Improvement Theory of Nonparametric Statistical Precise Inference and Its Applications

在这个项目中，我们获得了基于重复使用数据的重采样方法的统计推断的高阶渐近性质。我们还得到了核型估计量分布函数的近似，并应用这些结果提出了新的非参数检验统计量。此外，我们还开发了一种基于高斯基本函数的推理方法，可以应用于非线性复杂系统。对非线性回归模型进行了细致的研究，得到了一种灵活的方法，提高了状态空间数据的统计推断精度。

In this project, we obtain an higher order asymptotic properties for statistical inference based on resampling methods, which use the data repeatedly. We also obtain approximations of distribution functions of kernel type estimators, and applying these results, we propose new nonparametric test statistics. Furthermore, we develop an inference method based on Gaussian basic functions, which we can apply to non-linear complex systems. The non-linear regression model is studied precisely, and we obtain a flexible method which improve accuracy of statistical inferences for state space data.