Renyi statistics in directed families of exponential experiments

Renyi statistics are considered in a directed family of general exponential models. These statistics are defined as Renyi distances between estimated and hypothetical model. An asymptotically quadratic approximation to the Re nyi Statistics is established, leading to similar asymptotic distribution r esults as established in the literature For the likelihood ratio statistics . Some arguments in favour of the Renyi statistics are discussed, and a num erical comparison of the Renyi goodness-of-fit tests with the Likelihood ra tio test is presented.