Statistics for cross-sectional surveys : estimating total time In current state using only elapsed time to date

Abstract

As the number of openings for tenured academic positions has been stagnating over the last decades, postdoctoral appointments in the United States have become increasingly long and competitive. Knowledge of the total postdoc duration distribution for current postdocs is required to inform policy-makers and help them properly address related issues. This thesis studies a queueing approach to compute statistics of interest on the postdoc total duration distribution. Using a cross-sectional survey of individuals (postdocs) currently waiting in a queue, assumed to be operating in steady state, we wish to infer an accurate estimate of the probability distribution of a random individual's total time in that queue. The survey question asked to sampled individuals is: \How long have you been waiting in this queue?" A recent paper developed a probability-based solution to this problem [35], utilizing properties of longevity bias. This follow-up research investigates the practical implementation and statistical accuracy of the new method as a function of survey sample size, probability density function estimation technique, and properties of underlying distributions. We test several nonparametric estimation techniques and report results utilizing Monte Carlo simulations with both discrete and continuous distributions for several types of sampling. While this methodology applies to a wide range of problems, we purposely specialize the discussion to queues of postdocs in the United States. An example with NSF postdoc current career duration data is included to demonstrate the steps.