Nonparametric Kernel Estimation of Distribution Function Under Ranked Set Sampling
The ranked set sampling method is suitable for the situation where the sample measurement is difficult but the ranking is easy,and has been widely applied in clinical medicine,ecological environment,agriculture and forestry,and other fields.The distribution function is an important function in probability statistics.In order to improve the estimation efficiency of the distribution function of an unknown pop-ulation,this paper adopts the kernel estimation idea and the average rank method to construct a nonparametric estimator of the distribution function based on the ranked set sampling method.The new estimator is shown to have asymptotic unbiasedness,consistency,and uniformly strong consistency.The estimation efficiency is evalu-ated by the mean integrated square error of the estimator.The research results of asymptotic relative efficiency and simulated relative efficiency show that the estima-tion efficiency of the new estimator is higher than that of the corresponding estimator under simple random sampling,and as the sample size decreases,the relative advan-tage of the new estimator becomes more apparent.Finally,the application results of coniferous tree data further verify the correctness of the theoretical research results.
Ranked set samplingdistribution functionnonparametric kernel esti-mationmean integrated square error
万方数据
维普
