The sparse Laplacian shrinkage estimator for high-dimensional regression
نویسندگان
چکیده
منابع مشابه
The Sparse Laplacian Shrinkage Estimator for High-Dimensional Regression.
We propose a new penalized method for variable selection and estimation that explicitly incorporates the correlation patterns among predictors. This method is based on a combination of the minimax concave penalty and Laplacian quadratic associated with a graph as the penalty function. We call it the sparse Laplacian shrinkage (SLS) method. The SLS uses the minimax concave penalty for encouragin...
متن کاملNearly Optimal Minimax Estimator for High Dimensional Sparse Linear Regression
We present estimators for a well studied statistical estimation problem: the estimation for the linear regression model with soft sparsity constraints (`q constraint with 0 < q ≤ 1) in the high-dimensional setting. We first present a family of estimators, called the projected nearest neighbor estimator and show, by using results from Convex Geometry, that such estimator is within a logarithmic ...
متن کاملHigh dimensional thresholded regression and shrinkage effect
High dimensional sparse modelling via regularization provides a powerful tool for analysing large-scale data sets and obtaining meaningful interpretable models.The use of nonconvex penalty functions shows advantage in selecting important features in high dimensions, but the global optimality of such methods still demands more understanding.We consider sparse regression with a hard thresholding ...
متن کاملThe L1L1 penalized LAD estimator for high dimensional linear regression
In this paper, the high-dimensional sparse linear regression model is considered, where the overall number of variables is larger than the number of observations. We investigate the L1 penalized least absolute deviation method. Different from most of other methods, the L1 penalized LAD method does not need any knowledge of standard deviation of the noises or any moment assumptions of the noises...
متن کاملFIRST: Combining forward iterative selection and shrinkage in high dimensional sparse linear regression
We propose a new class of variable selection techniques for regression in high dimensional linear models based on a forward selection version of the LASSO, adaptive LASSO or elastic net, respectively to be called as forward iterative regression and shrinkage technique (FIRST), adaptive FIRST and elastic FIRST. These methods seem to work effectively for extremely sparse high dimensional linear m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2011
ISSN: 0090-5364
DOI: 10.1214/11-aos897