STATISTICS COLLOQUIUM
Chuan-Fa Tang
Assistant Professor
Department of Mathematical Sciences
University of Texas at Dallas
Taylor's law for semivariance and higher moments of heavy-tailed distributions
Abstract
The power law relates the population mean and variance is known as Taylor's law, proposed by Taylor in 1961. We generalize Taylor's law from the light-tailed distributions to heavy-tailed distributions with infinite mean. Instead of population moments, we consider the power-law between the sample mean and many other sample statistics, such as the sample upper and lower semivariance, the skewness, the kurtosis, and higher moments of a random sample. We show that, as the sample size increases, the preceding sample statistics increase asymptotically in direct proportion to the power of the sample mean. These power laws characterize the asymptotic behavior of commonly used measures of the risk-adjusted performance of investments, such as the Sortino ratio, the Sharpe ratio, the potential upside ratio, and the Farinelli-Tibiletti ratio, when returns follow a heavy-tailed nonnegative distribution. In addition, we find the asymptotic distribution and moments of the number of observations exceeding the sample mean. We propose estimators of tail-index based on these scaling laws and the number of observations exceeding the sample mean and compare these estimators with some prior estimators.
Bio: Dr. Chuan-Fa Tang is an Assistant Professor in the Department of Mathematical Sciences at the University of Texas at Dallas. His research interests include order-restricted inference, shaped-constrained inference, empirical processes, empirical likelihood, survival analysis, mathematical statistics, image processing, kernel smoothing, and model selection. Dr. Tang received his PhD in Statistics from the
University of South Carolina in 2017.
Wednesday, April 20, 2022
4:00 pm EDT, 1-hour duration
Join by meeting number | Meeting number (access code): 2624 258 0310 | Meeting password: MsC65M2X6U2 |
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For more information, contact: Tracy Burke at tracy.burke@uconn.edu