回归模型误差分布核估计的强收敛性

Strong Convergence of Estimating Error Distribution Based on Kernel Method in Regression Models

回归模型Ｙｉ＝ｇ（ｔｉ）＋ｅｉ中，｛ｅｉ｝是ｉｉｄ随机误差，具有密度函数ｆ（ｘ）。利用ｉｉｄ子样｛ｔｉ，Ｙｉ｝的观测值构造ｆ（ｘ）的核估计（式中，其中为ｇ（ｔｉ）的加权估计）。在｛ｔｉ｝与（ｅｉ）相互独立且ｔｉ∈［０，１］以及权系数、校函数和窗宽满足一般的条件下，证明了核估计（ｘ）的ａ．ｓ．收敛性。核估计（ｘ）的这种大样本性质对于回归模型的假设检验问题具有重要意义。

The regression model such as (Yi=g(ti)+ei),here,{ei} is lid radom error,has a density function f(x).The Kernel estimation fn(x) with{ti,Yi} is completed.On some conditions, the convergence of fn(x) is proved. This convergence is very important for examing hypothesis problems in regression models.