Rao-Blackwell Theorem and Minimum-Variance Unbiased Estimator

Flashcards covering key concepts related to the Rao-Blackwell Theorem and the properties of Minimum-Variance Unbiased Estimators.

Minimum Variance Unbiased Estimator (MVUE)

An estimator that is unbiased, consistent, and has the lowest variance among all unbiased estimators.

Sufficient Statistic

A statistic that summarizes all relevant information from the data about the parameter; the conditional distribution of the data given this statistic does not depend on the parameter.

Rao-Blackwell Theorem

A theorem that provides a method for improving an unbiased estimator by conditioning it on a sufficient statistic.

Unbiased Estimator

An estimator ˆθ for a parameter θ such that E( ˆθ) = θ.

Consistent Estimator

An estimator ˆθ that approaches the true parameter θ as the sample size n approaches infinity.

Likelihood Function

A function that gives the probability of observing the data given a specific parameter; often used to estimate parameters.

Factorization Criterion

A condition that allows the identification of sufficient statistics, stating that the likelihood can be factored into a product of functions where one depends only on the statistic and parameter.

Sample Mean

The average of the sample values, often used as an estimator for the population mean.

Variance

A measure of the dispersion or spread of a set of values; for an estimator, it refers to how much the estimates vary from the expected value.

Exponential Family

A class of probability distributions that has a specific form allowing for convenient mathematical treatment and includes distributions such as binomial, normal, and Poisson.