Likelihood Inference in Models with a High-Dimensional Nuisance Parameter

具有高维干扰参数的模型中的似然推断

• 批准号: 0906466
• 负责人: Thomas Severini
• 金额: $ 17.9万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906466&HistoricalAwards=false
• 关键词: Likelihood; Inference; Models; Dimensional; Nuisance

Likelihood methods, such as maximum likelihood estimation and likelihood ratio tests, play an important role in statistical theory and methodology. There is a large body of work showing that, under relatively weak conditions, likelihood-based methods of inference are optimal in large samples. Such results are based on asymptotic theory in which the dimension of the parameter remains fixed as the sample size increases indefinitely. However, the conclusions based on such a large-sample theory may not be valid for models in which the dimension of the parameter is large relative to the sample size. Thus, for many models used in practice, standard methods of likelihood-based inference may not perform well. The goal of this research is to study and develop likelihood-based methods of inference in models in which the dimension of the nuisance parameter is large relative to the sample size. The research will focus on three broad areas: the development of higher-order asymptotic approximations to the distribution of the likelihood-based statistics in models with stratum nuisance parameters, the development of a small-dispersion asymptotic theory for models with stratum nuisance parameters, and the development of methods of inference in models with an unknown function. The research will consider the theoretical properties of likelihood-based methods of inference as well as the development of new statistical methodology based on those results.Statistical methods are used in a wide range of fields. In particular, likelihood-based methods have been used in in applications ranging from the reliability of computer software to the analysis of genetic data. Much of current statistical theory is restricted to relatively simple models, in which the available data is large relative to the number of unknown parameters in the model. However, in complex models, it may be necessary to estimate a large number of parameters based on relatively little data. This research will develop statistical theory and methodology for this type of model and these results will lead to improved statistical methods that will be useful in many areas of application. The research will also further our understanding of the properties of statistical models and, hence, will be useful in the training of researchers in statistics and related fields.

似然方法，如极大似然估计和似然比检验，在统计理论和方法中起着重要的作用。 有大量的工作表明，在相对较弱的条件下，基于似然性的推理方法在大样本中是最佳的。 这样的结果是基于渐近理论，其中的尺寸的参数保持固定的样本量无限增加。然而，基于这样一个大样本理论的结论可能是无效的模型中的参数的尺寸是相对于样本大小大。 因此，对于实践中使用的许多模型，基于可能性的推理的标准方法可能无法很好地执行。 本研究的目的是研究和开发基于似然的推理方法，在模型中的滋扰参数的尺寸是相对于样本量大。该研究将集中在三个广泛的领域：高阶渐近近似的发展，以分布的似然统计模型与地层滋扰参数，一个小分散渐近理论的发展与地层滋扰参数模型，和发展的方法推断模型与未知函数。 该研究将考虑基于似然性的推理方法的理论特性以及基于这些结果的新统计方法的发展。统计方法在广泛的领域中使用。 特别是，基于可能性的方法已用于从计算机软件的可靠性到遗传数据分析的应用中。 目前的统计理论大多局限于相对简单的模型，其中可用的数据相对于模型中未知参数的数量来说很大。 然而，在复杂的模型中，可能需要根据相对较少的数据估计大量参数。 这项研究将为这种类型的模型开发统计理论和方法，这些结果将导致改进的统计方法，这将在许多应用领域是有用的。 研究也将进一步加深我们对统计模型性质的理解，因此，将有助于统计及相关领域研究人员的培训。