Likelihood
Score and Information - GLMMs
This post is just a catch-all for my derivations for my score test project. Our set-up is as follows. We have $n$ observations coming from $k$ different clusters, each of...
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...
Generalized Linear Mixed Models
This post is a primer on generalized linear mixed models (GLMM) and their associated estimation procedures. Throughout this post, we perform derivatives of matrices, vectors, and scalars. We denote all...
Generalized Linear Models
This post is a primer on generalized linear models and their associated estimation procedures. Set-Up Let’s assume we have covariate matrix, $\mathbf{X}$, response vector $\mathbf{y}$, and parameter (coefficient) vector, $\beta$,...
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...