Bartlett adjustments for two-parameter exponential family models
In this paper we derive a general closed-form expression for the Bartlett correction for testing a scalar parameter of a two-parameter exponential family model. The correction has the advantage for algebraical and numerical purposes since it involves only trivial operations on suitably defined functions. The formula derived is general enough to cover many important and commonly used distributions. Simulations show that the corrected likelihood ratio tests have empirical sizes closer to the nominal size than the classical uncorrected tests.
exponential family bartlett correction chi-squared distribution likelihood ratio statistic rejection rate