$\alpha$混合下非参数回归函数改良分割估计的强相合性及收敛速度

Strong Consistency and Convergence Rate of Modified Partitioning Estimate of Nonparametric Regression Function under $\alpha$-Mixing Sample

中文关键词:  改良分割估计  强相合性  收敛速度  $\alpha$混合.

英文关键词:nonparametric regression function  modified partitioning estimate  strong consistency  convergence rate  $\alpha$-mixing.

中文摘要:

      本文研究了在样本$(X_1,Y_1),(X_2,Y_2),\ldots,(X_n,Y_n)$ 为取值于$R^{d}\times R^{1}$的同分布的$\alpha$混合序列时,回归函数改良分割估计的强相合性和收敛速度.

英文摘要:

      In this paper, we study the strong consistency and convergence rate of modified partitioning estimate of nonparametric regression function under the sample $\{(X_i,Y_i), i\geq1\}$ that is $\alpha$ sequence taking values in $R^d\times R^1$ with identical distribution.