Introduction
A central object in asymptotic likelihood theory is the calculation of the second-order biases of the maximum likelihood estimates (MLEs). To improve the accuracy of these estimates, substantial effort has gone into computing the cumulants of log-likelihood derivatives which are, however, notoriously cumbersome. The MLEs typically have biases of order O(n − 1) for large sample size n, which are commonly ignored in practice, the justification being that they are small when compared to the standard errors of the parameter estimates that are of order \(O({n}^{-1/2})\). For small samples sizes, however, these biases can be appreciable and of the same magnitude as the corresponding standard errors. In such cases, the biases cannot be neglected, and for turning feasible estimation of their size in practical applications, corresponding formulae for their calculation need to be established for a wide range of probability distributions and regression models.
Bias correction has...
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Cordeiro, G.M. (2011). Bias Correction. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_145
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