Polygonal smoothing of the empirical distribution function

D. Blanke () and D. Bosq ()
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D. Blanke: Avignon University, LMA EA2151
D. Bosq: Sorbonne Université, CNRS, Laboratoire de Probabilités, Statistique et Modélisation, LPSM

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 2, No 2, 263-287

Abstract: Abstract We present two families of polygonal estimators of the distribution function: the first family is based on the knowledge of the support while the second addresses the case of an unknown support. Polygonal smoothing is a simple and natural method for regularizing the empirical distribution function $$F_n$$ F n but its properties have not been studied deeply. First, consistency and exponential type inequalities are derived from well-known convergence properties of $$F_n$$ F n . Then, we study their mean integrated squared error (MISE) and we establish that polygonal estimators may improve the MISE of $$F_n$$ F n . We conclude by some numerical results to compare these estimators globally, and also together with the integrated kernel distribution estimator.

Keywords: Distribution function estimation; Polygonal estimator; Cumulative frequency polygon; Order statistics; Mean integrated squared error; Exponential inequality; Smoothed processes; 62G05; 62G30; 62G20 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11203-018-9183-y

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