Relaxed Conditional Likelihood for Sparse Data Under a Rectangular Array Embedding

• Activity Number: 91 - High Dimensional Data, Causal Inference, Biostats Education, and More
• Type: Contributed
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: ENAR
• Author(s): Samuel Aiyedipe* and John Hanfelt
• Companies: Department of Biostatistics and Bioinformatics, Emory University and Emory University
• Keywords: Asymptotic; Asymptotic bias; Asymptotic mean square error; Nuisance parameters; Sparse data; Stratified bootstrap

Abstract

In a rectangular array asymptotic setting, fully unconditional inference often results in high bias. Fully conditional inference provides a reasonable alternative when complete sufficient statistics exist for the nuisance parameter. If the sufficient statistics are not complete, However, conditional inference often results in a loss of efficiency. To deal with this problem, Hanfelt and Wang (2014) proposed the simple relaxed conditional likelihood method. The simple relaxed conditional method performs adequately provided the data are not too sparse, but unfortunately yields a suboptimal point estimator and offers no means to conduct hypothesis tests. We propose a bootstrap estimator of the optimal relaxation index, and two large-sample hypothesis tests motivated by rectangular array asymptotic considerations. A simulation study demonstrates that, in medium-sized samples, the optimal relaxed conditional likelihood approach yields better inferences than the simple relaxed conditional method and the fully conditional method.