Related papers: Robust and sparse estimators for linear regression…
This paper reviews recent developments of robust estimation in linear time series models, with short and long memory correlation structures, in the presence of additive outliers. Based on the manuscripts Fajardo et al. (2009) and…
The Huber's criterion is a useful method for robust regression. The adaptive least absolute shrinkage and selection operator (lasso) is a popular technique for simultaneous estimation and variable selection. In the case of small sample size…
We study the problem of estimating a $p$-dimensional $s$-sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by at most $o$ adversarial outliers, we prove that the…
This paper considers inference in a linear regression model with random right censoring and outliers. The number of outliers can grow with the sample size while their proportion goes to zero. The model is semiparametric and we make only…
This paper studies oracle properties of $\ell_1$-penalized least squares in nonparametric regression setting with random design. We show that the penalized least squares estimator satisfies sparsity oracle inequalities, i.e., bounds in…
We consider the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression models, an extremely important problem in the recent era. The adaptive…
Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…
By treating intervals as inseparable sets, this paper proposes sparse machine learning regressions for high-dimensional interval-valued time series. With LASSO or adaptive LASSO techniques, we develop a penalized minimum distance…
For the problem of high-dimensional sparse linear regression, it is known that an $\ell_0$-based estimator can achieve a $1/n$ "fast" rate on the prediction error without any conditions on the design matrix, whereas in absence of…
In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while…
We point out some pitfalls related to the concept of an oracle property as used in Fan and Li (2001, 2002, 2004) which are reminiscent of the well-known pitfalls related to Hodges' estimator. The oracle property is often a consequence of…
We consider both $\ell _{0}$-penalized and $\ell _{0}$-constrained quantile regression estimators. For the $\ell _{0}$-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and…
Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…
This paper proposes a general framework for penalized convex empirical criteria and a new version of the Sparse-Group LASSO (SGL, Simon and al., 2013), called the adaptive SGL, where both penalties of the SGL are weighted by preliminary…
Many results have been proved for various nuclear norm penalized estimators of the uniform sampling matrix completion problem. However, most of these estimators are not robust: in most of the cases the quadratic loss function and its…
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…
We build a unifying convex analysis framework characterizing the statistical properties of a large class of penalized estimators, both under a regular and an irregular design. Our framework interprets penalized estimators as proximal…
Sparse penalized quantile regression provides an effective framework for variable selection and robust estimation in high-dimensional data analysis. When ex planatory variables are organized into groups, achieving sparsity both within and…
Linear models that contain a time-dependent response and explanatory variables have attracted much interest in recent years. The most general form of the existing approaches is of a linear regression model with autoregressive moving average…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…