Limited and full information estimation and goodness-of-fit testing in 2n contingency tables

(WP 14/03 Clave pdf)High-dimensional contingency tables tend to be sparse and standard goodness-of-fit statistics such as X 2 cannot be used without pooling categories.As an improvement on arbitrary pooling, for goodness-of-fit of large 2 n contingency tables, we propose a class of quadratic form statistics based on the residuals of margins or multivariate moments up to order r.Further,the marginal residuals are useful for diagnosing lack of fit of parametric models.These classes of test statistics are asymptotically chi-square and have better small sample properties than X 2 .We show that these classes of test statistics have better power than X 2 for some useful multivariate binary models.