Inferences for Multivariate Semiparametric and Nonparametric Models with Applications to Risk Management

摘要PI：Jianqing FanDMS-0204329该提案的目标是开发新的且广泛适用的半参数和非参数估计和推理方法，研究这些新方法的理论特性，并评估其在数据分析中的有效性。该提案不仅引入了许多创新技术，而且还为统计基础提供了各种新的、深入的见解。它将对未来统计方法、计算和理论的研究产生重大影响。特别是，建议研究三个相互关联的领域。首先，介绍了一系列灵活的半参数和非参数模型。这使得人们能够研究响应变量与其协变量相关的程度。提出广义似然比统计来检验多元半参数和非参数模型中的各种假设。其次，提出了新的半参数和非参数模型来理解利率动态和股票价格波动。此外，纳入状态域信息可以提高债券波动率估算的效率，更准确地估算投资组合的市场风险。第三，在存在大量变量的情况下，通过非凹惩罚似然提出了变量选择的新技术。创新之处在于他们同时估计参数和选择变量。上述技术广泛适用于许多科学和工程问题。多元非参数、半参数和大参数模型已得到广泛应用。经常出现统计问题，例如某些变量或因素是否对公共卫生很重要；某些危险因素是否对患者的生存时间有显着影响；利率动态或股票价格过程是否依赖于时间或遵循某些著名的假设等。然而，在多元半参数和非饱和非参数模型中，没有普遍适用的工具可以回答这些问题。这里提出的技术允许人们在没有限制性模型假设的情况下客观地检验科学假设。这些技术可以更好地为金融衍生品定价并管理投资风险，在大型流行病学研究分析中识别重要的风险变量及其可能的相互作用，并仔细审查有关股票价格的著名假设

AbstractPI: Jianqing FanDMS-0204329The objectives of this proposal are to develop new and widely applicable approaches for semiparametric and nonparametric estimation and inferences, to study theoretical properties of these new approaches, and to evaluate their efficacy in data analyses. This proposal not only introduces a number of innovative techniques, but also provides various new and deep insights into statistical foundation. It will have significant impact on the future research of statistical methodologies, computation and theories. In particular, three inter-related areas are proposed for study. Firstly, a family of flexible semiparametric and nonparametric models is introduced. This allows one to study the extent to which response variables are associated with their covariates. The generalized likelihood ratio statistics is proposed for testing various hypotheses in multivariate semiparametric and nonparametric models. Secondly, new semiparametric and nonparametric models are proposed for understanding interest-rate dynamics, and stock price volatilities. Furthermore, the information on state-domain is incorporated to improve the efficiency of volatility estimation for bonds and to more accurately estimate the market risks of a portofolio. Thirdly, new techniques for variable selection, in the presence of a large number of variables, are proposed via nonconcave penalized likelihood. The innovation is that they estimate parameters and select variables simultaneously. The above techniques are widely applicable to many scientific and engineering problems. Multivariate nonparametric, semiparametric and large parametric models have been widely used. Statistical questions often arise such as if certain variables or factors are important to public health; if some risk factors contribute significantly to the survival time of patients; and if interest-rate dynamics or stock price processes are time-dependent or follow certain famous hypotheses, among others. Yet, there are no generally applicable tools available to answer these questions in multivariate semiparametric and non-saturated nonparametric models. The techniques proposed here permit one to objectively test scientific hypotheses without restrictive model assumptions. The techniques allow to better price financial derivatives and manage investment risk, to identify important risk variables and their possible interactions in the analysis of large epidemiological studies and to scrutinize famous hypotheses on stock prices