CAJ | 학술논문

主要针对损失函数为最小二乘 LS(Least Squares)和最小绝对偏差 LAD (Least Absolute Deviation)的凸组合形式，研究了观测数 n 和预测数 p 均趋于无穷大( limn→∞p/n=κ，κ>0)时，高维稳健统计性质和高维罚稳健统计性质，得到了稳健估计和罚稳健估计的显示表达。结果显示这种凸组合损失函数的模型集成了 LS 和 LAD损失的优点，同时消弱了它们的不足，具有优良的高维统计性质。
주요침대손실함수위최소이승 LS(Least Squares)화최소절대편차 LAD (Least Absolute Deviation)적철조합형식，연구료관측수 n 화예측수 p 균추우무궁대( limn→∞p/n=κ，κ>0)시，고유은건통계성질화고유벌은건통계성질，득도료은건고계화벌은건고계적현시표체。결과현시저충철조합손실함수적모형집성료 LS 화 LAD손실적우점，동시소약료타문적불족，구유우량적고유통계성질。
This article studies a convex combination of the Least Squares(LS) and Least Absolute Devia-tion(LAD). By studying the robust statistical properties of high-dimensional and penalized robust statistical properties of high dimension when the number of observations n and the number of prediction p tends to infinity ( limn→∞p/n=κ,κ>0), the expressions of robust estimation and penalized robust estimation are obtained. The result reveals that the loss function model of convex combination combines the advantages of the LS and LAD, at the same time, it relatively weakens their shortcomings, thus it has excellent high dimensional statistical properties.