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

摘要PI：本提案的目标是开发新的和广泛适用的半参数和非参数估计和推断方法，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。这一建议不仅引入了一些创新的技术，但也提供了各种新的和深入的见解统计基础。它将对未来的统计方法、计算和理论研究产生重大影响。特别是，建议研究三个相互关联的领域。首先，介绍了一类灵活的半参数和非参数模型。这允许人们研究响应变量与其协变量相关的程度。提出了多元半参数和非参数模型中检验各种假设的广义似然比统计量。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，还引入了状态域的信息，提高了债券波动率估计的效率，更准确地估计了债券的市场风险。第三，在大量变量存在的情况下，通过非凹惩罚似然提出了新的变量选择技术。创新之处在于，它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被广泛应用。统计问题经常出现，如某些变量或因素对公共卫生是否重要;某些风险因素是否对患者的生存时间有显着影响;以及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，在多变量半参数和非饱和非参数模型中，还没有普遍适用的工具来回答这些问题。这里提出的技术允许一个客观地测试科学假设没有限制性的模型假设。该技术允许更好地定价金融衍生品和管理投资风险，以确定重要的风险变量及其在大型流行病学研究分析中可能的相互作用，并仔细检查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