  While robust divergence such as density power divergence and
$\gamma$-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.
