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Parametric likelihood inference for record breaking problems

Publication ,  Journal Article
Carlin, BP; Gelfand, AE
Published in: Biometrika
September 1, 1993

SUMMARY: In this paper we consider the analysis of record breaking data sets, where only observations that exceed, or only those that fall below, the current extreme value are recorded. Example application areas include industrial stress testing, meteorological analysis, sporting and athletic events, and oil and mining surveys. A closely related area is that of threshold modelling, where the observations are those that cross a certain threshold value. The inherent missing data structure present in these problems leads to likelihood functions that contain possibly high-dimensional integrals, rendering traditional maximum likelihood methods difficult or not feasible. Fortunately, we may obtain arbitrarily accurate approximations to the likelihood function by iteratively applying Monte Carlo integration methods (Geyer & Thompson, 1992). Subiteration using the Gibbs sampler may help to evaluate any multivariate integrals encountered during this process. This approach can handle far more sophisticated parametric models than have been used previously in record breaking and threshold data contexts. In particular, the methodology allows for observations that are dependent and subject to mean shifts over time. We present a numerical example involving records in Olympic high jump competition, where besides estimation we also address related issues in model selection and prediction. © 1993 Biometrika Trust.

Duke Scholars

Published In

Biometrika

DOI

ISSN

0006-3444

Publication Date

September 1, 1993

Volume

80

Issue

3

Start / End Page

507 / 515

Related Subject Headings

  • Statistics & Probability
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics
 

Citation

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Carlin, B. P., & Gelfand, A. E. (1993). Parametric likelihood inference for record breaking problems. Biometrika, 80(3), 507–515. https://doi.org/10.1093/biomet/80.3.507
Carlin, B. P., and A. E. Gelfand. “Parametric likelihood inference for record breaking problems.” Biometrika 80, no. 3 (September 1, 1993): 507–15. https://doi.org/10.1093/biomet/80.3.507.
Carlin BP, Gelfand AE. Parametric likelihood inference for record breaking problems. Biometrika. 1993 Sep 1;80(3):507–15.
Carlin, B. P., and A. E. Gelfand. “Parametric likelihood inference for record breaking problems.” Biometrika, vol. 80, no. 3, Sept. 1993, pp. 507–15. Scopus, doi:10.1093/biomet/80.3.507.
Carlin BP, Gelfand AE. Parametric likelihood inference for record breaking problems. Biometrika. 1993 Sep 1;80(3):507–515.
Journal cover image

Published In

Biometrika

DOI

ISSN

0006-3444

Publication Date

September 1, 1993

Volume

80

Issue

3

Start / End Page

507 / 515

Related Subject Headings

  • Statistics & Probability
  • 1403 Econometrics
  • 0104 Statistics
  • 0103 Numerical and Computational Mathematics