Parametric Likelihood Inference for Record Breaking Problems
Abstract
In this paper we consider the analysis of record breaking datasets, where only observations that exceed (or only those that fall below) the current extreme value are recorded. Examples of application areas leading to data of this type include industrial stress testing, meteorological analysis, sporting and athletic events, and oil and mining surveys. The inherent missing data structure present in such problems leads to likelihood functions that contain possibly high-dimensional integrals, thus rendering traditional maximum likelihood methods difficult or infeasible. Fortunately, we may obtain arbitrarily accurate approximations to the likelihood function by iteratively applying Monte Carlo integration methods. Subiteration using the Gibbs sampler may help to evaluate any multivariate integrals encountered during this process. This approach enables a far more sophisticated set of parametric models than have been applied previously in record breaking contexts. In particular, we illustrate the methodology for a wide array of discrete and continuous distributional settings, and for observations that may be correlated and subject to mean shifts over time. Related issues in model selection and prediction are also addressed. Finally, we present two numerical examples. The first uses a generated dataset exhibiting a high degree of autocorrelation, while the second involves records in Olympic high jump competition....Gibbs sampler, Missing data, Monte Carlo approximant.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 09, 1993
- Accession Number
- ADA262546
Entities
People
- Alan E. Gelfand
- Bradley P. Carlin
Organizations
- Stanford University