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NIASRA Seminar Series
November 15, 2018 @ 11:30 am - 12:30 pm
Advanced Modelling & Optimisation | Methodology Division | Australian Bureau of Statistics
Comparison of likelihood-based methods for size-biased sampling
This seminar explores three likelihood-based methods for estimating the rate parameter theta when a population is drawn from a gamma distribution and a sample is then drawn from the population using probability proportional to size sampling with replacement.
Estimators and anticipated variances are derived for three approaches: maximum likelihood estimation, sample likelihood and pseudo-likelihood. Simulation results will be presented, and the discussion will include a comparison of the performance of the three estimators for various combinations of sampling fractions and the shape parameter alpha. The sample likelihood and pseudo-likelihood approaches do not take into account the possibility of duplicate units being selected in the with-replacement sampling scheme, and this has an impact on the efficiency of the estimators even when the sampling fraction is not particularly large. It is possible to derive an explicit formula for the relative efficiency of the sample likelihood and pseudo-likelihood estimators for this example.
The simulation approaches used to obtain the results will be described, including the methods used to deal with cases when the original calculations became intractable in R.
After the seminar, NIASRA will sponsor coffee at The Yard for the audiences. All welcome!