Variable selection and coefficient estimation via composite quantile regression with randomly censored data

Composite quantile regression with randomly censored data is studied. Moreover, adaptive LASSO methods for composite quantile regression with randomly censored data are proposed. The consistency, asymptotic normality and oracle property of the proposed estimators are established. The proposals are illustrated via simulation studies and the Australian AIDS dataset.     

Variable selection for single-index varying-coefficient model

We consider the problem of variable selection for single-index varying-coefficient model, and present a regularized variable selection procedure by combining basis function approximations with SCAD penalty. The proposed procedure simultaneously selects significant covariates with functional coefficients and local significant variables with parametric coefficients. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. The proposed method can naturally be applied to deal with pure single-index model and varying-coefficient model. Finite sample performances of the proposed method are illustrated by a simulation study and the real data analysis.     

Variable selection for semiparametric varying-coefficient partially linear models with missing response at random

In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random. The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.     

Variable selection in the partially linear errors-in-variables models for longitudinal data

This paper proposes a new approach for variable selection in partially linear errors-in-variables (EV) models for longitudinal data by penalizing appropriate estimating functions. We apply the SCAD penalty to simultaneously select significant variables and estimate unknown parameters. The rate of convergence and the asymptotic normality of the resulting estimators are established. Furthermore, with proper choice of regularization parameters, we show that the proposed estimators perform as well as the oracle procedure. A new algorithm is proposed for solving penalized estimating equation. The asymptotic results are augmented by a simulation study.     

A Modified Random Survival Forests Algorithm for High Dimensional Predictors and Self-Reported Outcomes

We present an ensemble tree-based algorithm for variable selection in high-dimensional datasets, in settings where a time-to-event outcome is observed with error. This work is motivated by self-reported outcomes collected in large-scale epidemiologic studies, such as the Women’s Health Initiative. The proposed methods equally apply to imperfect outcomes that arise in other settings such as data extracted from electronic medical records. To evaluate the performance of our proposed algorithm, we present results from simulation studies, considering both continuous and categorical covariates. We illustrate this approach to discover single nucleotide polymorphisms that are associated with incident Type 2 diabetes in the Women’s Health Initiative. A freely available R package icRSF has been developed to implement the proposed methods. Supplementary material for this article is available online.     

Determining and Depicting Relationships Among Components in High-Dimensional Variable Selection

Many modern treatments of high-dimensional datasets involve reducing the initial collection of features to a much smaller set, from which a predictive model may be built. However, strong relationships between the remaining variables can limit the parsimony or even the predictive performance of such a model. We propose a semi-automatic approach using generalized correlation to detect and quantify these relationships, as well as exploring ways to represent this information graphically. The method can detect both symmetric and asymmetric relationships, as well as nonlinear patterns. Its utility is demonstrated on a range of real and simulated datasets. Supplemental material for performing the real-data analyses in this article is available online.     

Discrepancy based model selection in statistical inverse problems

The reconstruction of solutions in statistical inverse problems in Hilbert spaces requires regularization, which is often based on a parametrized family of proposal estimators. The choice of an appropriate parameter in this family is crucial. We propose a modification of the classical discrepancy principle as an adaptive parameter selection. This varying discrepancy principle evaluates the misfit in some weighted norm, and it also has an incorporated emergency stop. These ingredients allow the order optimal reconstruction when the solution owns nice spectral resolution. Theoretical analysis is accompanied with numerical simulations, which highlight the features of the proposed varying discrepancy principle.     

Variable neighbourhood search for redundancy allocation problems

^** Email: ycliang{at}saturn.yzu.edu.tw^*** Email: s929512{at}mail.yzu.edu.tw^**** Email: s927522{at}mail.yzu.edu.tw A variable neighbourhood search (VNS) algorithm has been developedto solve the redundancy allocation problem (RAP). The VNS methodis perfectly suited to those combinatorial problems with potentialneighbourhood structures, as in the case of the RAP. The moststudied configuration of the RAP is a series system of s-independentk-out-of-n:G subsystems the so-called series–parallelsystem. The RAP is to select the optimal combination and redundancylevels of components to meet system-level constraints. Two typesof objectives are considered in this study—system reliabilitymaximization and system cost minimization. The VNS algorithmis tested on sets of benchmark problems and compared to thebest heuristics in the literature such as tabu search, multipleweighted objective heuristic, ant colony optimization and geneticalgorithm. Computational results show the advantages and benefitsof VNS for solving both types of RAP while considering bothsolution quality and computational efficiency.     

无穷维Hilbert空间中的伪单调非线性互补问题

建立伪单调非线性互补问题在实Hilbert空间任意闭凸锥上的解的存在性理论,特别把互补问题在有限维实Hilbert空间上的一些重要理论推广到无限维实Hilbert空间,还证明了解的存在的可行性理论.     

响应变量随机缺失下变系数模型的变量选择

In this paper,we present a variable selection procedure by combining basis function approximations with penalized estimating equations for varying-coefficient models with missing response at random.With appropriate selection of the tuning parameters,we establish the consistency of the variable selection procedure and the optimal convergence rate of the regularized estimators.A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.     

Positive Semidefinite Rank-Based Correlation Matrix Estimation With Application to Semiparametric Graph Estimation

Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. In this article, we illustrate this fundamental tradeoff by studying a semiparametric graph estimation problem in high dimensions. We explain how novel computational techniques help to solve this type of problem. In particular, we propose a nonparanormal neighborhood pursuit algorithm to estimate high-dimensional semiparametric graphical models with theoretical guarantees. Moreover, we provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Though this article focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures. We also report thorough experimental results on text, stock, and genomic datasets.     

Variable Selection Diagnostics Measures for High-Dimensional Regression

Markov chain Monte Carlo (MCMC) is nowadays a standard approach to numerical computation of integrals of the posterior density π of the parameter vector η. Unfortunately, Bayesian inference using MCMC is computationally intractable when the posterior density π is expensive to evaluate. In many such problems, it is possible to identify a minimal subvector β of η responsible for the expensive computation in the evaluation of π. We propose two approaches, DOSKA and INDA, that approximate π by interpolation in ways that exploit this computational structure to mitigate the curse of dimensionality. DOSKA interpolates π directly while INDA interpolates π indirectly by interpolating functions, for example, a regression function, upon which π depends. Our primary contribution is derivation of a Gaussian processes interpolant that provably improves over some of the existing approaches by reducing the effective dimension of the interpolation problem from dim(η) to dim(β). This allows a dramatic reduction of the number of expensive evaluations necessary to construct an accurate approximation of π when dim(η) is high but dim(β) is low.

We illustrate the proposed approaches in a case study for a spatio-temporal linear model for air pollution data in the greater Boston area.

Supplemental materials include proofs, details, and software implementation of the proposed procedures.     

An Iterative Coordinate Descent Algorithm for High-Dimensional Nonconvex Penalized Quantile Regression

We propose and study a new iterative coordinate descent algorithm (QICD) for solving nonconvex penalized quantile regression in high dimension. By permitting different subsets of covariates to be relevant for modeling the response variable at different quantiles, nonconvex penalized quantile regression provides a flexible approach for modeling high-dimensional data with heterogeneity. Although its theory has been investigated recently, its computation remains highly challenging when p is large due to the nonsmoothness of the quantile loss function and the nonconvexity of the penalty function. Existing coordinate descent algorithms for penalized least-squares regression cannot be directly applied. We establish the convergence property of the proposed algorithm under some regularity conditions for a general class of nonconvex penalty functions including popular choices such as SCAD (smoothly clipped absolute deviation) and MCP (minimax concave penalty). Our Monte Carlo study confirms that QICD substantially improves the computational speed in the p ? n setting. We illustrate the application by analyzing a microarray dataset.     

Variable neighbourhood structures for cycle location problems

Variable neighbourhood search is a metaheuristic used mainly to tackle combinatorial optimization problems. Its performance depends on having a good variable neighbourhood structure: that is, a sequence of neighbourhoods that are ideally pairwise disjoint and contain feasible solutions further and further from a given feasible solution. This article defines a variable neighbourhood structure with these properties that is new for cycle location problems. It find bounds for the neighbourhood sizes and shows how to iterate over then when the cycle is a circuit. It tests the structure and iteration method using variable neighbourhood search on a range of median cycle problems and finds a neighbourhood size beyond which there is, on average, no benefit in applying local search. This neighbourhood size is found not to depend on problem size or bound on circuit length.     

A best-response approach for equilibrium selection in two-player generalized Nash equilibrium problems

ABSTRACT

In this paper, we propose a best-response approach to select an equilibrium in a two-player generalized Nash equilibrium problem. In our model we solve, at each of a finite number of time steps, two independent optimization problems. We prove that convergence of our Jacobi-type method, for the number of time steps going to infinity, implies the selection of the same equilibrium as in a recently introduced continuous equilibrium selection theory. Thus the presented approach is a different motivation for the existing equilibrium selection theory, and it can also be seen as a numerical method. We show convergence of our numerical scheme for some special cases of generalized Nash equilibrium problems with linear constraints and linear or quadratic cost functions.     

带有变量选择过程的分类模型误差分析

偏倚一方差分析方法是在模型选择过程中权衡模型对现有样本解释程度和未知样本估计准确度的分析方法,目的是使选定的模型检验误差尽量小.在分类或回归过程中进行有效的变量筛选可以获得更准确的模型表达,但也会因此带来一定误差.提出"选择误差"的概念,用于刻画带有变量选择的分类问题中由于变量的某种选择方法所引起的误差.将分类问题的误差分解为偏倚—方差—选择误差进行研究,考察偏倚、方差和选择误差对分类问题的总误差所产生的影响.     

纵向数据下线性EV模型的变量选择

本文考虑了纵向数据线性EV模型的变量选择.基于二次推断函数方法和压缩方法的思想提出了一种新的偏差校正的变量选择方法.在选择适当的调整参数下,我们证明了所得到的估计量的相合性和渐近正态性.最后通过模拟研究验证了所提出的变量选择方法的有限样本性质.     

An effective selection of regression variables when the error distribution is incorrectly specified

Summary An asymptotically efficient selection of regression variables is considered in the situation where the statistician estimates regression parameters by the maximum likelihood method but fails to choose a likelihood function matching the true error distribution. The proposed procedure is useful when a robust regression technique is applied but the data in fact do not require that treatment. Examples and a Monte Carlo study are presented and relationships to other selectors such as Mallows'C _p are investigated. Research supported by Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123 “Stochastische Mathematische Modelle” and AFOSR Contract No. F49620 82 C 0009.     

以多输入为决策变量的DEA模型的解法

给出了以多输入为决策变量的DEA模型的解法.