Interval Estimation under Multiple Imputation: From Binary to Multinomial Data

Abstract

Missing data are common in medical studies, public health surveys, and social science research, and can substantially affect statistical inference. Multiple imputation is a widely used approach for handling incomplete data; however, constructing accurate confidence intervals under multiple imputation remains challenging, particularly for discrete data. This talk presents two recent methodological developments. In the first part, we study confidence interval construction for the means of discrete distributions, including binomial and Poisson models, in the presence of missing data. We propose modified multiple imputation confidence intervals that achieve improved coverage probabilities while maintaining shorter interval lengths compared with existing methods. In the second part, we extend the framework to multinomial data by developing simultaneous confidence intervals and confidence regions under multiple imputation. Both Wald and score approaches are considered, together with comparisons under homogeneous and heterogeneous settings. The results show that the proposed methods provide more reliable inference, especially in challenging scenarios such as boundary cases. Simulation studies and real data applications demonstrate the effectiveness of the proposed approaches. Overall, this work provides a unified framework for interval estimation under multiple imputation, bridging binary and general multinomial settings.

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