几类随机过程的局部稳健估计研究及其应用

项目名称： 几类随机过程的局部稳健估计研究及其应用

项目编号： No.11461032

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 王允艳

作者单位： 江西理工大学

项目金额： 36万元

中文摘要： 非参数稳健统计方法对模型假设的小偏差具有稳定性，对数据中的异常值有较强的抗扰性，并且在多个典型模型下都有较好的性能。而局部稳健估计不仅保留了局部线性估计量的优点，而且克服了最小二乘估计量缺乏稳健性的缺点，是一种很受欢迎的估计方法。本项目研究几类随机过程的非参数局部稳健估计，内容包括：(1) 结合局部线性平滑技术和稳健技术建立扩散过程的漂移系数和扩散系数的变带宽局部稳健估计量；(2) 建立二阶扩散过程的漂移系数和扩散系数的局部稳健估计量；(3) 构造带跳扩散过程的无穷小条件矩的局部稳健估计量；(4) 分别在独立样本和相依样本的情况下，构造非参数异方差回归模型中条件方差函数的局部稳健估计量；等。在温和的条件下，建立以上得到的稳健估计量的极限理论，并通过数值模拟来检验这些估计量的表现。本项目将以几类随机过程的稳健估计为基础来深入分析研究非参数局部稳健方法，为稳健方法的研究与应用提供新的理论。

中文关键词： 稳健性；局部线性估计；相合性；渐近正态性；随机过程

英文摘要： Nonparametric robust methods is stability for small deviations of model assumptions, have strong anti-jamming for abnormal values in the data, and have a better performance under several typical model. The local robust estimation inherits the advantages of local linear smoother and overcomes the shortcoming of lack of robustness of least-squares estimator, so it is a very popular robust methods. This project aims to study the nonparametric local robust estimation for some stochastic processes, the research content includes: (1) Establishes variable bandwidth local robust estimators for drift coefficient and diffusion coefficient in diffussion process by combining of the local linear smoothing technique and the M-estimation technique; (2) Establishes local robust estimators for drift coefficient and diffusion coefficient in second order diffussion process; (3) Constructs local robust estimators for the infinitesimal moments in the jump-diffusion model; (4) Constructs local robust estimator for conditional variance function in nonparametric heteroscedastic regression model under independent samples and dependent samples, respectively; and so on. The limit theory of these local robust estimators mentioned above are considered under mild conditions, and the simulation studies are demonstrated to show the performance of the local robust estimators. The project will give a profound analysis of nonparametric local robust methods based on the local robust estimation for some stochastic processes, and provide a new theory for the research and application of robust methods.

英文关键词： robustness;local linear estimation;consistency;asymptotic normality;stochastic processes