论文标题
对数符号投影的局部连续性，并应用于模型错误指定下的估计
Local continuity of log-concave projection, with applications to estimation under model misspecification
论文作者
论文摘要
对数符号投影是一个映射D维分布P到近似对数孔密度的运算符。 D {ü} Mbgen等人的先前工作。 （2011年）确定，在基础空间上有适当的指标，该投影是连续的，但不是统一的。在这项工作中，我们证明了对数孔孔投影的局部统一连续性结果 - 特别是，确定该地图是局部h {Ö} lder-（1/4）的连续性。匹配的下限验证该指数无法改善。我们还研究了这种连续性结果对经验环境的含义 - 鉴于从分布p绘制的样品，我们在样品的经验分布的对数凸孔投影之间的平方距离绑定了平方的距离，以及P的对数孔的投影。
The log-concave projection is an operator that maps a d-dimensional distribution P to an approximating log-concave density. Prior work by D{ü}mbgen et al. (2011) establishes that, with suitable metrics on the underlying spaces, this projection is continuous, but not uniformly continuous. In this work we prove a local uniform continuity result for log-concave projection -- in particular, establishing that this map is locally H{ö}lder-(1/4) continuous. A matching lower bound verifies that this exponent cannot be improved. We also examine the implications of this continuity result for the empirical setting -- given a sample drawn from a distribution P, we bound the squared Hellinger distance between the log-concave projection of the empirical distribution of the sample, and the log-concave projection of P. In particular, this yields interesting statistical results for the misspecified setting, where P is not itself log-concave.
