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Title: Optimal estimation of the sparsity index in Poisson size-biased sampling Authors:  Laura Bondi - University of Cambridge and Bocconi University (United Kingdom) [presenting]
Marco Bonetti - Bocconi University (Italy)
Marcello Pagano - Harvard School of Public Health (United States)
Abstract: If the probability that an individual is in the sample is proportional to a size variable, then we have size-bias. For example, when studying cancer history via a Cancer Registry, then a large family will have a higher chance of representation in the registry. Another example of this bias is provided by a study of the plague that hit Europe in 1630. When modeling the internment process into a plague ward (lazzaretto), an infected member of a household results in the whole household being admitted to the ward. The sparsity index (reciprocal of the intensity) is a parameter of interest. With size biased sampling caution must be taken when choosing an estimator. We explore these two examples and compute the uniformly minimum variance unbiased estimator for the sparsity index in size-biased Poisson sampling. We propose two exact algorithms, which are computationally burdensome even for small sample sizes. As an alternative, a third, approximate algorithm based on the inverse fast Fourier transform, is presented. An exact confidence interval based on the optimal estimator is also proposed. The performance of the estimation procedure is compared to classical maximum likelihood inference, both in terms of mean squared error and average coverage and width of the corresponding confidence intervals.