# What is the objective of maximum likelihood estimation?

I was reading in "Using Maximum Likelihood Estimation" from "Econometrics for Dummies", and here's what the author had to say: "The objective of maximum likelihood (ML) estimation is to choose values for the estimated parameters (betas) that would maximize the probability of observing the Y values in the sample with the given X values. This probability is summarized in what is called the likelihood function. " (Source: http://www.dummies.com/how-to/content/using-maximum-likelihood-ml-estimation.html)

He seems to be saying that we want to find the parameters that make Y most likely to occur given an X value, but I thought the objective might be to find the parameters that most likely reveal the true P(Y|X).

• The quote can only make sense in a certain context; not all MLE is for regression functions. Dec 2, 2015 at 21:28
• Jun 20, 2019 at 21:18

$$P(Y|X, \theta)$$ is a function relating the predictor variables $$X$$ and the output variables $$Y$$, parametrized by parameters $$\theta$$. Its functional form is chosen a priori and limits how close it can be to the "true" distribution (if such a "true" distribution exists at all): e.g., normal/Gaussian function can well approximate many distributions (gamma distribution, lognormal, etc.) but it will never reveal that the underlying distribution is not normal.