# Likelihood Ratio Statistic

Encyclopedia
Edited by: Published: 2010

• ## Subject Index

The likelihood ratio statistic evaluates the relative plausibility of two competing hypotheses on the basis of a collection of sample data. The favored hypothesis is determined by whether the ratio is greater than or less than one.

To introduce the likelihood ratio, suppose that yOBS denotes a vector of observed data. Assume that a parametric joint density is postulated for the random vector Y corresponding to the realization yOBS. Let f(y; θ) represent this density, with parameter vector θ. The likelihood of θ based on the data yOBS is defined as the joint density: Although the likelihood and the density are the same function, they are viewed differently: The density f(y; θ) assigns probabilities to various outcomes for the random vector Y based on a fixed value ...

• All
• A
• B
• C
• D
• E
• F
• G
• H
• I
• J
• K
• L
• M
• N
• O
• P
• Q
• R
• S
• T
• U
• V
• W
• X
• Y
• Z

## Methods Map Research Methods

Copy and paste the following HTML into your website