Abstract
Pearson residuals aid the task of identifying model misspecification because they compare the estimated, using data, model with the model assumed under the null hypothesis. We present different formulations of the Pearson residual system that account for the measurement scale of the data and study their properties. We further concentrate on the case of mixed-scale data, that is, data measured in both categorical and interval scale. We study the asymptotic properties and the robustness of minimum disparity estimators obtained in the case of mixed-scale data and exemplify the performance of the methods via simulation.
Highlights
Minimum disparity estimation has been studied extensively in models where the scale of the data is either interval or ratio (Beran [1], Basu and Lindsay [2])
The estimators can be viewed as an extension/generalization of the Maximum Likelihood Estimator (MLE)
Simpson [6] demonstrated that minimum Hellinger distance estimators fulfill desirable robustness properties and for this reason can be effective in the analysis of count data prone to outliers
Summary
Minimum disparity estimation has been studied extensively in models where the scale of the data is either interval or ratio (Beran [1], Basu and Lindsay [2]). It has been studied in the discrete outcomes case. If the measurement scale is interval/ratio, the Pearson residuals are modified to reflect and adjust for the discrepancy of scale between data, that are always discrete, and the assumed continuous probability model (see Basu and Lindsay [2]).
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