Research on implementations of computer-intensive selection methods for regularized statistical models

(1)在从交易债券数据中对利率期限结构进行非参数估计时，根据经验众所周知，近似远期利率通常会得到更好的结果。然而，这种方法的问题是，使用广义交叉验证不能证明选择正则化参数是合理的。在这个项目中，我们建立了一个版本的广义信息准则(GIC)，它在确定正则化参数时具有理论上的有效性。(2)比较了不同类型的GARCH模型和多元GARCH模型在下行风险，特别是风险价值(VaR)的一致性方面的表现。在给定估计参数的情况下，我们进行了预测模拟，并通过二项检验将经验超越率与名义规模进行了比较。我们的结论是，动态条件相关模型及其简约的参数形式表现最好。(3)研究了带干扰项的不可观测分量时间序列模型的估计问题。数据来自动物剂量管理测试。这些是时间序列数据，如收缩压、舒张压、心率等。我们考虑了一个时间序列模型，将观察分解为趋势、平稳自回归部分和指数型干预项，使我们能够通过模型选择来估计急性毒性。(4)以向公众公开研究成果为目标，研究了基于时间序列分析软件的网络在线学习系统。

(1) In nonparametric estimation of term structures of interest rates from traded bond data, it is empirically well-known that approximating forward rate often yields better result. The problem of this approach is, however, that the use of generalized cross-validation cannot be justified to choose regularization parameters. In this project, we established a version of generalized information criteria (GIC) that holds theoretical validity in the determination of regularization parameter. (2) We compared the performance of various types of GARCH models and multivariate GARCH models in terms of the coherency of downside risks, especially Value at Risk (VaR). Given the parameters estimated, we performed prediction simulation and compared the empirical exceedance rate with nominal size through a binomial test. Our conclusion is that Dynamic Conditional Correlation model performs best, together with its parsimonious parametric form. (3) Estimation of unobserved components time series models with intervention terms are studied. Data come from animal dose administration testing. These are time series data such as systolic blood pressure, diastolic blood pressure, heart rate and so on. We considered a time series model to decompose observation into trend, stationary autoregressive part and an exponential type intervention term, which enabled us to estimate acute toxicity through model selection. (4) Aiming disclosure of the research results to the public, online learning system on the web based time series analysis software was studied.