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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 consider a general monotone regression estimation where we allow for independent and dependent regressors. We propose a modification of the classical isotonic least squares estimator and establish its rate of convergence for the…
Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key…
This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the…
We construct efficient robust truncated sequential estimators for the pointwise estimation problem in nonparametric autoregression models with smooth coefficients. For Gaussian models we propose an adaptive procedure based on the…
We study the task of learning Generalized Linear models (GLMs) in the agnostic model under the Gaussian distribution. We give the first polynomial-time algorithm that achieves a constant-factor approximation for \textit{any} monotone…
Relative error estimation has been recently used in regression analysis. A crucial issue of the existing relative error estimation procedures is that they are sensitive to outliers. To address this issue, we employ the $\gamma$-likelihood…
Marginal structural models are a popular method for estimating causal effects in the presence of time-varying exposures. In spite of their popularity, no scalable non-parametric estimator exist for marginal structural models with…
This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those…
This paper illustrates the use of selected robust estimators of covariance or correlation in the identification of anomalous laboratory results in inter-laboratory data. It is shown that robust estimators can substantially reduce the impact…
Gradient boosting algorithms construct a regression predictor using a linear combination of ``base learners''. Boosting also offers an approach to obtaining robust non-parametric regression estimators that are scalable to applications with…
We consider the problem of adaptive estimation of the functional component in a multivariate partial linear model where the argument of the function is defined on a $q$-dimensional grid. Obtaining an adaptive estimator of this functional…
This paper reviews recent developments of robust estimation in linear time series models, with short and long memory correlation structures, in the presence of additive outliers. Based on the manuscripts Fajardo et al. (2009) and…
We consider a robust estimation of linear regression coefficients. In this note, we focus on the case where the covariates are sampled from an $L$-subGaussian distribution with unknown covariance, the noises are sampled from a distribution…
Analyzing polytomous response from a complex survey scheme, like stratified or cluster sampling is very crucial in several socio-economics applications. We present a class of minimum quasi weighted density power divergence estimators for…
We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…
In predictive modeling with simulation or machine learning, it is critical to accurately assess the quality of estimated values through output analysis. In recent decades output analysis has become enriched with methods that quantify the…
Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…
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…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…