非参数回归函数的置信区间

The Confidence Intervals of the Nonparametric Regression Function

利用随机加权法构造非参数回归函数的随机加权统计量 ,证明了用随机加权统计量的分布去逼近原估计量的误差分布 ,其精度可达到 o( n- 1 /( d + 2 ) lnn Mn) ,a.s.,其中 0 <Mn→∞ .该结果可以用于构造未知回归函数 m( x)

In the paper, we apply random weighting methods to construct random weighting statistic for the unknown regression function m(x) and prove that the random weighting approximation can attain the accuracy of o(n -1/(d+2) ln n M n ),where 0< M n →∞. The confidence intervals of m(x) can be constructed by this result.