Illinois Journal of Mathematics

Maximum product of spacings method: A unified formulation with illustration of strong consistency

Yongzhao Shao and Marjorie G. Hahn

Full-text: Open access

Abstract

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.

Article information

Source
Illinois J. Math., Volume 43, Issue 3 (1999), 489-499.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255985105

Digital Object Identifier
doi:10.1215/ijm/1255985105

Mathematical Reviews number (MathSciNet)
MR1700604

Zentralblatt MATH identifier
0932.62027

Subjects
Primary: 62F10: Point estimation
Secondary: 62G20: Asymptotic properties 62N05: Reliability and life testing [See also 90B25]

Citation

Shao, Yongzhao; Hahn, Marjorie G. Maximum product of spacings method: A unified formulation with illustration of strong consistency. Illinois J. Math. 43 (1999), no. 3, 489--499. doi:10.1215/ijm/1255985105. https://projecteuclid.org/euclid.ijm/1255985105


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