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Advances in computing power enable more widespread use of the mode, which is a natural measure of central tendency since, as the most probable value, it is not influenced by the tails in the distribution. The properties of the half-sample…
Distributed statistical inference has recently attracted immense attention. The asymptotic efficiency of the maximum likelihood estimator (MLE), the one-step MLE, and the aggregated estimating equation estimator are established for…
Motivated by the increasing popularity of transformers in computer vision, in recent times there has been a rapid development of novel architectures. While in-domain performance follows a constant, upward trend, properties like robustness…
Learning in the presence of outliers is a fundamental problem in statistics. Until recently, all known efficient unsupervised learning algorithms were very sensitive to outliers in high dimensions. In particular, even for the task of robust…
Ever since the proof of asymptotic normality of maximum likelihood estimator by Cramer (1946), it has been understood that a basic technique of the Taylor series expansion suffices for asymptotics of $M$-estimators with…
To successfully work on variable selection, sparse model structure has become a basic assumption for all existing methods. However, this assumption is questionable as it is hard to hold in most of cases and none of existing methods may…
Robust estimators of large covariance matrices are considered, comprising regularized (linear shrinkage) modifications of Maronna's classical M-estimators. These estimators provide robustness to outliers, while simultaneously being…
The instrumental variable method is widely used in the health and social sciences for identification and estimation of causal effects in the presence of potentially unmeasured confounding. In order to improve efficiency, multiple…
Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…
Additive regression models have a long history in multivariate nonparametric regression. They provide a model in which each regression function depends only on a single explanatory variable allowing to obtain estimators at the optimal…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
In this paper we revisit the classical problem of nonparametric regression, but impose local differential privacy constraints. Under such constraints, the raw data $(X_1,Y_1),\ldots,(X_n,Y_n)$, taking values in $\mathbb{R}^d \times…
Random coefficient regression models are a popular tool for analyzing unobserved heterogeneity, and have seen renewed interest in the recent econometric literature. In this paper we obtain the optimal pointwise convergence rate for…
Cluster-randomized experiments are increasingly used to evaluate interventions in routine practice conditions, and researchers often adopt model-based methods with covariate adjustment in the statistical analyses. However, the validity of…
We deal with the equivariant estimation of scatter and location for p-dimensional data, giving emphasis to scatter. It it important that the estimators possess both a high efficiency for normal data and a high resistance to outliers, that…
Predicting scalar outcomes using functional predictors is a classic problem in functional data analysis. In many applications, however, only specific locations or time-points of the functional predictors have an impact on the outcome. Such…
The Receiver Operating Characteristic (ROC) curve is a useful tool that measures the discriminating power of a continuous variable or the accuracy of a pharmaceutical or medical test to distinguish between two conditions or classes. In…
Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semiparametric efficiency theory for more…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…