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首页> 外文学位 >Shrinkage-based variable selection methods for linear regression and mixed-effects models.
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Shrinkage-based variable selection methods for linear regression and mixed-effects models.

机译：基于收缩的变量选择方法用于线性回归和混合效果模型。

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摘要

In this dissertation we propose two new shrinkage-based variable selection approaches. We first propose a Bayesian selection technique for linear regression models, which allows for highly correlated predictors to enter or exit the model, simultaneously. The second variable selection method proposed is for linear mixed-effects models, where we develop a new technique to jointly select the important fixed and random effects parameters. We briefly summarize each of these methods below.;The problem of selecting the correct subset of predictors within a linear model has received much attention in recent literature. Within the Bayesian framework, a popular choice of prior has been Zellner's g-prior which is based on the inverse of empirical covariance matrix of the predictors. We propose an extension of Zellner's g-prior which allow for a power parameter on the empirical covariance of the predictors. The power parameter helps control the degree to which correlated predictors are smoothed towards or away from one another. In addition, the empirical covariance of the predictors is used to obtain suitable priors over model space. In this manner, the power parameter also helps to determine whether models containing highly collinear predictors are preferred or avoided. The proposed power parameter can be chosen via an empirical Bayes method which leads to a data adaptive choice of prior. Simulation studies and a real data example are presented to show how the power parameter is well determined from the degree of cross-correlation within predictors. The proposed modification compares favorably to the standard use of Zellner's prior and an intrinsic prior in these examples.;We propose a new method of simultaneously identifying the important predictors that correspond to both the fixed and random effects components in a linear mixed-effects model. A reparameterized version of the linear mixed-effects model using a modified Cholesky decomposition is proposed to aid in the selection by dropping out the random effect terms whose corresponding variance is set to zero. We propose a penalized joint log-likelihood procedure with an adaptive penalty for the selection and estimation of the fixed and random effects. A constrained EM algorithm is then used to obtain the final estimates. We further show that our penalized estimator enjoys the Oracle property, in that, asymptotically it performs as well as if the true model was known beforehand. We demonstrate the performance of our method based on a simulation study and a real data example.
机译：本文提出了两种新的基于收缩的变量选择方法。我们首先提出用于线性回归模型的贝叶斯选择技术，该技术允许高度相关的预测变量同时进入或退出模型。提出的第二种变量选择方法是用于线性混合效应模型，在该模型中，我们开发了一种新技术来共同选择重要的固定效应和随机效应参数。我们在下面简要地总结了每种方法。在线性模型中选择正确的预测变量子集的问题在最近的文献中受到了很多关注。在贝叶斯框架内，先验的一种流行选择是Zellner's g-prior，它基于预测变量的经验协方差矩阵的逆矩阵。我们提出了Zellner g-prior的扩展，该扩展允许在预测变量的经验协方差上使用幂参数。幂参数有助于控制相互关联的预测变量朝着彼此或远离彼此平滑的程度。另外，预测变量的经验协方差用于获得模型空间上的合适先验。以这种方式，功率参数还有助于确定是首选还是避免使用包含高度共线预测变量的模型。可以通过经验贝叶斯方法选择建议的功率参数，该方法导致先验数据自适应选择。给出了仿真研究和一个实际数据示例，以显示如何根据预测变量内的互相关程度很好地确定功率参数。在这些示例中，所提出的修改与Zellner先验和固有先验的标准用法相比较。我们提出了一种同时识别与线性混合效应模型中的固定效应和随机效应分量相对应的重要预测变量的新方法。提出了使用改进的Cholesky分解的线性混合效果模型的重新参数化版本，以通过删除其相应方差设置为零的随机效应项来辅助选择。我们提出了一种带有惩罚性的联合对数似然法，用于选择和估计固定效应和随机效应。然后使用约束EM算法获得最终估计值。我们进一步证明，我们的惩罚估计器具有Oracle属性，因为它渐近地表现出与预先知道真实模型一样好的性能。我们基于仿真研究和真实的数据示例演示了我们方法的性能。

著录项

  • 作者

    Krishna, Arun.;

  • 作者单位

    North Carolina State University.;

  • 授予单位 North Carolina State University.;
  • 学科 Statistics.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 104 p.
  • 总页数 104
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 统计学;
  • 关键词

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