Statistical methods for finite mixture, hidden Markov anddensity 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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=610623
• 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材产品超过预先规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计质量指数。这一过程既费钱又费力，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通过密度比将几个人口分布联系起来。与经验似然（EL）一起，DRM池来自几个独立样本的信息，以提高效率。将进行更多的研究，以提高林业和其他工业应用。该组合也适用于调查抽样中的小区域估计。在调查之后，在最高级别上可以进行具有适当精度的推断，但对于个别地区则不可能。概率抽样计划的随机性可能对许多感兴趣的区域产生很少或没有直接信息，导致需要进行小面积估计。统计分析必须以小区域的结构假设为基础，而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，而不是局限于均值（如平均收入）。 准确预测股票指数的唐斯是“不可能完成的使命。“对运动的随机描述可能是我们所能做的最好的。我们的目标是找到最合适的金融时间序列的数学模型，然后制定有效的分析方法。状态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中的波动性。标准的推理平台是全似然;我们认为复合似然提供了一种有效的替代方案。我已经开发了一个特定的复合可能性，提供了一个可以忽略不计的效率损失的点估计。它有一个更简单的数学结构，便于深入的理论研究。我的目标是开发一致的方差估计，并探讨潜在的复合似然比检验的各个方面的模型和置信区间的建设。 患有相同疾病的患者在许多方面都有差异，因此需要个性化医疗。通常可以通过检验有限混合模型的阶来发现总体异质性。我们已经开发了一些测试的顺序混合模型。它们具有易于使用的大样本特性，并填补了统计推断中的一个大空白。我打算大大扩展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，添加一个伪观测巧妙地解决了经验似然性应用中的一个技术问题。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所应用。还有许多其他的研究问题需要探讨。