Integrated Likelihood Functions for Non-Bayesian Inference

处理干扰参数的问题是统计理论和方法的一个基本方面，特别是在基于似然性的推断中。 从统计模型中消除干扰参数的常用方法包括边际和条件推断以及使用轮廓似然函数。 另一种方法是使用积分似然，其中通过相对于给定权重函数的积分从似然函数中消除干扰参数。综合似然的优点是它们总是可用的，并且与轮廓似然不同，它们基于平均而不是最大化，这在许多感兴趣的模型中已被证明是更可靠的方法。综合似然方法的主要缺点是必须选择其实现所需的权重函数。本研究的目的是研究在非贝叶斯的，基于似然的推理中使用综合似然。其中最重要的方面是权重函数的构造，使得所得到的集成似然函数对于非贝叶斯推断是有用的。在研究中考虑的其他主题包括高阶渐近理论的发展，计算算法的发展，与现有方法的比较，应用程序与高维滋扰参数的模型，并在practice.This研究开发了一种新的方法，统计理论和方法的基础上，使用一个集成的似然函数的应用methodologytomodels。 这些方法被用于几乎所有统计模型的分析和所有应用领域。特别是，综合似然方法已被用于从计算机软件的可靠性到遗传数据分析的各种应用中。与其他一些最近开发的方法相比，这些方法需要相当多的先进统计理论背景，综合似然方法相对简单，易于理解和实施。因此，这项研究的结果是有用的研究人员在广泛的领域。这些结果也进一步加深了我们对统计模型性质的理解，因此，在统计及相关领域的研究人员的教育中发挥着重要作用。

The problem of dealing with nuisance parameters is a fundamental aspect of statistical theory and methodology, particularly in likelihood-based inference. Commonly used approaches to eliminating a nuisance parameter from a statistical model include marginal and conditional inference and the use of the profile likelihood function. An alternative approach is to use an integrated likelihood, in which the nuisance parameter is eliminated from the likelihood function by integration with respect to a given weight function. Integrated likelihoods have the advantage that they are always available and, unlike the profile likelihood, they are based on averaging rather than maximization, which has been shown to be a more reliable approach in many models of interest. The primary drawback of the integrated likelihood approach is that weight function needed for its implementation must be chosen. The goal of this research is to study the use of integrated likelihoods in non-Bayesian, likelihood-based, inference. The most important aspect of this is the construction of the weight function so that the resulting integrated likelihood function is useful for non-Bayesian inference. Other topics considered in the research include development of higher-order asymptotic theory, development of computational algorithms, comparisons with existing methods, applications to models with a high-dimensional nuisance parameter, and the application of the methodologyto models used in practice.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 fieldsof application. In particular, integrated likelihood methods have been used 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 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.