the marginal mean inferences and in predicting…

We investigate robust linear regression where data may be contaminated by an oblivious adversary, i.e., an adversary than may know the data distribution but is otherwise oblivious to the realizations of the data samples. This model has been…

In this paper, we propose self-tuned robust estimators for estimating the mean of heavy-tailed distributions, which refer to distributions with only finite variances. Our approach introduces a new loss function that considers both the mean…

A function-on-function regression model with quadratic and interaction effects of the covariates provides a more flexible model. Despite several attempts to estimate the model's parameters, almost all existing estimation strategies are…

In this paper we analyze different ways of performing principal component analysis throughout three different approaches: robust covariance and correlation matrix estimation, projection pursuit approach and non-parametric maximum entropy…

Principal component regression uses principal components as regressors. It is particularly useful in prediction settings with high-dimensional covariates. The existing literature treating of Bayesian approaches is relatively sparse. We…

We develop an asymptotic theory for the jump robust measurement of covariations in the context of stochastic evolution equation in infinite dimensions. Namely, we identify scaling limits for realized covariations of solution processes with…

Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…

In a missing-data setting, we have a sample in which a vector of explanatory variables x_i is observed for every subject i, while scalar outcomes y_i are missing by happenstance on some individuals. In this work we propose robust estimates…

In the context of multivariate functional data with individual phase variation, we develop a robust depth-based approach to estimate the main pattern function when cross-component time warping is also present. In particular, we consider the…

For covariance test in functional data analysis, existing methods are developed only for fully observed curves, whereas in practice, trajectories are typically observed discretely and with noise. To bridge this gap, we employ a…

The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extensions of statistical methods for standard multivariate data to the functional data setting…

When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that…

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…

It is of importance to develop statistical techniques to analyze high-dimensional data in the presence of both complex dependence and possible outliers in real-world applications such as imaging data analyses. We propose a new robust…

In many situations, data are recorded over a period of time and may be regarded as realizations of a stochastic process. In this paper, robust estimators for the principal components are considered by adapting the projection pursuit…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

Functional principal components analysis is a popular tool for inference on functional data. Standard approaches rely on an eigendecomposition of a smoothed covariance surface in order to extract the orthonormal functions representing the…

Statistical analysis on compositional data has gained a lot of attention due to their great potential of applications. A feature of these data is that they are multivariate vectors that lie in the simplex, that is, the components of each…

To the best of our knowledge, there are no general well-founded robust methods for statistical unsupervised learning. Most of the unsupervised methods explicitly or implicitly depend on the kernel covariance operator (kernel CO) or kernel…