Related papers: Combining Empirical Likelihood and Robust Estimati…
When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that…
Regression analysis is a central topic in statistical modeling, aimed at estimating the relationships between a dependent variable, commonly referred to as the response variable, and one or more independent variables, i.e., explanatory…
As machine learning models are deployed ever more broadly, it becomes increasingly important that they are not only able to perform well on their training distribution, but also yield accurate predictions when confronted with distribution…
We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk…
Bayesian methods, distributionally robust optimization methods, and regularization methods are three pillars of trustworthy machine learning combating distributional uncertainty, e.g., the uncertainty of an empirical distribution compared…
In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is…
When outcomes are missing for reasons beyond an investigator's control, there are two different ways to adjust a parameter estimate for covariates that may be related both to the outcome and to missingness. One approach is to model the…
We propose regularization methods for linear models based on the $L_q$-likelihood, which is a generalization of the log-likelihood using a power function. Some heavy-tailed distributions are known as $q$-normal distributions. We find that…
To address the computational issue in empirical likelihood methods with massive data, this paper proposes a grouped empirical likelihood (GEL) method. It divides $N$ observations into $n$ groups, and assigns the same probability weight to…
Regression with a spherical response is challenging due to the absence of linear structure, making standard regression models inadequate. Existing methods, mainly parametric, lack the flexibility to capture the complex relationship induced…
We study robust linear regression in high-dimension, when both the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha=n/d$, and study a data model that includes outliers. We provide exact asymptotics for the…
Logistic regression is a standard method in multivariate analysis for binary outcome data in epidemiological and clinical studies; however, the resultant odds-ratio estimates fail to provide directly interpretable effect measures. The…
Several recently developed methods have the potential to harness machine learning in the pursuit of target quantities inspired by causal inference, including inverse weighting, doubly robust estimating equations and substitution estimators…
Extreme learning machine (ELM) is a network model that arbitrarily initializes the first hidden layer and can be computed speedily. In order to improve the classification performance of ELM, a $\ell_2$ and $\ell_{0.5}$ regularization ELM…
A non linear regression approach which consists of a specific regression model incorporating a latent process, allowing various polynomial regression models to be activated preferentially and smoothly, is introduced in this paper. The model…
This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…
Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…
The composite likelihood (CL) is amongst the computational methods used for the estimation of high-dimensional multivariate normal (MVN) copula models with discrete responses. Its computational advantage, as a surrogate likelihood method,…
The problem of robust mean estimation in high dimensions is studied, in which a certain fraction (less than half) of the datapoints can be arbitrarily corrupted. Motivated by compressive sensing, the robust mean estimation problem is…
Unlike the ordinary least-squares (OLS) estimator for the linear model, a ridge regression linear model provides coefficient estimates via shrinkage, usually with improved mean-square and prediction error. This is true especially when the…