Intensive comparative analysis of likelihood-based dimension reduction methods

In the realm of sufficient dimension reduction, traditional non-parametric inverse regression methods have been widely utilized. However, these methods come with inherent limitations, such as reduced flexibility in capturing complex relationships between variables. To address these shortcomings, various alternative approaches have been developed. This paper focuses on comparing two advanced methods of likelihood acquired directions (LAD) and unstructured principal fitted components (UPFC). While these methods share a common foundation in likelihood principles, they differ in several key aspects-including their theoretical foundation, model assumptions, treatment of the response variable, estimation procedures, interpretation of log-likelihood terms, and overall robustness. Numerical studies comparing their performance across a range of error structures reveal the distinct strengths and weaknesses of each method.