Estimation

Estimation is the process of using observed data to infer the value of an unknown quantity. It appears across sciences and disciplines whenever direct measurement is difficult or impossible. Estimation combines data with a model of how data arise and yields a number, a range, or a distribution that is judged to be informative about the quantity of interest.

In statistics, estimation typically concerns a parameter of a population or a model. A point estimator supplies a single value as the best guess of the parameter, while interval estimation provides a range that is believed to contain the parameter with a stated probability. Estimators have properties such as bias (the difference between the expected estimator and the true value), variance, and mean squared error.

Common estimation methods include maximum likelihood estimation, which chooses parameter values that maximize the likelihood of the observed data; method of moments; and least squares in regression contexts. Bayesian estimation combines prior beliefs with data to form a posterior distribution, from which point estimates and credible intervals are derived.

The quality of estimation depends on the model and data quality. Properties such as unbiasedness, consistency, and efficiency are idealized targets in frequentist estimation, while robustness concerns arise when assumptions fail. Techniques such as bootstrapping or cross-validation help assess uncertainty and improve reliability.

Outside statistics, estimation also refers to rough or provisional calculations of quantities like cost, time, or resources, often using expert judgment, analogies, or formal estimation methods used in project management and engineering.