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Fall 1999 Maximum product of spacings method: A unified formulation with illustration of strong consistency
Yongzhao Shao, Marjorie G. Hahn
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Illinois J. Math. 43(3): 489-499 (Fall 1999). DOI: 10.1215/ijm/1255985105


A simple unified formulation for generating an estimator of a univariate distribution (not necessarily continuous) is proposed. It is a variant of the maximum likelihood method and also a generalization of the maximum product of spacings (MPS) method for estimating continuous univariate distributions. The general formulation is then applied to monotone hazard rate families which arise frequently in applications. It is shown that any asymptotic MPS estimator for any family of distributions with monotone hazard rate is always strongly consistent (whether the setting is parametric or not). The MPS estimator of a distribution function with a monotone hazard rate can be derived explicitly and is asymptotically minimax for the Kolmogorov-Smirnov type loss functions.


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Yongzhao Shao. Marjorie G. Hahn. "Maximum product of spacings method: A unified formulation with illustration of strong consistency." Illinois J. Math. 43 (3) 489 - 499, Fall 1999.


Published: Fall 1999
First available in Project Euclid: 19 October 2009

zbMATH: 0932.62027
MathSciNet: MR1700604
Digital Object Identifier: 10.1215/ijm/1255985105

Primary: 62F10
Secondary: 62G20, 62N05

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign


Vol.43 • No. 3 • Fall 1999
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