Statistical Methodology for Stochastic Systems with Parameters Jumps and Applications to Economics, Genetics and Engineering

具有参数跳跃的复杂随机系统中的统计推断问题存在于经济、金融、遗传学、工业质量控制和公共卫生等科学和工程领域。解决这些问题的一个重要因素是有效地估计具有未知跳跃的时变参数。在提出的研究中，研究者研究了一些新出现的具有未知参数跳跃的不同学科的随机模型，并开发了相关的推理程序。特别是，提案中对不同领域的四类问题进行了研究。首先研究了纵向研究中协变量效应突变的半参数变点回归模型及其推导过程。第二种方法建立了一个存在未知结构突变的信用评级转换模型，以及一个分析美国信贷市场结构性突变与宏观经济和特定企业协变量之间关系的估计程序。第三章讨论了一类具有随机机制的马尔可夫切换模型及其在经济周期分析和基因组研究中的经常性拷贝数变异分析中的应用。第四个问题讨论了序贯监视问题中的监视规则及其在风险管理中的应用。调查员将展示如何通过开发的统计模型和推理程序来统一和解决不同领域中的这些具有挑战性的问题。具有未知参数跳跃的复杂随机系统在经济、金融、生物、风险管理和控制等各种科学和工程实践中经常遇到。虽然参数平稳变化的系统在文献中得到了广泛的讨论，但自然科学和社会科学的最新进展表明，具有未知参数跳跃的随机系统的重要性越来越大。在目前的基因组研究中，DNA拷贝数变异是癌症、HIV感染、阿尔茨海默病和帕金森病等多种疾病发生和发展过程中的关键遗传事件，而研究这些遗传事件的一个重要步骤是识别变异区域。在经济研究中，当局热衷于对实际经济状态进行更详细和量化的描述，而不是经济文献中常见的一些简单描述，如繁荣或衰退，以便发布适当的货币和财政政策。在金融研究中，2008-2009年金融危机使监管当局迫切需要根据可靠的统计和计量经济学模型和程序对信贷市场和银行系统进行监管和监测，因此应建立一个早期预警系统，以监测金融和经济系统的稳定性。拟议的研究是探索为金融市场和经济活动建立量化和可执行的预警系统的可能性的首批尝试之一，该系统汇总了个别公司和银行的微观经济信息以及一般经济活动的宏观经济统计数据。

Statistical inference problems in complex stochastic systems with parameter jumps arise in science and engineering, including economics, finance, genetics, industrial quality control, and public health. An important ingredient in the solution to these problems is efficient estimation of time-varying parameters with unknown jumps. In the proposed research, the investigator studies some newly emerged stochastic models with unknown parameter jumps in different disciplines and develops the related inference procedure. In particular, four types of problems in different areas are studied in the proposal. The first investigates a semi-parametric change-point regression model and its inference procedure for abrupt changes of covariate effect in longitudinal studies. The second develops a credit rating transition model in the presence of unknown structural breaks and an estimation procedure for the analysis of the relationship between the structural breaks in the U.S. credit market and macroeconomic and firm-specific covariates. The third considers a class of Markov switching models with stochastic regimes and their applications in economic analysis of business cycles and recurrent copy number variation analysis in genomic studies. The fourth problem discusses surveillance rules in sequential surveillance problems and their applications in risk management. The investigator will show how these challenging problems in different areas can be unified and solved by the developed statistical models and inference procedures. Complex stochastic systems with unknown parameter jumps are often encountered in various scientific and engineering practices including economics, finance, biology, risk management and control. While systems with smoothly changing parameters have been discussed intensively in the literature, recent advances in natural and social sciences show the growing importance of stochastic systems with unknown parameter jumps. In current genomic research, DNA copy number variations are key genetic events in the development and progression of numerous diseases including cancer, HIV acquisition, and Alzheimer and Parkinson's disease, and an important step in studying these genetic events is to identify the regions of variations. In economic studies, the authorities are keen to have a more detailed and quantitative characterization of the real economic states, instead of some simple descriptions such as booming or recession that are commonly discussed in the economic literature, so that proper monetary and fiscal policies can be issued. In financial studies, the 2008-2009 financial crisis raises the immediate needs for the regulatory authorities that the credit market and banking systems should be regulated and monitored based on solid statistical and econometric models and procedures, and hence an early warning system should be established to surveillance the stability of financial and economic systems. The proposed research is one of the first attempts to explore the possibility of building quantitative and implementable early-warning systems for financial markets and economic activities, which aggregates microeconomic information among individual firms and banks and macroeconomic statistics from general economic activities.