相依数据之下的非参数回归函数最近邻估计

THE NEAREST NEIGHBOR ESTIMATE OF NONPARAMETRIC FUNCTION FOR DEPENDENT OBSERVATION

当观察数据是相依的。即误差序列{ε_i,i≥1}是一个严平稳的φ-混合过程时,本文得到非参数回归函数的最近邻估计及相应的Stein估计的相合性,并证明了此Stein估计是一个稳健的“光滑者”.

When observation data is dependent,i. e. the error sequence{ε_(?),i≥1}is a strictly stationary φ-mixing process, the paper obtains the consistencies of the nearest neighbor estimate and the associate Stein estimate of the nonparametric function. Moreover, we show that the Stein estimate is a robust 'smoother'.