Nonconvex penalties including the smoothly clipped absolute deviation penalty and the minimax concave penalty enjoy the properties of unbiasedness, continuity and sparsity,and the ridge regression can deal with the co...Nonconvex penalties including the smoothly clipped absolute deviation penalty and the minimax concave penalty enjoy the properties of unbiasedness, continuity and sparsity,and the ridge regression can deal with the collinearity problem. Combining the strengths of nonconvex penalties and ridge regression（abbreviated as NPR）, we study the oracle property of the NPR estimator in high dimensional settings with highly correlated predictors, where the dimensionality of covariates pn is allowed to increase exponentially with the sample size n. Simulation studies and a real data example are presented to verify the performance of the NPR method.展开更多
Large-scale simulation optimization(SO)problems encompass both large-scale ranking-and-selection problems and high-dimensional discrete or continuous SO problems,presenting significant challenges to existing SO theori...Large-scale simulation optimization(SO)problems encompass both large-scale ranking-and-selection problems and high-dimensional discrete or continuous SO problems,presenting significant challenges to existing SO theories and algorithms.This paper begins by providing illustrative examples that highlight the differences between large-scale SO problems and those of a more moderate scale.Subsequently,it reviews several widely employed techniques for addressing large-scale SOproblems,such as divide-and-conquer,dimension reduction,and gradient-based algorithms.Additionally,the paper examines parallelization techniques leveraging widely accessible parallel computing environments to facilitate the resolution of large-scale SO problems.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11401340)China Postdoctoral Science Foundation(Grant No.2014M561892)+1 种基金the Foundation of Qufu Normal University(Grant Nos.bsqd2012041xkj201304)
文摘Nonconvex penalties including the smoothly clipped absolute deviation penalty and the minimax concave penalty enjoy the properties of unbiasedness, continuity and sparsity,and the ridge regression can deal with the collinearity problem. Combining the strengths of nonconvex penalties and ridge regression（abbreviated as NPR）, we study the oracle property of the NPR estimator in high dimensional settings with highly correlated predictors, where the dimensionality of covariates pn is allowed to increase exponentially with the sample size n. Simulation studies and a real data example are presented to verify the performance of the NPR method.
基金supported by the National Natural Science Foundation of China(Nos.72071146,72091211,72293562,and 72031006).
文摘Large-scale simulation optimization(SO)problems encompass both large-scale ranking-and-selection problems and high-dimensional discrete or continuous SO problems,presenting significant challenges to existing SO theories and algorithms.This paper begins by providing illustrative examples that highlight the differences between large-scale SO problems and those of a more moderate scale.Subsequently,it reviews several widely employed techniques for addressing large-scale SOproblems,such as divide-and-conquer,dimension reduction,and gradient-based algorithms.Additionally,the paper examines parallelization techniques leveraging widely accessible parallel computing environments to facilitate the resolution of large-scale SO problems.
