We extend projection theorems concerning Hellinger and Jones et al. divergences to the continuous case. These projection theorems reduce certain estimation problems on generalized exponential models to linear problems. We introduce the notion of regularity for generalized exponential models and show that the projection theorems in this case are similar to the ones in discrete and canonical case. We also apply these ideas to solve certain estimation problems concerning Student and Cauchy distributions.

中文翻译：

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幂律模型的投影定理和估计方程

我们扩展了有关Hellinger和Jones等人的投影定理。与连续案例存在分歧。这些投影定理将广义指数模型上的某些估计问题简化为线性问题。我们介绍了广义指数模型的正则性概念，并证明了在这种情况下的投影定理与在离散和规范情况下的投影定理相似。我们还将这些想法用于解决有关Student和Cauchy分布的某些估计问题。