This paper focuses on the consequences of assuming a wrong model for multinomial data when using minimum penalized ϕ -divergence, also known as minimum penalized disparity estimators, to estimate the model parameters. These estimators are shown to converge to a well-defined limit. An application of the results obtained shows that a parametric bootstrap consistently estimates the null distribution of a certain class of test statistics for model misspecification detection. An illustrative application to the accuracy assessment of the thematic quality in a global land cover map is included.
Keywords: asymptotic normality; bootstrap distribution estimator; consistency; goodness-of-fit; minimum penalized ϕ-divergence estimator; thematic quality assessment.