Related papers: Qualitative robustness for bootstrap approximation…

We consider a robust estimation of the mean vector for a sequence of i.i.d. observations in the domain of attraction of a stable law with different indices of stability, $DS(\alpha_1, \ldots, \alpha_p)$, such that $1<\alpha_{i}\leq 2$,…

This article introduces an iterative distributed computing estimator for the multinomial logistic regression model with large choice sets. Compared to the maximum likelihood estimator, the proposed iterative distributed estimator achieves…

The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible,…

This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have…

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a…

The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a…

The robustness of classifiers has become a question of paramount importance in the past few years. Indeed, it has been shown that state-of-the-art deep learning architectures can easily be fooled with imperceptible changes to their inputs.…

This study proposes a robust estimator for stochastic frontier models by integrating the idea of Basu et al. [1998, Biometrika 85, 549-559] into such models. We verify that the suggested estimator is strongly consistent and asymptotic…

Stochastic gradient descent (SGD) or stochastic approximation has been widely used in model training and stochastic optimization. While there is a huge literature on analyzing its convergence, inference on the obtained solutions from SGD…

We provide a functional view of distributional robustness motivated by robust statistics and functional analysis. This results in two practical computational approaches for approximate distributionally robust nonlinear optimization based on…

Parametric empirical Bayes (EB) estimators have been widely used in variety of fields including small area estimation, disease mapping. Since EB estimator is constructed by plugging in the estimator of parameters in prior distributions, it…

We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where…

Wasserstein distributionally robust optimization estimators are obtained as solutions of min-max problems in which the statistician selects a parameter minimizing the worst-case loss among all probability models within a certain distance…

Distance covariance is a popular measure of dependence between random variables. It has some robustness properties, but not all. We prove that the influence function of the usual distance covariance is bounded, but that its breakdown value…

To identify the estimand in missing data problems and observational studies, it is common to base the statistical estimation on the "missing at random" and "no unmeasured confounder" assumptions. However, these assumptions are unverifiable…

Bootstrap is a useful tool for making statistical inference, but it may provide erroneous results under complex survey sampling. Most studies about bootstrap-based inference are developed under simple random sampling and stratified random…

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…

The challenge of noisy multi-objective optimization lies in the constant trade-off between exploring new decision points and improving the precision of known points through resampling. This decision should take into account both the…

We propose an estimator of a concave cumulative distribution function under the measurement error model, where the non-negative variables of interest are perturbed by additive independent random noise. The estimator is defined as the least…

We consider inference in linear regression models that is robust to heteroskedasticity and the presence of many control variables. When the number of control variables increases at the same rate as the sample size the usual…