Related papers: Robust and sparse estimators for linear regression…
The problems of outliers detection and robust regression in a high-dimensional setting are fundamental in statistics, and have numerous applications. Following a recent set of works providing methods for simultaneous robust regression and…
We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear…
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…
The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general…
We give a general result concerning the rates of convergence of penalized empirical risk minimizers (PERM) in the regression model. Then, we consider the problem of agnostic learning of the regression, and give in this context an oracle…
Penalized smoothing is a standard tool in regression analysis. Classical approaches often rely on basis or kernel expansions, which constrain the estimator to a fixed span and impose smoothness assumptions that may be restrictive for…
Semiparametric discrete choice models are widely used in a variety of practical applications. While these models are point identified in the presence of continuous covariates, they can become partially identified when covariates are…
In this article we consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises observed in discrete time moments. An adaptive model selection procedure is proposed. A sharp…
An adaptive nonparametric estimation procedure is constructed for the estimation problem of heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (an oracle…
Penalized spline estimation with discrete difference penalties (P-splines) is a popular estimation method for semiparametric models, but the classical least-squares estimator is highly sensitive to deviations from its ideal model…
Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…
Regression adjustments are often considered by investigators to improve the estimation efficiency of causal effect in randomized experiments when there exists many pre-experiment covariates. In this paper, we provide conditions that…
Censored data are quite common in statistics and have been studied in depth in the last years. In this paper we consider censored high-dimensional data. High-dimensional models are in some way more complex than their low-dimensional…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…
For high-dimensional linear regression models, we review and compare several estimators of variances $\tau^2$ and $\sigma^2$ of the random slopes and errors, respectively. These variances relate directly to ridge regression penalty…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…
The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index…
In high-dimensional data, many sparse regression methods have been proposed. However, they may not be robust against outliers. Recently, the use of density power weight has been studied for robust parameter estimation and the corresponding…
The subject of robust estimation in time series is widely discussed in literature. One of the approaches is to use GM-estimation. This method incorporates a broad class of nonparametric estimators which under suitable conditions includes…