Improved Score Tests for One-parameter Exponential Family Models

Under suitable regularity conditions, an improved score test was derived by Cordeiro and Ferrari (1991). The test is based on a corrected score statistic which has a chi-squared distribution to order 1/n under the null hypothesis, where n is the sample size. In this paper we follow their approach and obtain a Bartlett-corrected score statistic for testing the null hypothesis theta = theta_0 where theta is the scalar parameter of a one-parameter exponential family model and theta_0 is a real number. We apply our main result to a number of special cases and derive approximations for corrections that involve unusual functions. We also obtain Bartlett-type corrections for natural exponential families.