Point estimation


In statistics, point estimation involves the use of sample data to calculate a single value which is to serve as a "best guess" or "best estimate" of an unknown population parameter. More formally, it is the application of a point estimator to the data to obtain a point estimate.
Point estimation can be contrasted with interval estimation: such interval estimates are typically either confidence intervals, in the case of frequentist inference, or credible intervals, in the case of Bayesian inference.

Point estimators

There are a variety of point estimators, each with different properties.
Bayesian inference is typically based on the posterior distribution. Many Bayesian point estimators are the posterior distribution's statistics of central tendency, e.g., its mean, median, or mode:
The MAP estimator has good asymptotic properties, even for many difficult problems, on which the maximum-likelihood estimator has difficulties.
For regular problems, where the maximum-likelihood estimator is consistent, the maximum-likelihood estimator ultimately agrees with the MAP estimator.
Bayesian estimators are admissible, by Wald's theorem.
The Minimum Message Length point estimator is based in Bayesian information theory and is not so directly related to the posterior distribution.
Special cases of Bayesian filters are important:
Several methods of computational statistics have close connections with Bayesian analysis: