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In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
Two important goals of high-dimensional modeling are prediction and variable selection. In this article, we consider regularization with combined $L_1$ and concave penalties, and study the sampling properties of the global optimum of the…
High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional…
High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of…
This paper compares convex and non-convex penalized likelihood methods in high-dimensional statistical modeling, focusing on their strengths and limitations. Convex penalties, like LASSO, offer computational efficiency and strong…
High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we…
We develop a set of variable selection methods for the Cox model under interval censoring, in the ultra-high dimensional setting where the dimensionality can grow exponentially with the sample size. The methods select covariates via a…
We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…
Mixed-effect models are very popular for analyzing data with a hierarchical structure, e.g. repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to…
High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional…
A class of variable selection procedures for parametric models via nonconcave penalized likelihood was proposed by Fan and Li to simultaneously estimate parameters and select important variables. They demonstrated that this class of…
Penalized methods are applied to quasi likelihood analysis for stochastic differential equation models. In this paper, we treat the quasi likelihood function and the associated statistical random field for which a polynomial type large…
Sparse high dimensional graphical model selection is a topic of much interest in modern day statistics. A popular approach is to apply l1-penalties to either (1) parametric likelihoods, or, (2) regularized regression/pseudo-likelihoods,…
This paper studies macroeconomic forecasting and variable selection using a folded-concave penalized regression with a very large number of predictors. The penalized regression approach leads to sparse estimates of the regression…
Fan and Li propose a family of variable selection methods via penalized likelihood using concave penalty functions. The nonconcave penalized likelihood estimators enjoy the oracle properties, but maximizing the penalized likelihood function…
Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…
Variable selection is fundamental to high-dimensional statistical modeling. Many variable selection techniques may be implemented by maximum penalized likelihood using various penalty functions. Optimizing the penalized likelihood function…
We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is…