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Abstract:
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Capture-recapture models are used to estimate sizes of finite populations, with substantial applications in analyses of survey and/or census data. Most of these methods rely on logistic regression models to provide weighting schemes. However, the nonlinear approaches to estimation may not produce stable estimators. Power transformations are explored as a method to reduce the impact of unstable estimators on model selection. While these transformations can provide a better set of covariates, they can also introduce nonlinearities, leading to non-identifiable parameterizations. This paper proposes a big-data approach to address these issues via a quasi-optimal estimation of power transformations. These transformations are then computed over corresponding covariates and, finally, used in fully specified logistic models that provide capture-recapture weights for each data record. Simulation analyses, as well as results from a case study based on data from the 2017 U.S. Census of Agriculture, are used to discuss statistical improvements.
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