Statistical Inference Based on an Integrated Likelihood

综合似然法提供了一种很有前途的似然推断方法，它通过对模型中的干扰参数的权重函数取平均值来消除干扰参数，这种综合似然比其他似然推断方法有许多优点：它总是可用的;它基于平均值而不是最大值，这种方法往往更可靠;它具有某种类型的有限样本最优性;通过适当地选择权重函数，它具有许多与边际和条件似然函数相同的性质，当这些函数中的任何一个可用时。 综合似然方法结合了联合收割机的想法，从贝叶斯和非贝叶斯 推理，并因此提供了具有两种方法的许多优点的混合方法。 这些方法代表了一种新的思维方式的似然推断模型中的滋扰参数，其中通过最大化消除滋扰参数的传统方法被平均取代。该研究将集中在三个广泛的领域：研究点估计量的渐近性质和最大综合似然估计量的相关标准误差;使用综合似然方法估计模型中的未知函数，以及综合似然理论和方法的应用与随机效应的模型。 在每个领域，具有高维滋扰参数的模型将特别感兴趣。这项工作将导致更好地理解的属性的似然为基础的推理方法，以及开发新的统计方法的基础上，这些result.This研究开发了一种新的方法，统计理论和方法，基于使用的综合似然函数。 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，integratedlikelihood方法是有用的，在复杂的统计模型和这些方法已被成功地用于从计算机软件的可靠性的遗传数据的分析应用。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，综合似然方法是基于计算的，并且理解和实施起来相对简单。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。

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.