Related papers: Robust Covariance Estimation for Approximate Facto…
Accurate platform localization is an integral component of most robotic systems. As these robotic systems become more ubiquitous, it is necessary to develop robust state estimation algorithms that are able to withstand novel and…
Robust M-estimation uses loss functions, such as least absolute deviation (LAD), quantile loss and Huber's loss, to construct its objective function, in order to for example eschew the impact of outliers, whereas the difficulty in analysing…
Consider the problem of simultaneous estimation of location and variance matrix under Huber's contaminated Gaussian model. First, we study minimum $f$-divergence estimation at the population level, corresponding to a generative adversarial…
We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood,…
Mixtures of Gaussian factors are powerful tools for modeling an unobserved heterogeneous population, offering - at the same time - dimension reduction and model-based clustering. Unfortunately, the high prevalence of spurious solutions and…
The accurate specification of the number of factors is critical to the validity of factor models and the topic almost occupies the central position in factor analysis. Plenty of estimators are available under the restrictive condition that…
In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at…
In the realm of high-dimensional data analysis, the estimation of covariance matrices is a fundamental task, and this holds true for interval-valued data as well. However, there is no unified definition for the covariance matrix of…
Let $X$ be a centered random vector taking values in $\mathbb{R}^d$ and let $\Sigma= \mathbb{E}(X\otimes X)$ be its covariance matrix. We show that if $X$ satisfies an $L_4-L_2$ norm equivalence, there is a covariance estimator…
We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…
The Cox proportional hazards model is widely used in survival analysis to model time-to-event data. However, it faces significant computational challenges in the era of large-scale data, particularly when dealing with time-dependent…
Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a…
We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e.,…
We consider mixed finite element approximation of a singularly perturbed fourth-order elliptic problem with two different boundary conditions, and present a new measure of the error, whose components are balanced with respect to the…
Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data…
The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As non-parametric model, it offers a very flexible way of modeling…
This paper addresses the scalar regression problem through a novel solution to exactly optimize the Huber loss in a general semi-supervised setting, which combines multi-view learning and manifold regularization. We propose a principled…
In biometrics and related fields, the Cox proportional hazards model are widely used to analyze with covariate adjustment. However, when some covariates are not observed, an unbiased estimator usually cannot be obtained. Even if there are…
The semiparametric accelerated failure time model is not as widely used as the Cox relative risk model mainly due to computational difficulties. Recent developments in least squares estimation and induced smoothing estimating equations…
We propose a novel framework for approximate factor models that integrates an S-vine copula structure to capture complex dependencies among common factors. Our estimation procedure proceeds in two steps: first, we apply principal component…