SIGNATURE WORK
CONFERENCE & EXHIBITION 2023

This signature work is a literature review of applications of zonal polynomials in economic estimators through Wishart distribution. Definitions of zonal polynomials, mathematical proofs of k-class estimators, and literature of k-class estimators are presented in the paper. Zonal polynomials are important tools in multivariate analysis, particularly for representing power functions and deriving non‐central distributions for various multivariate tests. They are also widely applied statistics for expressing the movement of multivariate tests such as the likelihood ratio test and sphericity test and are receiving increasing attention in real‐life applications in engineering and physics. In econometrics, zonal polynomials are linked via the Wishart distribution, and are applied to k‐class estimators (Ordinary Least Square, Two‐Stage Least Square, and Limited Information Maximum Likelihood) which are distinguished from one another by taking different k value and Wishart random matrix. Due to the inconsistency and the bias‐variance trade‐off within these estimators, it is hard to rank one over another in different situations. Founded by Theil and Nagar, much research has aimed to derive the exact distribution of finite sample distributions and bias of these estimators, with a focus on extending and optimizing k value while doing bias reduction.