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The least concave majorant of the empirical distribution function
Author(s) -
Carolan Christopher A.
Publication year - 2002
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315954
Subject(s) - pointwise , estimator , mathematics , empirical distribution function , concave function , function (biology) , distribution (mathematics) , distribution function , norm (philosophy) , statistics , mathematical analysis , geometry , physics , regular polygon , evolutionary biology , quantum mechanics , political science , law , biology
The author compares two estimators of a continuous, concave distribution function having support on the positive half line. In terms of samples from uniform distributions, he gives stochastic bounds for the pointwise and sup‐norm differences between the least concave majorant of the empirical distribution function and the underlying distribution function. He also offers evidence demonstrating the almost paradoxical result that the empirical distribution function is not as good an estimator as its least concave majorant in terms of sup‐norm error but a better pointwise estimator of the true distribution function in terms of mean squared error.