BARTLETT-TYPE CORRECTIONS FOR TWO-PARAMETER EXPONENTIAL FAMILY MODELS

ABSTRACT

Cordeiro and Ferrari[1] obtained a Bartlett-type correction to the score statistic that is given by a polynomial of second degree in the statistic itself with coefficients that depend on cumulants of log–likelihood derivatives. Although the corrected statistic has good size properties, it is not always a monotone transformation of the original statistic. Recently, some monotone transformations of the score statistic have been proposed as alternatives to the polynomial transformation. In this paper we derive simple formulae for various modified score statistics for testing a scalar parameter in two-parameter exponential models which do not require knowledge of cumulants. The formulae are readily applicable to cover many important and commonly used distributions and involve only trivial operations on certain functions and their derivatives.

Keywords:

• Bartlett-type correction
• Chi-squared distribution
• Exponential family
• Orthogonal parameters
• Score statistic

Acknowledgments