Theory
Estimation Theory
In my work trying to work through the proofs in Lin1 and Moran2, I’ve run into some confusion in parameter estimation. In this post, I’ll cover the relevant sections in...
Betting-Based Confidence Sequences
A colleague introduced me to some recent work from Waudby-Smith and Ramdas here at Carnegie Mellon. Since I’ve been working on applications of concentration bounds, it certainly seems important to...
Martingales
This post works through highlights of Aaditya Ramdas’ 2018 minicourse on martingales at Carnegie Mellon University1 with some supplemental information taken Durrett2 and some definitions from Wikipedia. Additional definitions are...
Measure Theory
My work has become much more technical that I am used to, so I thought it would be good to take some notes on basic measure and probability theory in...
Concentration Inequalities
In this post, I’m going to take myself through a review of standard concentration inequalities in probability theory with an ultimate goal of exploring empirical Bernstein bounds. Note: Not all...
One-Sided Score Test
In many cases, we may want to test the null hypothesis that a parameter is zero against a one-sided alternative (e.g. the parameter is non-negative). In this setting, we are...
Likelihood and Large-Sample Theory
The score test in non-standard conditions has been the motivation for much of my reading these past few months. However, it has led me to wonder about the small details...