Shih-Kang Chao

Shih-Kang Chao

Machine Learning Scientist

Blog posts

2021

On a variation of the Hausman test

2 minute read

Published:

In econometric, Hausman test is frequently used to test if two estimators are both consistent for an unknown model coefficient, under the condition that one estimator is more efficient than the other. In mathematical terms, suppose we have two estimators $\hat\beta_1$ and $\hat\beta_2$ for a model coefficient $\beta$, and $\hat\beta_1$ is asymptotically efficient (achieving the Cramer-Rao lower bound), according to Wikipedia, the testing statistics of the Hausman test is

2015

On Borel and Lebesgue measurability

3 minute read

Published:

Walter Rudin’s book is hard to read probably because of two characteristics in his style: he likes to start with great generality, and “sneak in” (well, every now and then) many important details/ideas in lemmas and theorems (even proofs), without explaining the ideas with extra text or example that under which context they are important (again, every now and then). Here I would like to make a comment on measure construction in his book “Real and Complex Analysis” (3 ed, 1986). The following numberings are from this book, unless otherwise stated.