Year

2026

Season

Spring

Paper Type

Master's Thesis

College

College of Arts and Sciences

Degree Name

Master of Science in Mathematical Sciences (MS)

Department

Mathematics & Statistics

NACO controlled Corporate Body

University of North Florida. Department of Mathematics and Statistics

Committee Chairperson

Dr. Elena Buzaianu

Second Advisor

Dr. Ping Sa

Rights Statement

http://rightsstatements.org/vocab/InC/1.0/

Third Advisor

Dr. Fei Heng

Fourth Advisor

Dr. Peiyao Wang

Department Chair

Dr. Richard F. Patterson

College Dean

Dr. Kaveri Subrahmanyam

Abstract

Dunnett’s procedure is widely used for comparing multiple treatments with a control, but its application becomes challenging in the presence of missing data and multiple com- parisons. An improved Dunnett-type procedure addresses this by using multiple imputation under Rubin’s framework and constructing unified confidence intervals based on a multi- variate t distribution, allowing valid simultaneous inference while controlling the family-wise error rate (FWER). This work further extends the method by incorporating shrinkage-based variance estimation. Specifically, individual group variances are shrunk toward a common value to improve stability. This approach is particularly effective when group variances are similar or moderately different, as it reduces estimation variability, though it may intro- duce bias when variances differ substantially. Simulation results show that the proposed method maintains nominal joint coverage, preserves good precision as missingness increases, and achieves reliable FWER control. Overall, this approach provides a practical and robust extension of Dunnett-type inference for incomplete data.

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