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The nested error regression model is a useful tool for analyzing clustered (grouped) data, and is especially used in small area estimation. The classical nested error regression model assumes normality of random effects and error terms, and…
This paper presents a selective survey of recent developments in statistical inference and multiple testing for high-dimensional regression models, including linear and logistic regression. We examine the construction of confidence…
We propose a new estimator, the thresholded scaled Lasso, in high dimensional threshold regressions. First, we establish an upper bound on the $\ell_\infty$ estimation error of the scaled Lasso estimator of Lee et al. (2012). This is a…
The bootstrap procedure has emerged as a general framework to construct prediction intervals for future observations in autoregressive time series models. Such models with outlying data points are standard in real data applications,…
We study the problem of treatment effect estimation in randomized experiments with high-dimensional covariate information, and show that essentially any risk-consistent regression adjustment can be used to obtain efficient estimates of the…
This paper develops bootstrap procedures for inference in linear regression models with two-way clustered data. We characterize the estimator's asymptotic behavior in five mutually exclusive and exhaustive regimes: three Gaussian and two…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
A current strand of research in high-dimensional statistics deals with robustifying the available methodology with respect to deviations from the pervasive light-tail assumptions. In this paper we consider a linear mean regression model…
We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…
This paper studies transfer learning for ridge-regularized robust linear regression in the moderate-dimensional regime, where the number of predictors is of the same order as the sample size and the regression coefficients are not assumed…
This paper studies the Gaussian and bootstrap approximations for the probabilities of a non-degenerate U-statistic belonging to the hyperrectangles in $\mathbb{R}^d$ when the dimension $d$ is large. A two-step Gaussian approximation…
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…
Motivated by recent works on the high-dimensional logistic regression, we establish that the existence of the maximum likelihood estimate exhibits a phase transition for a wide range of generalized linear models with binary outcome and…
In this paper we propose a flexible nested error regression small area model with high dimensional parameter that incorporates heterogeneity in regression coefficients and variance components. We develop a new robust small area specific…
Motivated by questions about dense (non-sparse) signals in high-dimensional data analysis, we study the unconditional out-of-sample prediction error (predictive risk) associated with three popular linear estimators for high-dimensional…
In this paper, we consider the beta prime regression model recently proposed by \cite{bour18}, which is tailored to situations where the response is continuous and restricted to the positive real line with skewed and long tails and the…
We study high-dimensional linear models with error-in-variables. Such models are motivated by various applications in econometrics, finance and genetics. These models are challenging because of the need to account for measurement errors to…
We consider the problem of estimating a meta-model of an unknown regression model with non-Gaussian and non-bounded error. The meta-model belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to…
We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of…
This paper develops robust confidence intervals in high-dimensional and left-censored regression. Type-I censored regression models are extremely common in practice, where a competing event makes the variable of interest unobservable.…