Mathematical Sciences: Likelihood Functions for Estimating Equations

我的研究集中在构建可能性上 用于估计方程的函数。 这些功能的必要性 当估计方程不能积分到 潜在功能 似然函数可以是 从真实得分函数到 一类保守估计方程或从 一对中心似然比的投影。 的 为拟似然法开发预测， 对于广义估计方程，以及其他一些 估计方程类。 它们可以同时适用于 独立和依赖的情况。 这些功能将 用于构造不变置信区间，以区分 在一致和不一致的解决方案之间 方程，并测试统计假设。 我也有 引入了测试中包含的信息的概念 函数，并将用它来研究一些常用的测试 功能协调发展的与此相关，一阶性质 获得辅助。 统计学中的关键问题是建立一种关系 事实和数据之间的关系，并利用这种关系， 根据数据推断真相。 这往往是 我们称之为似然法。 有时 传统的似然方法面临困难：它可能需要 做出难以满足的假设;可能是 在计算上难以实现;它可能不够丰富 以适应某些应用。面对这些挑战， 拟似然估计的理论与方法 在最近的一段时间里， 年 扩展和丰富的似然方法，新的 方法可以在更现实的假设下应用， 方便地，在更广泛的情况下。 我的研究是 准似然和估计方程的某些方面， 特别是构造似然函数， 估计方程及其在统计推断中的应用。

My research focuses on the construction of likelihood functions for estimating equations. The need for such functions arises when the estimating equations do not integrate to potential functions. The likelihood functions can be either obtained from the projection of the true score function onto a class of conservative estimating equations or from the projection of a pair of centered likelihood ratios. The projections are developed for the quasi-likelihood method, and for the generalized estimating equations, as well as some other classes of estimating equations. They can be applied to both independent and dependent situations. These functions will be used to construct invariant confidence intervals, to distinguish between consistent and inconsistent solutions to estimating equations, and to test statistical hypotheses. I also have introduced a notion of the information contained in a testing function, and will use it to study some commonly used testing functions. In relation to this, a property of the first order ancillarity is obtained. The key issue in statistics is to establish a relation between the truth and the data, and to use the relation to make inference about the truth based on the data. This is often achieved by what we call the likelihood methods. Sometimes the traditional likelihood method faces difficulties: it may need to make assumptions that are difficult to satisfy; it may be computationally difficult to realize; it may not be rich enough to accommodate certain applications. Meeting these challenges, the theories and methods of quasi-likelihood and estimating equations have been developed and widely used during recent years. Extending and enriching the likelihood method, the new methods can be applied under more realistic assumptions, more conveniently, and in wider situations. My research is on certain aspects of quasi-likelihood and estimating equations, and in particular the construction of likelihood functions for estimating equations and their use in statistical inference.