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Improved Estimation for a New Class of Parametric Link Functions in Binary Regression

Artur J. Lemonte () and Germán Moreno–Arenas
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Artur J. Lemonte: Universidade Federal do Rio Grande no Norte
Germán Moreno–Arenas: Universidad Industrial de Santander

Sankhya B: The Indian Journal of Statistics, 2020, vol. 82, issue 1, No 4, 84-110

Abstract: Abstract We develop nearly unbiased maximum likelihood estimators for a new class of asymmetric link functions proposed recently in the statistic literature by Lemonte and Bazán (TEST 27, 597–617 2018). These authors have introduced a broad class of parametric link functions in binary regression that contains as special cases both symmetric as well as asymmetric links. We discuss maximum likelihood estimation for the model parameters and derive a closed-form expression for the second order bias of these estimators. The second order bias can be easily computed as an ordinary weighted least-squares regression and is then used to define bias corrected maximum likelihood estimators. Monte Carlo simulation experiments are conducted in order to investigate the performance of the corrected estimators. The numerical results reveal that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Empirical applications are considered for illustrative purposes.

Keywords: Bias correction; Binary response model; Maximum likelihood estimation; Parametric link function; Primary 62F10; Secondary 62J12 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13571-018-0179-9

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