一个由方差估计引出的极值问题

An Optimization Problem Arising from Variance Function Estimation

在文献[1]中提出的一种非参数方差估计方法,引出了下面的极值问题:在∑i=1iω=0,∑m0,∑mi=1ω2i=1的约束下,使∑mi=1ω4i达到最小或最大.本文给出了这个问题的解.

Ref. [ 1 ] proposed a nonparametric method for estimating the error variance in a regression model. This method induces the following optimization problem：maximize or minimize m∑i=1ω^4i under the restrictionm∑i=1 ωi=0 ωi=0,m∑i=1 ω^2i=1 . This article gives the solution of this problem.