Probabilistic Foundations of Econometrics, part 3

This post is the third one of our series on the history and foundations of econometric and machine learning models. Part 2 is online here. Exponential family and linear models The Gaussian linear model is a special case of a large family of linear models, obtained when the conditional distribution of [latex]Y[/latex] (given the covariates) belongs to the exponential family[latex display="true"] f(y_i|\theta_i,\phi)=\exp\left(\frac{y_i\theta_i-b(\theta_i)}{a(\phi)}+c(y_i,\phi)\right) [/latex] ..