Constrained Statistical Inference: Inequality, Order, and Shape Restrictions
Constrained Statistical Inference: Inequality, Order, and Shape Restrictions
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DOI：
10.1198/jasa.2006.s69
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发表时间：
2006-03
影响因子：
3.7
通讯作者：
A. Micheas
中科院分区：
文献类型：
--
作者：
A. Micheas
本书的其余部分转向更多的统计和应用问题，但与前述材料相比相对较短。第10章讨论了多元t分布的参数估计，包括使用期望最大化算法或其变体之一来获得最大似然估计。第11章讨论了当误差来自不相关的多元t分布时，回归模型中的经典和贝叶斯推断。这个模型的含义是，错误是相同的分布，但统计依赖，尽管他们缺乏相关性。第12章中的应用实际上是进一步阅读的注释。投影寻踪，投资组合优化，聚类分析，和多个决策问题。总之，这本书对于任何对非高斯连续多元分布感兴趣的人来说都是一本有用的参考书。某种形式的重尾多变量t分布通常是正态分布的自然替代模型，本书成功地总结了关于这种分布的已知知识。毫无疑问，有一些遗漏，这是可以预期的，当有关文献非常分散，但作者做了有益的服务，汇集了大量有用的材料在一个紧凑的卷。
The remainder of the book turns to more statistical and applied issues but is relatively short in comparison to the foregoing material. Chapter 10 discusses estimation of the parameters of a multivariate t distribution including the use of the expectation maximization algorithm or one of its variants to obtain maximum likelihood estimates. Chapter 11 deals with classical and Bayesian inference in regression models when the errors are assumed to come from an uncorrelated multivariate t distribution. The implications of this model are that the errors are identically distributed but statistically dependent despite their lack of correlation. The applications in Chapter 12 are really notes for further reading. Projection pursuit, portfolio optimization, cluster analysis, and multiple decision problems are mentioned. In summary, this book is a useful reference work for anyone with an interest in non-Gaussian continuous multivariate distributions. Some form of heavytailed multivariate t distribution is often a natural alternative model to the normal distribution, and this book successfully summarizes what is known about such distributions. No doubt there are some omissions, as is to be expected when the relevant literature is very scattered, but the authors have done a useful service in bringing together a lot of useful material in one compact volume.