An efficient estimator in statistics is one that achieves the lowest possible variance among all unbiased estimators for a parameter, making it the most precise estimator available. It adheres to the Cramér-Rao lower bound, which provides a benchmark for the minimum variance achievable by an unbiased estimator.

Efficient Estimator

efficient estimator

Statistics is the science of collecting, analyzing, interpreting, presenting, and organizing data to make informed decisions and predictions. It provides the tools to handle variability and uncertainty in data, enabling researchers and analysts to draw valid conclusions and insights from empirical evidence.

statistics

lowest possible variance

An unbiased estimator is a statistical tool used to estimate a population parameter, where the expected value of the estimator equals the true parameter value. This ensures that the estimator does not systematically overestimate or underestimate the parameter, making it a reliable tool for statistical inference.

unbiased estimators

most precise estimator

The Cramér-Rao lower bound provides a theoretical lower limit on the variance of unbiased estimators of a parameter, indicating the best precision that can be achieved by any estimator given the data. It is a fundamental result in estimation theory, enabling the assessment of estimator efficiency and guiding the development of optimal estimation techniques.

Cramér-Rao lower bound

benchmark for the minimum variance

minimum variance achievable

A parameter is a variable in a mathematical model or statistical analysis that is constant within a specific context but can vary across different scenarios. Parameters are crucial for defining the behavior of models and are often estimated from data to make predictions or infer relationships.

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