Empirical Likelihood
- A nonparametric technique to estimate the likelihood of observed data when the underlying distribution is unknown.
- Produces empirical estimates (e.g., sample proportion or fitted regression parameters) from the observed data.
- Commonly used to construct confidence intervals around those estimates when standard likelihood methods are unsuitable.
Definition
Section titled “Definition”Empirical likelihood is a statistical method that is used to estimate the likelihood of a given set of observations. It is often used when the underlying distribution of the data is unknown or when the standard methods of likelihood estimation are not applicable.
Explanation
Section titled “Explanation”Empirical likelihood proceeds by using the observed data to form an empirical estimate of the quantity of interest (for example, a sample proportion or parameters from a fitted regression model). That empirical estimate is then used to construct a confidence interval, which represents the range of values the population quantity is likely to fall within given the observed data. The approach is particularly useful when one prefers not to assume a specific parametric form for the data-generating distribution or when traditional likelihood-based methods cannot be applied.
Examples
Section titled “Examples”Survey data: estimating a population proportion
Section titled “Survey data: estimating a population proportion”A researcher collects education levels from a random sample and calculates the observed proportion of individuals in the sample who have a college degree. That observed proportion serves as the empirical likelihood estimate of the population proportion. The researcher then uses this estimate to construct a confidence interval for the population proportion.
Regression models: estimating a relationship between variables
Section titled “Regression models: estimating a relationship between variables”A researcher fits a regression model to sample data (for example, income versus education level) to estimate the relationship between the variables. The fitted model parameters from the observed data provide empirical likelihood estimates, and the researcher constructs a confidence interval around the estimated relationship.
Use cases
Section titled “Use cases”- Estimation and inference when the underlying distribution of the data is unknown.
- Situations where standard likelihood estimation methods are not applicable.
Related terms
Section titled “Related terms”- Confidence interval
- Likelihood estimation
- Regression model