Abstract:

Let $m_{n}(x)$ and $M_{n}(x)$ be a partitioning estimate and the kernel estimate, respectively, of a regression function $ m(x)=E(Y\vert X=x)$ for the i.i.d. sample $(X_{1},Y_{1}),\ldots , (X_{n},Y_{n})$. Under the condition $E \vert Y\vert^p <\infty $, where $p>1$, and some conditions on the partition and the kernel function, the strong $L_{1}$-consistency is proved.