通过模型选择估计独立分类变量的联合分布
Estimating the joint distribution of independent categorical variables via model selection
摘要：
假设一个观察独立的分类变量，或者等价地，一个观察相应的多项式变量。估计观测序列的分布相当于估计多项式序列的期望。提出了一种新的估计，这意味着是非参数的，非渐近的和可实现的，即使是大序列。它是一种基于小波的惩罚最小二乘估计，惩罚项的灵感来自Birgé和Massart的论文。证明了该估计量满足一个预言不等式，并且在极大极小意义下是自适应的。该方法是嵌入在一个通用的框架，使我们能够恢复现有的分割方法。除了理论结果，模拟研究报告和实际数据上的应用程序提供。
英文摘要：
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial sequence. A new estimator for this mean is proposed that is nonparametric, non-asymptotic and implementable even for large sequences. It is a penalized least-squares estimator based on wavelets, with a penalization term inspired by papers of Birgé and Massart. The estimator is proved to satisfy an oracle inequality and to be adaptive in the minimax sense over a class of Besov bodies. The method is embedded in a general framework which allows us to recover also an existing method for segmentation. Beyond theoretical results, a simulation study is reported and an application on real data is provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
