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Statistical Prediction of Future Sports Records Based on Record Values. STATS 2023. [DOI: 10.3390/stats6010008] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
Point prediction of future record values based on sequences of previous lower or upper records is considered by means of the method of maximum product of spacings, where the underlying distribution is assumed to be a power function distribution and a Pareto distribution, respectively. Moreover, exact and approximate prediction intervals are discussed and compared with regard to their expected lengths and their percentages of coverage. The focus is on deriving explicit expressions in the point and interval prediction procedures. Predictions and forecasts are of interest, e.g., in sports analytics, which is gaining more and more attention in several sports disciplines. Previous works on forecasting athletic records have mainly been based on extreme value theory. The presented statistical prediction methods are exemplarily applied to data from various disciplines of athletics as well as to data from American football based on fantasy football points according to the points per reception scoring scheme. The results are discussed along with basic assumptions and the choice of underlying distributions.
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Abstract
AbstractThe purpose of the paper is to provide a general method based on conditional quantile curves to predict record values from preceding records. The predictions are based on conditional median (or median regression) curves. Moreover, conditional quantiles curves are used to provide confidence bands for these predictions. The method is based on the recently introduced concept of multivariate distorted distributions that are used instead of copulas to represent the dependence structure. This concept allows us to compute the conditional quantile curves in a simple way. The theoretical findings are illustrated with a non-parametric model (standard uniform), two parametric models (exponential and Pareto), and a non-parametric procedure for the general case. A real data set and a simulated case study in reliability are analysed.
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Volovskiy G, Kamps U. Comparison of likelihood-based predictors of future Pareto and Lomax record values in terms of Pitman closeness. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1941112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
| | - Udo Kamps
- Institute of Statistics, RWTH Aachen University, Aachen, Germany
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Abstract
AbstractA spacings-based prediction method for future upper record values is proposed as an alternative to maximum likelihood prediction. For an underlying family of distributions with continuous cumulative distribution functions, the general form of the predictor as a function of the estimator of the distributional parameters is established. A connection between this method and the maximum observed likelihood prediction procedure is shown. The maximum product of spacings predictor turns out to be useful to predict the next record value in contrast to likelihood-based procedures, which provide trivial predictors in this particular case. Moreover, examples are given for the exponential and the Pareto distributions, and a real data set is analyzed.
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