Estimation Methods Based on Statistical Distances for Model Adequacy for Discrete and Mixed-Scale Data

• Activity Number: 386 - Nonparametric Modeling II
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 12:00 PM to 1:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Elisavet M Sofikitou* and Marianthi Markatou
• Companies: University at Buffalo, Department of Biostatistics and University at Buffalo, Department of Biostatistics, USA
• Keywords: mixed-scale data; Pearson residuals; disparity; Evidence functions; statistical distances; robustness

Abstract

Real world data-sets, especially the ones collected from clinical experience, are comprised of both interval/ratio scale measurements and categorical (ordinal/nominal) variables. However, the analysis of such mixed-type data is complicated. In this work, we introduce a method to obtain efficient and robust estimators. In particular, we present different formulations of Pearson residual systems, focusing on the mixed type case, to identify model misspecification as they compare the estimated, using data, model with the model assumed under the null hypothesis. We study their asymptotic properties, the robustness of minimum disparity estimators based on mixed-scale data and exemplify their performance via simulation. Evidence generation is also closely related to biomedical sciences. We use statistical distances to construct evidence function to check model adequacy/assessment and measure model misspesification cost. Finally, we introduce an explanatory plot, based on quadratic distances, to visualize the strength of evidence provided by the ratio of standardized quadratic distances.