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是至关重要的。为此，实验室每年随机抽取样本，找出其优势，并根据实验数据估计质量指标。这个过程既昂贵又费力；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通过密度比连接了几个种群分布。与经验似然（EL）一起，DRM从多个独立的样本中汇集信息以提高效率。将开展更多的研究，以增强林业和其他工业应用。这种组合也适用于调查抽样中的小区域估计。经过调查后，可以在最高水平上进行适当精度的推断，但不能对个别地区进行推断。概率抽样计划的随机性质可能对许多感兴趣的区域产生很少或没有直接信息，导致需要进行小区域估计。统计分析必须以小区域的结构假设为基础，而这种假设的可行性至关重要。DRM提出了一个非限制性的“结构性假设”。它提供了一种新的方法，其优点是能够对平均值和分位数（如收入中位数）进行高质量的估计，而不是局限于平均值（如平均收入）。**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。我们的目标是为金融时间序列找到最合适的数学模型，然后制定有效的分析方法。状态切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。这条链的结构揭示了时间序列的波动性。标准推理平台已经具备了全可能性；我们认为，复合可能性提供了一个有效的替代方案。我已经开发了一个特定的复合可能性，它提供了一个可以忽略不计的效率损失的点估计器。它有一个更简单的数学结构，便于深入的理论研究。我的目标是发展一致的方差估计，并探索复合似然比检验对模型的各个方面和置信区间的构建的潜力。**患有同一种疾病的患者在许多方面存在差异，因此需要个性化医疗。群体异质性通常可以通过检验有限混合模型的阶数来发现。我们已经为混合模型的阶数开发了一些测试。它们具有易于使用的大样本特性，填补了统计推断的巨大空白。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，添加一个伪观测值很好地解决了应用经验似然的一个技术问题。它还提高了所得统计推断的精度。自从我提出这个想法以来，它已经被许多研究人员，特别是计量经济学家应用。还有许多其他的研究问题有待探索。