Related papers: Robust Inference for High-dimensional Linear Model…
Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is…
In many important statistical analyses, the number of covariates $p$ often exceeds the data size $n$, a regime commonly referred to as high-dimensional. While considerable progress has been made in high-dimensional regression under the…
Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…
For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important…
The focus of modern biomedical studies has gradually shifted to explanation and estimation of joint effects of high dimensional predictors on disease risks. Quantifying uncertainty in these estimates may provide valuable insight into…
High-dimensional data often arise from clinical genomics research to infer relevant predictors of a particular trait. A way to improve the predictive performance is to include information on the predictors derived from prior knowledge or…
High-dimensional penalized rank regression is a powerful tool for modeling high-dimensional data due to its robustness and estimation efficiency. However, the non-smoothness of the rank loss brings great challenges to the computation. To…
Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…
This work studies applications and generalizations of a simple estimation technique that provides exponential concentration under heavy-tailed distributions, assuming only bounded low-order moments. We show that the technique can be used…
This paper is concerned with inference on the regression function of a high-dimensional linear model when outcomes are missing at random. We propose an estimator which combines a Lasso pilot estimate of the regression function with a bias…
Modelling non-homogeneous and multi-component data is a problem that challenges scientific researchers in several fields. In general, it is not possible to find a simple and closed form probabilistic model to describe such data. That is why…
We consider the application of a popular penalised regression method, Ridge Regression, to data with very high dimensions and many more covariates than observations. Our motivation is the problem of out-of-sample prediction and the setting…
Test-time defenses are used to improve the robustness of deep neural networks to adversarial examples during inference. However, existing methods either require an additional trained classifier to detect and correct the adversarial samples,…
In the field of statistical learning and data analysis, estimating precision matrices (i.e., the inverse of covariance matrices) is a critical task, particularly for understanding dependency structures among variables. However, traditional…
We propose a method for high dimensional multivariate regression that is robust to random error distributions that are heavy-tailed or contain outliers, while preserving estimation accuracy in normal random error distributions. We extend…
We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that…
Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…
Deep networks for computer vision are not reliable when they encounter adversarial examples. In this paper, we introduce a framework that uses the dense intrinsic constraints in natural images to robustify inference. By introducing…
We propose a new covariance matrix called Gini covariance matrix (GCM), which is a natural generalization of univariate Gini mean difference (GMD) to the multivariate case. The extension is based on the covariance representation of GMD by…
We propose two robust methods for testing hypotheses on unknown parameters of predictive regression models under heterogeneous and persistent volatility as well as endogenous, persistent and/or fat-tailed regressors and errors. The proposed…