Related papers: Robust penalized estimators for functional linear …
The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
We address the statistical estimation of composite functionals which may be nonlinear in the probability measure. Our study is motivated by the need to estimate coherent measures of risk, which become increasingly popular in finance,…
This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time)…
We propose a dynamic multiplicative factor model for process data, which arise from complex problem-solving items, an emerging testing mode in large-scale educational assessment. The proposed model can be viewed as an extension of the…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
Weighting estimators based on propensity scores are widely used for causal estimation in a variety of contexts, such as observational studies, marginal structural models and interference. They enjoy appealing theoretical properties such as…
Many modern datasets are collected automatically and are thus easily contaminated by outliers. This led to a regain of interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the…
Many applications that use empirically estimated functions face a curse of dimensionality, because the integrals over most function classes must be approximated by sampling. This paper introduces a novel regression-algorithm that learns…
Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where $\Lop\Lo/N^\alpha$ is…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…
Finite mixture regression models are useful for modeling the relationship between response and predictors, arising from different subpopulations. In this article, we study high-dimensional predic- tors and high-dimensional response, and…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…
We consider training decision trees using noisily labeled data, focusing on loss functions that can lead to robust learning algorithms. Our contributions are threefold. First, we offer novel theoretical insights on the robustness of many…
Functional linear regression is an important topic in functional data analysis. It is commonly assumed that samples of the functional predictor are independent realizations of an underlying stochastic process, and are observed over a grid…
Meta-analyses frequently include trials that report multiple effect sizes based on a common set of study participants. These effect sizes will generally be correlated. Cluster-robust variance-covariance estimators are a fruitful approach…
High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective…
We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…