On Selection Criteria for the Tuning Parameter in Robust Divergence

While robust divergence such as density power and $\gamma$-divergence is helpful for statistical inference in the presence of outliers, tuning parameter that controls degree robustness chosen a rule-of-thumb, which may lead to an inefficient inference. We here propose selection criterion based on asymptotic approximation Hyvarinen score applied unnormalized model defined by divergence. The proposed only requires first second-order partial derivatives assumed function with respect observations, can be easily computed regardless number parameters. demonstrate usefulness method via numerical studies using normal distributions regularized linear regression.