We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters $\lambda_n$ and suitable regularity conditions. The random-weighting methods in view concern repeated optimization of a randomized objective function, motivated by the need for computational approximations to Bayesian posterior sampling. In the context of LASSO regression, we repeatedly assign analyst-drawn random weights to terms in the objective function (including the penalty terms), and optimize to obtain a sample of random-weighting estimators. We show that existing approaches have conditional model selection consistency and conditional asymptotic normality at different growth rates of $\lambda_n$ as $n \to \infty$. We propose an extension to the available random-weighting methods and establish that the resulting samples attain conditional sparse normality and conditional consistency in a growing-dimension setting. We find that random-weighting has both approximate-Bayesian and sampling-theory interpretations. Finally, we illustrate the proposed methodology via extensive simulation studies and a benchmark data example.

翻译：我们根据不同的正规化参数($\lambda_n$n)和适当的常规条件,在LASSO回归中确定随机加权方法的统计特性。考虑到随机加权方法涉及反复优化随机客观功能,其动机是需要为Bayesian远地点取样进行计算近似值。在LASSO回归中,我们反复指定分析师-拖动随机加权值为客观功能(包括惩罚条件)中的条件,并优化随机加权估计值样本。我们表明,现有方法具有有条件的模型选择一致性,并且以美元/lambda_n$作为美元/美元的不同增长率为条件。我们提议扩展现有的随机加权方法,并确定由此产生的样品在日益多样化的环境下达到有条件的稀疏常态和有条件的一致性。我们发现,随机加权既具有近似的Bayesian和抽样理论解释。最后,我们通过广泛的模拟研究和基准数据示例来说明拟议的方法。