Models, Parameters, and Estimation

Abstract

The class of models to be discussed is a generalization of the multiple regression model. Observations y = y₁,…, y _n are assumed to be random samples from a specified distribution f(y|θ) where θ = θ₁,…, θ _p is a vector of parameters. The observations may be raw data or functions of raw data such as logarithms or proportions. The mean of the distribution, μ = E(y), also known as the vector of expectations, is often a function of one or more independent variables, x₁, x₂, etc., and the parameters. The distribution about the mean, referred to as the error distribution or random part of the model, may involve further parameters representing variances, correlations, or weight functions.