Improvement Theory of Nonparametric Statistical Precise Inference and Its Applications

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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.