Statistical methods for finite mixture, hidden Markov and*density ratio models.

有限混合、隐马尔可夫和*密度比模型的统计方法。

• 批准号: RGPIN-2014-03743
• 负责人: Chen, Jiahua
• 金额: $ 2.77万
• 依托单位: University of British Columbia
• 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=647343
• 关键词: Statistical; methods; finite; mixture; hidden

The strength of a wood structure strongly depends on the quality of the lumber. It is vital to ensure that the vast majority of specific wood products exceed a prespecified quality standard. For this purpose, every year labs find the strengths of a random sample, and quality indices are estimated based on the lab data. This process is costly and laborious; efficient statistical methods are therefore in demand. Our density ratio model (DRM) project is designed for this purpose. DRM connects several population distributions through a density ratio. Together with the empirical likelihood (EL), DRM pools information from several independent samples to improve efficiency. More research will be carried out to enhance the forestry and other industrial applications. The combination is also useful for small-area estimation in survey sampling. After a survey, inferences with appropriate precisions are possible at the top level but not for individual regions. The random nature of the probability sampling plan may yield little or no direct information for many regions of interest, leading to a need for small-area estimation. Statistical analyses have to be based on structural assumptions for small areas, and the viability of the assumption is crucial. The DRM posts a nonrestrictive "structural assumption." It provides a fresh approach and has the advantage of enabling quality estimates for both means and quantiles (such as the median income) rather than being limited to means (such as the average income).**Accurately predicting the ups and downs of a stock index is "mission impossible." A stochastic description of the movement is probably the best we can do. We aim to find the most appropriate mathematical models for financial times series and then to craft efficient analysis methods. A regime-switch model postulates that the day-to-day fluctuations of a time series are reflections of hidden states governed by a Markov chain. The structure of this chain sheds light on the volatility in the time series. The standard inference platform has been the full likelihood; we have argued that composite likelihoods offer an effective alternative. I have developed a specific composite likelihood that provides point estimators with a negligible efficiency loss. It has a simpler mathematical structure that facilitates thorough theoretical investigation. I aim to develop consistent variance estimation and to explore the potential of the composite likelihood ratio test for various aspects of the model and for the construction of confidence intervals.**Patients with the same disease differ in many ways, and there is thus a need for personalized medicine. Population heterogeneity can often be discovered by testing the order of a finite mixture model. We have developed a number of tests for the order of mixture models. They have easy-to-use large-sample properties and fill a large void in statistical inference. I intend to vastly expand the horizon of the EM-test and to develop easy-to-use software packages.**Last but not least, adding a pseudo-observation elegantly solves a technical issue in the application of the empirical likelihood. It also improves the precision of the resulting statistical inference. Since I introduced this idea, it has been applied by many researchers, particularly econometricians. There are many additional research problems to be explored.

木材结构的强度在很大程度上取决于木材的质量。确保绝大多数特定木材产品超过预先指定的质量标准至关重要。为此，每年实验室都会发现随机样本的优势，并根据实验室数据估算质量指数。这个过程是昂贵和费力的。因此，有效的统计方法需要。我们的密度比模型（DRM）项目是为此目的而设计的。 DRM通过密度比连接几个人群分布。与经验可能性（EL）一起，DRM从几个独立样本中汇集了信息，以提高效率。将进行更多的研究以增强林业和其他工业应用。该组合对于调查采样中的小区域估计也很有用。经过调查后，可以在最高级别但对于单个地区进行适当精确的推论。概率采样计划的随机性质可能几乎没有或没有直接信息，从而导致需要小区域的估计。统计分析必须基于对小区域的结构假设，并且该假设的可行性至关重要。 DRM发布了非限制性的“结构假设”。它提供了一种新的方法，并具有对手段和分位数（例如中位收入）的质量估算的优势，而不是限于手段（例如平均收入）。**准确地预测股票的起伏索引是“不可能的任务”。对运动的随机描述可能是我们能做的最好的。我们旨在为《金融时报》系列找到最合适的数学模型，然后制定有效的分析方法。政权开关模型假定时间序列的日常波动是由马尔可夫链支配的隐藏状态的反映。该链的结构阐明了时间序列中的波动性。标准的推理平台是完全的可能性。我们认为复合可能性提供了有效的选择。我已经开发了一种特定的复合可能性，它为点估计器提供了可忽略的效率损失。它具有更简单的数学结构，可促进彻底的理论研究。我旨在制定一致的方差估计，并探索模型各个方面的复合似然比测试的潜力和置信区间的构建。用于个性化医学。人口异质性通常可以通过测试有限混合模型的顺序来发现。我们已经为混合模型的顺序开发了许多测试。它们具有易于使用的大样本特性，并在统计推断中填充了较大的空隙。我打算大大扩展EM测试的视野并开发易于使用的软件包。它还提高了由此产生的统计推断的精度。自从我介绍这个想法以来，它已被许多研究人员，特别是计量经济学家应用。还有许多其他研究问题要探讨。