Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 43, Issue 3 (1999), 489-499.
Maximum product of spacings method: A unified formulation with illustration of strong consistency
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.
Illinois J. Math., Volume 43, Issue 3 (1999), 489-499.
First available in Project Euclid: 19 October 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62F10: Point estimation
Secondary: 62G20: Asymptotic properties 62N05: Reliability and life testing [See also 90B25]
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