By constructing the conditions consistent with its solution, and employing the theorem of the immobile point in functional analysis, it is proved that the existence and uniqueness of the local M-estimate with some conditions.

• 摘要通过构造解存在所满足的条件及引入泛函分析中的不动点定理证明了稳健的变窗宽局部线性回归估计在一定条件下解的存在性和唯一性。