On exactness and unbiasedness of confidence bands for a continuous distribution function  

作　　者：DING XiaoBo1,2,XU XingZhong2 & ZHAO ShuRan3 1Institute of Applied Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China 2Department of Mathematics,Beijing Institute of Technology,Beijing 100081,China 3School of Economics,Ocean University of China,Qingdao 266071,China 

出　　处：《Science China Mathematics》2010年第10期2665-2678,共14页中国科学：数学（英文版）

基　　金：supported by National Science Foundation for Post-doctoral Scientists of China (Grant No.20090450603);National Natural Science Foundation of China (Grant No.10771015)

摘　　要：We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed bands not belonging to the class,e.g.,the kernel smoothed bands.It is shown that under some mild assumptions,the simple bands with exact coverage for continuous distribution functions are all step bands.The unbiasedness problem of the step bands is also investigated.It is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.We define a class of confidence bands for distribution functions,named simple confidence bands.The class of bands includes the common step bands and continuous bands,some of which may perform better than the smoothed bands not belonging to the class,e.g.,the kernel smoothed bands.It is shown that under some mild assumptions,the simple bands with exact coverage for continuous distribution functions are all step bands.The unbiasedness problem of the step bands is also investigated.It is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.

关 键 词：exact coverage GOODNESS of fit kernel smoothing simple CONFIDENCE BANDS UNBIASEDNESS 

分 类 号：O211.3[理学—概率论与数理统计]