论文标题
线性模型在广义线性模型中最有利
Linear Models are Most Favorable among Generalized Linear Models
论文作者
论文摘要
我们为一类广义线性模型的$ L_2 $ minimax风险建立了一个非反应下限。进一步表明，规范线性模型的minimax风险匹配该下部界限到通用常数。因此，规范线性模型可以认为是在考虑一类的广义线性模型中（就最小风险而言）中最有利的。该证明利用了Aras等人建立的信息理论理论贝叶斯cramér-rao绑定了对数洞穴先验的约束。 （2019）。
We establish a nonasymptotic lower bound on the $L_2$ minimax risk for a class of generalized linear models. It is further shown that the minimax risk for the canonical linear model matches this lower bound up to a universal constant. Therefore, the canonical linear model may be regarded as most favorable among the considered class of generalized linear models (in terms of minimax risk). The proof makes use of an information-theoretic Bayesian Cramér-Rao bound for log-concave priors, established by Aras et al. (2019).
