Asymptotic analysis for point and interval estimation in some statistical models

某些统计模型中点估计和区间估计的渐近分析

• 批准号: RGPIN-2017-06304
• 负责人: Volodin, Andrei
• 金额: $ 1.17万
• 依托单位: University of Regina
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759160
• 关键词: Asymptotic; analysis; point; interval; estimation

Although my research program concerns many different aspects of statistics and probability theory, it revolves around a single theme: asymptotics (expansion of a statistic or of a distribution). My research involves the following four main components: statistical testing for expression of genes (pFDR and d-risk approaches); dependent structures; point estimation for parameters of some statistical distributions; and the interval estimation problem for the ratio of two binomial proportions.1. I consider the problem of data analysis of gene expression as a special case of the problem of multiple hypothesis testing in the framework of the so-called d-posterior approach. It is based on the Bayesian paradigm and can be applied to the various cases of statistical experiments. Each experiment leads to a decision and the falsity rate must be guaranteed. I will apply the optimal test to the problem of identifying of hyperactive genes responsible for a disease and will establish a general Bayesian model for solving similar problems, in particular problems of hypoactive genes selection.2. My interest in dependent structures arose from their fascinating applications to some statistical procedures where the assumption of independency of observations is violated. A classical example would be the dependent bootstrap procedure where resampling is done without replacement. I have been working on these problems for many years, and my main goal is to obtain the Law of the Iterated Logarithm for the dependent bootstrap procedure. This will lead me to a complete description of the asymptotic behaviour of the dependent bootstrap random variables.Another interesting component of my investigation on dependent structures is connected with an investigation on the assumptions of applicability of the law of large numbers in weak and strong forms to negatively associated random variables. A derivation of exponential inequalities for maximum sums of bounded negatively associated random variables is crucial for limit theorems, especially establishing weak and strong laws of large numbers for negatively associated random variables. The main difficulty here is to show that the moment assumptions are necessary and sufficient, that is, to establish criteria.3. My next component of the proposal is connected with a confidence interval construction for a ratio of two binomial proportions. To date, this statistical problem has been solved only for sampling schemes with a fixed number of observations in both samples. My goal is to find a universal approach for confidence interval construction for the ratio of proportions with different sampling schemes.4. There is a problem with the method of moments estimation of parameters of the binomial distribution. These estimators do not even have expectation and can have values which are out of the natural range of the parameters. Hence, modifications of these estimators are required.

尽管我的研究计划涉及统计和概率理论的许多不同方面，但它围绕一个主题：渐近学（统计量的扩展或分布的扩展）。我的研究涉及以下四个主要组成部分：基因表达的统计测试（PFDR和D-风险方法）；依赖结构；某些统计分布的参数的点估计；以及两个二项式比例比率的间隔估计问题1。我认为，基因表达的数据分析问题是在所谓的D-Posteror方法的框架中多个假设检验问题的特殊情况。它基于贝叶斯范式，可以应用于统计实验的各种情况。每个实验都会导致决策，必须保证虚假率。我将应用最佳测试，以鉴定导致疾病的多活跃基因的问题，并将建立一个通用贝叶斯模型，以解决类似问题，特别是选择性基因选择的问题。2。我对依赖结构的兴趣来自它们的迷人应用，这些统计程序违反了对观察的独立性的假设。一个经典的示例将是依赖的引导程序，在没有更换的情况下进行重新采样。多年来，我一直在研究这些问题，而我的主要目标是为依赖的引导程序获得迭代对数的法律。这将使我完全描述依赖性自举变量的渐近行为。负相关的随机变量。指数不平等的衍生范围对有限相关的随机变量的最大总和对于限制定理至关重要，尤其是建立大数字的弱和强定律，以实现负相关的随机变量。这里的主要困难是表明那一刻的假设是必要和足够的，即建立标准3。该提案的下一个组成部分与置信区间结构相关，其比例为两个二项式比例。迄今为止，仅针对两个样本中具有固定数量观测值的抽样方案解决了此统计问题。我的目标是找到一种通用方法，以使用不同的采样方案的比例比例的比例。4。矩估计二项式分布参数的矩估计方法存在问题。这些估计器甚至没有期望，并且可以具有超出参数自然范围的值。因此，需要对这些估计器进行修改。