2005年布劳威尔讲座：模型选择的统计估计
The Brouwer Lecture 2005: Statistical estimation with model selection
摘要：
本文的目的是解释的兴趣和重要性的（近似）模型和模型选择的统计。从非常基本的例子直方图，我们提出了一个一般的概念，有限维模型的统计估计，我们解释了什么类型的风险范围可以预期从使用这样的模型。然后，我们从一个家庭这样的模型的性能合适的模型选择程序。我们说明了我们的观点，两个主要的例子：从一个n样本的直方图设计的分区的选择和高斯回归的背景下的变量选择的问题。
英文摘要：
The purpose of this paper is to explain the interest and importance of (approximate) models and model selection in Statistics. Starting from the very elementary example of histograms we present a general notion of finite dimensional model for statistical estimation and we explain what type of risk bounds can be expected from the use of one such model. We then give the performance of suitable model selection procedures from a family of such models. We illustrate our point of view by two main examples: the choice of a partition for designing a histogram from an n-sample and the problem of variable selection in the context of Gaussian regression.
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。
