Sugasawa Shonosuke, Yonekura Shouto
Center for Spatial Information Science, The University of Tokyo, Chiba 277-8568, Japan.
Nospare Inc., Tokyo 107-0061, Japan.
Entropy (Basel). 2021 Sep 1;23(9):1147. doi: 10.3390/e23091147.
Although robust divergence, such as density power divergence and γ-divergence, is helpful for robust statistical inference in the presence of outliers, the tuning parameter that controls the degree of robustness is chosen in a rule-of-thumb, which may lead to an inefficient inference. We here propose a selection criterion based on an asymptotic approximation of the Hyvarinen score applied to an unnormalized model defined by robust divergence. The proposed selection criterion only requires first and second-order partial derivatives of an assumed density function with respect to observations, which can be easily computed regardless of the number of parameters. We demonstrate the usefulness of the proposed method via numerical studies using normal distributions and regularized linear regression.
尽管诸如密度幂散度和γ散度之类的稳健散度有助于在存在异常值的情况下进行稳健统计推断，但控制稳健程度的调谐参数是凭经验选择的，这可能导致推断效率低下。我们在此基于应用于由稳健散度定义的未归一化模型的Hyvarinen得分的渐近近似提出一种选择标准。所提出的选择标准仅需要假设密度函数相对于观测值的一阶和二阶偏导数，无论参数数量多少都可以轻松计算。我们通过使用正态分布和正则化线性回归的数值研究证明了所提出方法的有用性。
