0-1回归的非参数区间估计

Nonparametric interval estimation of binary regressions

综合非参数方法和Bayes思想提出0-1回归的区间估计方法,并证明了该估计的均方收敛性.通过数值模拟,对各种不同情况下区间估计的覆盖率、相对覆盖率及区间长度进行了对比分析.结果表明:区间估计的效果与样本观测总量有关,样本观测总量越大,覆盖率的波动越稳定,区间长度越短,相对覆盖率也就越大.对于较小的样本量,所得的区间估计仍然具有较好的效果.

By combining nonparametric methods and Bayesian thoughts, a new interval estimator for binary regression is proposed. Its convergence properties in mean square are proved. By numerical simulation, we inspect and analyze the coverage rate, the relative coverage rate and the interval length in different conditions. The results show that the efficiency of interval estimation is affected by the total sample size. The larger the sample size is, the stabler the the coverage rate will be, the shorter the interval length, and the higher the relative coverage rate. The method also performs well with a smaller sample.