Speaker: Seagle (Yang) Liu, UBC
Title: Lower quantile estimation with censored Weibull MLE (Slides)
Abstract: The lower quantile of wood strength is a critical quantity in the application of wood materials and its estimation is an important topic both in statistics and engineering. The parametric quantile estimate can be efficient but sensitive to model specification while the empirical quantile is model free but inefficient. The current industrial standard suggests obtaining the quantile estimate from a censored Weibull maximum likelihood estimate of the lower tail density, in which part of a complete data set will be subjectively censored. We have found that this subjective censored Weibull MLE actually trades efficiency under a Weibull model for additional accuracy under some mis-specified models, as Weibull distribution is flexible to approximate the left tail of some other distributions. To further improve the efficiency-accuracy trade-off, a bootstrap estimate of the mean squared error is proposed to select the optimal censoring threshold.