各向异性回归函数的小波点态估计

Wavelet pointwise estimation of anisotropic regression function

针对强混条件下各向异性回归函数的点态估计问题,利用小波方法构造了线性小波估计器,并在B_(p,q)^(S)(R^(d))空间讨论了估计器在l^(p)(1≤p<∞)点态误差意义下的收敛阶。研究结果表明,在强混条件下的结论比样本独立时的结果更接近实际应用,且当空间B_(p,q)^(S)(R^(d))的各向异性指标相等时,结论与各向同性Besov空间中的结果保持一致。

For pointwise estimation of anisotropic regression function under strong mixing condition,a linear wavelet estimator was constructed by wavelet method,and the convergence rate over l^(p)(1≤p<∞) pointwise error was discussed in B_(p,q)^(S)(R^(d)).The results of the research show that the conclusions under strong mixing conditions are closer to practical applications than the results when the samples are independent,and when the anisotropy index of space B_(p,q)^(S)(R^(d)) is equal,the conclusion is consistent with the result in the isotropic Besov space.