Statistical inference with applications

统计推断与应用

• 批准号: RGPIN-2017-05719
• 负责人: Wong, Augustine
• 金额: $ 1.17万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=668781
• 关键词: Statistical; inference; applications

In recent year, likelihood-based higher order asymptotic methods have been extensively studied to accurately approximate the p-value for testing a scalar parameter of interest. One problem of these methods is to obtain the constrained maximum likelihood estimate for a given value of the parameter of interest. In some cases, standard software may either report an optimal value, but in fact, is not the actual optimum, or the methods completely failed to converge. Goffe et al. (1994) showed that the simulated annealing algorithm could uncover optima missed by traditional software. The aim of the first project is to implement the simulated annealing technique into R to obtain both the unconstrained and the constrained maximum likelihood estimates. Hence, the p-value of a scalar parameter of interest for any given parametric model can be accurately approximated. The proposed method can be applied to reliability, survival data analysis, time series analysis, and econometrics where the parameter of interest may not have a closed form.******A limitation of the current likelihood-based higher order asymptotic methods is that they are only applicable to a scalar parameter of interest. However, in many common statistics problems, the parameter of interest is a vector. The common approaches for these problems usually have only first order convergence. The aim of the second project is to combine the higher order method with the direction test to obtain an approximate p-value for testing a vector parameter of interest in a general model setting. The theoretical accuracy of the proposed method will be determined. Applications include the general Behrens-Fisher problem, testing for homogeneity of variance for general mixed model, and structural equation models.******The first two projects depend on the existence of the full likelihood function. When the full likelihood function is too complex to deal with, can the composite likelihood function be used? It is well-known that under this form of model mis-specification, the asymptotic distribution of the log composite likelihood ratio statistic involves a linear combination of weighted independent chi-square variates. The aim of the third project is to obtain the asymptotic distribution of the weighted independent chi-square variates via the saddlepoint approximation. The result allow us to study the asymptotic distribution of the weighted double partial sum statistic for change point detection.******The last project deviates from the first three proposed projects. The aim is to apply the Bayesian approach to calculate the odds of a document being relevant with respect to the user task such that more personalized and accurate search results can be retrieved. The proposed research will generate novel information retrieval techniques and tools over big data. These tools will lead to more effective information retrieval applications which will bring broad benefits to the society.

近年来，基于似然性的高阶渐近方法得到了广泛研究，以准确逼近用于测试感兴趣的标量参数的 p 值。这些方法的一个问题是获得给定的感兴趣参数值的约束最大似然估计。 在某些情况下，标准软件可能会报告最佳值，但实际上并不是实际的最佳值，或者方法完全无法收敛。戈夫等人。 (1994) 表明模拟退火算法可以发现传统软件错过的最佳值。 第一个项目的目标是将模拟退火技术应用到 R 中，以获得无约束和约束最大似然估计。 因此，可以准确地近似任何给定参数模型的感兴趣标量参数的 p 值。 所提出的方法可应用于可靠性、生存数据分析、时间序列分析和计量经济学，其中感兴趣的参数可能不具有封闭形式。******当前基于似然的高阶渐近方法的局限性在于它们仅适用于感兴趣的标量参数。 然而，在许多常见的统计问题中，感兴趣的参数是向量。 这些问题的通用方法通常仅具有一阶收敛性。 第二个项目的目标是将高阶方法与方向测试相结合，以获得近似 p 值，用于测试一般模型设置中感兴趣的向量参数。 将确定所提出方法的理论准确性。 应用包括一般的 Behrens-Fisher 问题、一般混合模型的方差同质性测试以及结构方程模型。******前两个项目取决于完全似然函数的存在。 当完全似然函数太复杂而无法处理时，可以使用复合似然函数吗？ 众所周知，在这种形式的模型错误指定下，对数复合似然比统计量的渐近分布涉及加权独立卡方变量的线性组合。 第三个项目的目的是通过鞍点近似获得加权独立卡方变量的渐近分布。 结果使我们能够研究用于变化点检测的加权双部分和统计量的渐近分布。*****最后一个项目偏离了前三个提出的项目。 目的是应用贝叶斯方法来计算文档与用户任务相关的几率，以便检索更加个性化和准确的搜索结果。拟议的研究将产生新的大数据信息检索技术和工具。这些工具将带来更有效的信息检索应用，从而为社会带来广泛的利益。