TY - JOUR
T1 - Uniform Convergence Of An Empirical Cdf Based On A Relatively Small Number Of Order Statistics
AU - Michalek, Joel E
PY - 1976/1/1
Y1 - 1976/1/1
N2 - An empirical distribution function Fm, defined on a subset of order statistics of a random sample of size n taken from the distribution of a random variable with continuous distribution function F, is shown to converge uniformly with probability one to F. Small sample distributions of the one and two sided deviations and the asymptotic normality of the standardized Fm are established. The relative efficiency of Fm as compared to the classical empirical distribution function is calculated and tabled-for n = 10, 20, 50, 100, 200.
AB - An empirical distribution function Fm, defined on a subset of order statistics of a random sample of size n taken from the distribution of a random variable with continuous distribution function F, is shown to converge uniformly with probability one to F. Small sample distributions of the one and two sided deviations and the asymptotic normality of the standardized Fm are established. The relative efficiency of Fm as compared to the classical empirical distribution function is calculated and tabled-for n = 10, 20, 50, 100, 200.
KW - asymptotic normality
KW - empirical distribution function
KW - one and two sided deviations
KW - relative efficiency
KW - selected order statistics
UR - http://www.scopus.com/inward/record.url?scp=84950176104&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84950176104&partnerID=8YFLogxK
U2 - 10.1080/03610927608827347
DO - 10.1080/03610927608827347
M3 - Article
AN - SCOPUS:84950176104
SN - 0361-0926
VL - 5
SP - 241
EP - 250
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
IS - 3
ER -