Where does estimator collide?

A fixed rule or function that takes a sample of data and returns a value meant to approximate an unknown quantity of the whole population, such as its true mean or variance. Fisher's 1922 On the mathematical foundations of theoretical statistics set out the modern framing, judging such rules by properties like consistency, efficiency, and sufficiency, and giving the method of maximum likelihood; the sample mean, for instance, is an estimator of the population mean. The referent here is a mathematical function of data, assessed by its long-run behaviour over many possible samples, not a tracking algorithm inside a moving machine or a person costing a building.[1]

Unit

A function from a data sample to a single estimated value of a parameter

Recovery means

Not applicable

Measured by

Judged by bias, variance, and mean squared error computed over the distribution of possible samples

An algorithm that reconstructs the hidden internal state of a moving dynamic system, such as the position and velocity of a vehicle, from a stream of noisy and incomplete measurements over time. Kalman's 1960 A New Approach to Linear Filtering and Prediction Problems gave the recursive filter that became the standard state estimator, blending each new reading with a running prediction to keep a best current guess; Luenberger's observer is a related deterministic version. The referent is a running computational process embedded in a system and updated as data arrive, not a one-off function scoring a static sample, and not a human role in a building trade.[2]

Unit

A recursive procedure that outputs a current best estimate of a system's state vector

Recovery means

Not applicable

Measured by

Evaluated by estimation error covariance and how quickly the estimate converges as measurements accumulate