- Published 2006

If X is a random variable (or vector) with density or mass function fθ(x) that depends on a parameter θ, then the function fθ(X) viewed as a function of θ is called the likelihood function of θ. We often denote this function by L(θ). Note that L(θ) = fθ(X) is implicitly a function of X, but we suppress this fact in the notation. Since repeated references to the “density or mass function” would be awkward, we will use the term “density” to refer to fθ(x) throughout this chapter, even if the distribution function of X is not continuous. (Allowing noncontinuous distributions to have density functions may be made technically rigorous; however, this is a measure theoretic topic beyond the scope of this book.)

@inproceedings{2006Chapter8M,
title={Chapter 8 Maximum Likelihood Estimation 8 . 1 Consistency},
author={},
year={2006}
}