“The first principle is that you must not fool yourself — and you are the easiest person to fool.” — Richard Feynman
The covariance matrix is a fundamental object that appears frequently in econometrics. I review its definition and properties.
I derive the inverse covariance matrix and interpreting its elements.
Intuition for the perspective that linear regression is the process of approximating the conditional expectation function (CEF).
I motivate linear regression broadly as a way to estimate the conditional expectation function, describe the three perspectives on linear regression, and introduce the OLS estimator.
I walk through the basics of structural equation modeling, focusing on model specification and estimation.
Introducing frequentist statistical inference under the random sampling framework.
I describe point estimation under the frequentist framework and motivate the need for statistical models.
I introduce key concepts in hypothesis testing using the running example of the normal sampling model.
I provide a detailed treatment of the summary index used in Anderson (2008) for multiple inference.
Discussion of fundamental concepts in linear algebra, including vector spaces, linear combination and independence, basis vectors, and subspaces.
A detailed discussion of the linear regression model and the ordinary least squares (OLS) estimation method for its parameters.
MLE is one of the most important estimation principles in statistics and is widely used in econometrics. I introduce the concept and its properties in this post.
Building a mental framework for how data, models, inference, and probability come together.