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Big data analytics: integrating penalty strategies

机译：大数据分析：整合惩罚策略

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摘要

We present efficient estimation and prediction strategies for the classical multiple regression model when the dimensions of the parameters are larger than the number of observations. These strategies are motivated by penalty estimation and Stein-type estimation procedures. More specifically, we consider the estimation of regression parameters in sparse linear models when some of the predictors may have a very weak influence on the response of interest. In a high-dimensional situation, a number of existing variable selection techniques exists. However, they yield different subset models and may have different numbers of predictors. Generally speaking, the least absolute shrinkage and selection operator (Lasso) approach produces an over-fitted model compared with its competitors, namely the smoothly clipped absolute deviation (SCAD) method and adaptive Lasso (aLasso). Thus, prediction based only on a submodel selected by such methods will be subject to selection bias. In order to minimize the inherited bias, we suggest combining two models to improve the estimation and prediction performance. In the context of two competing models where one model includes more predictors than the other based on relatively aggressive variable selection strategies, we plan to investigate the relative performance of Stein-type shrinkage and penalty estimators. The shrinkage estimator improves the prediction performance of submodels significantly selected from existing Lasso-type variable selection methods. A Monte Carlo simulation study is carried out using the relative mean squared error (RMSE) criterion to appraise the performance of the listed estimators. The proposed strategy is applied to the analysis of several real high-dimensional data sets.
机译：当参数的尺寸大于观测值的数量时，我们提出了经典多元回归模型的有效估计和预测策略。这些策略是由罚金估算和Stein型估算程序驱动的。更具体地说，当某些预测变量可能对目标响应的影响非常弱时，我们考虑在稀疏线性模型中估算回归参数。在高维情况下，存在许多现有的变量选择技术。但是，它们产生不同的子集模型，并且可能具有不同数量的预测变量。一般而言，与竞争对手相比，最小绝对收缩和选择算子（Lasso）方法会产生过度拟合的模型，即平滑裁剪的绝对偏差（SCAD）方法和自适应Lasso（aLasso）。因此，仅基于通过这种方法选择的子模型的预测将受到选择偏差的影响。为了最小化继承的偏差，我们建议组合两个模型以提高估计和预测性能。在两个竞争模型的背景下，其中一个模型基于相对激进的变量选择策略，比另一个模型包含更多的预测变量，我们计划研究Stein型收缩率和罚分估计量的相对性能。收缩估计器改善了从现有套索类型变量选择方法中显着选择的子模型的预测性能。使用相对均方误差（RMSE）准则进行了蒙特卡洛模拟研究，以评估所列估计器的性能。所提出的策略被应用于分析几个真实的高维数据集。

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