Related papers: Robust explicit estimation of the log-logistic dis…
This paper is based on our personal notes for the short course we gave on January 5, 2017 at Institut Henri Poincar\'e, after an invitation of the SFdS. Our purpose is to give an overview of the method of $\rho$-estimation and of the…
We study nonparametric maximum likelihood estimation of a log-concave probability density and its distribution and hazard function. Some general properties of these estimators are derived from two characterizations. It is shown that the…
The problem of estimating the coefficient of bivariate tail dependence is considered here from the robustness point of view; it combines two apparently contradictory theories of robust statistics and extreme value statistics. The usual…
This paper proposes a novel method to estimate the rate parameter of the Poisson distribution. The proposed method employs the Cramer-von Mises type optimization which has been commonly used in estimating parameters of continuous…
Data-driven Distributionally Robust Optimization (DD-DRO) via optimal transport has been shown to encompass a wide range of popular machine learning algorithms. The distributional uncertainty size is often shown to correspond to the…
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…
Many standard estimators such as several maximum likelihood estimators or the empirical estimator for any law-invariant convex risk measure are not (qualitatively) robust in the classical sense. However, these estimators may nevertheless…
We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…
We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings.…
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…
We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with…
We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation algorithm, which combines statistical and computational efficiency in high-dimensions.…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
A crucial part of data analysis is the validation of the resulting estimators, in particular, if several competing estimators need to be compared. Whether an estimator can be objectively validated is not a trivial property. If there exists…
In this paper, we propose improved estimation method for logistic regression based on subsamples taken according the optimal subsampling probabilities developed in Wang et al. 2018 Both asymptotic results and numerical results show that the…
We study the problem of robustly estimating the posterior distribution for the setting where observed data can be contaminated with potentially adversarial outliers. We propose Rob-ULA, a robust variant of the Unadjusted Langevin Algorithm…
Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…
Robust design is one of the main tools employed by engineers for the facilitation of the design of high-quality processes. However, most real-world processes invariably contend with external uncontrollable factors, often denoted as outliers…