A large deviation approach to normality testing

A new approach to the classical problem of determining whether or not a set of data has been sampled from a univariate normal distribution is considered. The problem is posed in a pattern recognition framework and the concept of an asymptotically optimal expert is introduced. Some results of Large Deviation theory are used in the selection of experts so that their combined abilities lead to a suitable discrimination procedure. The fact that good asymptotical properties can be extended to finite samples with small sizes is the basis for the rest of the work. The performance of the proposed procedure is also compared to that of some known normality tests. An additional advantage of the procedure is the possibility of computing a reliable measure of support such as the Bayesian posterior probabilities as opposed to the P-values. Furthermore, some extra information can be obtained concerning the type of deviation from normality which is present in the data.