Estimating Model Discrepancy

Abstract A quantity, λ2 is defined as the discrepancy between an actual and an assumed statistical model. An estimator is developed for the case in which data are grouped. The estimator is based on Pearson's X 2 goodness-of-fit statistic, and permits comparisons of lack of fit among data sets having dissimilar sample sizes (N's) or numbers of bins (n's). Although is equivalent to X 2/N when N is large and n is fixed, it is less biased and has smaller variance than X 2/N. These effects are most pronounced in small samples and in sparse-data situations. Use and interpretation of as a data-analytic tool are discussed, and an example involving several sets of data from particle-scattering experiments is presented. KEY WORDS: Directed distance metricGoodness of fitParticle scatteringPearson's X 2 Power divergence statistic