Statistical Inference Based on an Integrated Likelihood

基于综合似然的统计推断

• 批准号: 1308009
• 负责人: Thomas Severini
• 金额: $ 10万
• 依托单位: Northwestern University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2016-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1308009&HistoricalAwards=false
• 关键词: Statistical; Inference; Based; Integrated; Likelihood

Integrated likelihood methods provide a promising approach to likelihood inference in which any nuisance parameters in the model are eliminated by averaging the likelihood with respect to a weight function for the nuisance parameter.Such an integrated likelihood offers a number of advantages over other approaches to likelihood inference: it is always available; it is based on averaging rather than maximization, an approach that is often more reliable; it has a certain type of finite-sample optimality; by appropriate selection of the weight function it has many of the same properties of marginal and conditional likelihood functions, when either of those is available. Integrated likelihood methods combine ideas from both Bayesian and non-Bayesian inference and, hence, provide a hybrid method with many of the benefits of both approaches. These methods represent a new way of thinking about likelihood inference in models with nuisance parameters in which the traditional approach of eliminating nuisance parameters through maximization is replaced by averaging. The research will focus on three broad areas: a study of the asymptotic properties of point estimators and the associated standard errors of maximum integrated likelihood estimators; the use of integrated likelihood methods for estimation in models with an unknown function, and the application of integrated likelihood theory and methodology to models with random effects. In each of the areas, models with a high-dimensional nuisance parameter will be of particular interest. This work will lead to better understanding of the properties of likelihood-based methods of inference as well as the development of new statistical methodology based on those results.This research develops a new approach to statistical theory and methodology, based on the use of an integrated likelihood function. These methods are used in the analysis of virtually all statistical models and in all fields of application. In particular, integratedlikelihood methods are useful in complex statistical models and these methods have been used successfully in applications ranging from the reliability of computer software to the analysis of genetic data. In contrast to some other recently-developed methods, which require considerable background in advanced statistical theory, the integrated likelihood approach is computation-based and relatively straightforward to understand and to implement. Thus, the results of this proposed research are useful for researchers in a wide range of fields. The results also further our understanding of the properties of statistical models and, hence, play an important role in the education of researchers in statistics and related fields.

综合似然方法提供了一种很有前途的似然推断方法，通过对干扰参数的加权函数平均似然来消除模型中的任何滋扰参数。这种综合似然方法与其他似然推断方法相比具有许多优点：它总是可用的；它基于平均而不是最大化，这是一种通常更可靠的方法；它具有某种类型的有限样本最优性；通过适当地选择权函数，它具有边际似然函数和条件似然函数的许多相同的性质。综合似然方法结合了贝叶斯和非贝叶斯推理的思想，因此提供了一种混合方法，具有这两种方法的许多优点。这些方法为含干扰参数模型的似然推断提供了一种新的思路，将传统的通过取最大值来消除干扰参数的方法改为求平均值。这项研究将集中在三个方面：研究点估计器的渐近性质和最大集成似然估计量的相关标准误差；在具有未知函数的模型中使用集成似然方法进行估计；以及将集成似然理论和方法应用于具有随机影响的模型。在每个地区，具有高维干扰参数的模型将特别令人感兴趣。这项工作将有助于更好地理解基于似然的推理方法的性质，并在这些结果的基础上开发新的统计方法。本研究开发了一种基于集成似然函数的统计理论和方法的新途径。这些方法被用于几乎所有统计模型和所有应用领域的分析。特别是，综合似然方法在复杂的统计模型中很有用，这些方法已经成功地应用于从计算机软件的可靠性到遗传数据分析的各种应用。与其他一些最近开发的方法不同，这些方法需要相当多的高级统计理论背景，而综合似然方法是以计算为基础的，理解和实施起来相对简单。因此，这项拟议的研究结果对广泛领域的研究人员是有用的。这些结果也加深了我们对统计模型性质的理解，从而对统计及相关领域的研究人员的教育起到了重要作用。