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: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=587391
• 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.

木结构的强度很大程度上取决于木材的质量。确保绝大多数特定木制品超过预先规定的质量标准至关重要。为此，实验室每年都会找到随机样本的优势，并根据实验室数据估计质量指数。这个过程既费钱又费力；因此需要有效的统计方法。我们的密度比模型（DRM）项目就是为此目的而设计的。 DRM 通过密度比将多个人口分布连接起来。 DRM 与经验似然 (EL) 一起汇集来自多个独立样本的信息以提高效率。将进行更多研究以增强林业和其他工业应用。该组合对于调查抽样中的小区域估计也很有用。经过调查后，高层可以做出适当精度的推论，但不能针对个别地区。 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.统计分析必须基于小区域的结构假设，而假设的可行性至关重要。 DRM 发布了一个非限制性的“结构假设”。 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). 准确预测股指的涨跌是“不可能完成的任务”。对运动的随机描述可能是我们能做的最好的了。我们的目标是找到最适合金融时间序列的数学模型，然后制定有效的分析方法。政权转换模型假设时间序列的日常波动是由马尔可夫链控制的隐藏状态的反映。该链的结构揭示了时间序列的波动性。标准推理平台已经是完全似然；我们认为复合可能性提供了一种有效的选择。我开发了一种特定的复合可能性，为点估计器提供了可忽略不计的效率损失。它具有更简单的数学结构，有利于彻底的理论研究。 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. 同一疾病的患者有很多差异，因此需要个体化医疗。总体异质性通常可以通过测试有限混合模型的阶数来发现。我们针对混合模型的阶数开发了许多测试。它们具有易于使用的大样本特性，并填补了统计推断中的巨大空白。我打算极大地扩展 EM 测试的范围并开发易于使用的软件包。 最后但并非最不重要的一点是，添加伪观察巧妙地解决了经验可能性应用中的技术问题。它还提高了统计推断结果的精度。自从我提出这个想法以来，它已经被许多研究人员应用，特别是计量经济学家。还有许多其他研究问题有待探索。