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Density power divergence (DPD) is designed to robustly estimate theunderlying distribution of observations, in the presence of outliers. However,DPD involves an integral of the power of the parametric density models to beestimated; the explicit form of the integral term can be derived only forspecific densities, such as normal and exponential densities. While we mayperform a numerical integration for each iteration of the optimizationalgorithms, the computational complexity has hindered the practical applicationof DPD-based estimation to more general parametric densities. To address theissue, this study introduces a stochastic approach to minimize DPD for generalparametric density models. The proposed approach also can be employed tominimize other density power-based $\gamma$-divergences, by leveragingunnormalized models.

Minimizing robust density power-based divergences for general parametric density models