Abstract
Inflated beta regression models bear practical applicability in modeling rates and proportions measured continuously in the presence of zeros and/or ones. In this article, the second-order bias of maximum likelihood estimators for zero-or-one inflated beta regression model parameters is derived. This enables one to obtain corrected estimators that are approximately unbiased. Numerical results exhibit that corrected estimators show better performance in terms of mean-square error and bias when compared to maximum likelihood estimators.
Highlights
Conventional estimation methods in statistical models may not be viable or appropriate in small samples
Through Monte Carlo simulations, we investigate the performances of maximum likelihood estimator (MLE) for the inflated beta regression model parameters and their corrected versions in finite-sized samples
We showed that the second-order biases obtained using the Cox and Snell (1968) formula may be written in terms of generalized least square regressions, which facilitates the calculation
Summary
Conventional estimation methods in statistical models may not be viable or appropriate in small samples. It is useful to obtain the second-order biases of MLEs, which allow us to evaluate the quality of the estimates and to obtain bias corrected estimates, for small and moderate sample sizes. This term will be used to define corrected estimators that have bias of order O(n−2).
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