arXiv subjects

Hrishikesh D Vinod

Publications and source records attributed to Hrishikesh D Vinod.

2 recordsLinked to original sources

arXiv2025

New Axioms for Dependence Measurement and Powerful Tests

We build a context-free, comprehensive, flexible, and sound footing for measuring the dependence of two variables based on three new axioms, updating Renyi's (1959) seven postulates. We illustrate the superior footing of axioms by Vinod's (2014) asymmetric matrix of generalized correlation coefficients R*. We list five limitations explaining the poorer footing of axiom-failing Hellinger correlation proposed in 2022. We also describe a new implementation of a one-sided test with Taraldsen's (2021) exact density. This paper provides a new table for more powerful one-sided tests using the exact Taraldsen density and includes a published example where using Taraldsen's method makes a practical difference. The code to implement all our proposals is in R packages.

stat.ME↗

arXiv2022

Material Facts Obscured in Hansen's Modern Gauss-Markov Theorem

We show that the abstract and conclusion of Hansen's {\it Econometrica} paper, \cite{Hansen22}, entitled a modern Gauss-Markov theorem (MGMT), obscures a material fact, which in turn can confuse students. The MGMT places ordinary least squares (OLS) back on a high pedestal by bringing in the Cramer-Rao efficiency bound. We explain why linearity and unbiasedness are linked, making most nonlinear estimators biased. Hence, MGMT extends the reach of the century-old GMT by a near-empty set. It misleads students because it misdirects attention back to the unbiased OLS from beneficial shrinkage and other tools, which reduce the mean squared error (MSE) by injecting bias.

stat.ME↗