Efficient nonparametric regression when the support is bounded

在非参数回归中，如果误差分布的支持度有一个尖锐的边界，则回归函数及其泛函的估计可以比常规模型具有更高的收敛速度。我们研究了这种不规则统计实验的几何形状，并开发了有效的统计程序，既适应回归函数的光滑性，又适应误差分布的不规则性。此外，将对模型假设进行拟合优度检验，并将制定订单数据的具体估计程序。

If in nonparametric regression the support of the error distribution has a sharp boundary, then the regression function and functionals thereof can be estimated with a higher rate of convergence than in regular models. We examine the geometry of such irregular statistical experiments and develop efficient statistical procedures that adapt both to the smoothness of the regression functionand to the degree of irregularity of the error distribution. Moreover, goodness-of-fit tests for the model assumptions will be constructed and concrete estimation procedures for order-book data will be developed.