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"Estimating Aging Effects in Running Events," with Edward H. Kaplan, August 2017.
pdf file.


This paper uses world running records by age to estimate a biological frontier of decline rates. Two models are compared: a linear/quadratic (LQ) model and a nonparameteric model. Two estimation methods are used: 1) minimizing the squared difference between the observed records and the modeled biological frontier and 2) using extreme value theory to estimate the biological frontier that maximizes the probability of observing the existing world records by age. The results support the LQ model and suggest there is linear percentage decline up to the late 70's and quadradic decline after that. The extreme value estimates suggest that the true biological frontier is on average about 8 percent below the existing world records. The estimated age factors are also compared to the World Master Athletics (WMA) age factors. The two sets of age factors are close except at the old ages, where the WMA factors are noticeably smaller. Also, the WMA age factors do not meet an important biological constraint.