Point estimation

In statistics, point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" for an unknown (fixed or random) population parameter.

More formally, it is the application of a point estimator to the data.

In general, point estimation should be contrasted with interval estimation.

Point estimation should be contrasted with general Bayesian methods of estimation, where the goal is usually to compute (perhaps to an approximation) the posterior distributions of parameters and other quantities of interest. The contrast here is between estimating a single point (point estimation), versus estimating a weighted set of points (a probability density function). However, where appropriate, Bayesian methodology can include the calculation of point estimates, either as the expectation or median of the posterior distribution or as the mode of this distribution.

In a purely frequentist context (as opposed to Bayesian), point estimation should be contrasted with the specific interval estimation calculation of confidence intervals.

Routes to deriving point estimates directly

• maximum likelihood (ML)
• method of moments, generalized method of moments
• minimum mean squared error (MMSE)
• minimum variance unbiased estimator (MVUE)
• best linear unbiased estimator (BLUE)

Routes to deriving point estimates via Bayesian Analysis

• maximum a posteriori (MAP)
• particle filter
• Markov chain Monte Carlo (MCMC)
• Kalman filter
• Wiener filter

Properties of Point estimates

• bias of an estimator
• Cramér-Rao bound

Bibliography

• Bickel, Peter J. and Doksum, Kjell A. (2001). Mathematical Statistics: Basic and Selected Topics. I (Second (updated printing 2007) ed.). Pearson Prentice-Hall. 
• Lehmann, Erich (1983). Theory of Point Estimation. 
• Liese, Friedrich and Miescke, Klaus-J. (2008). Statistical Decision Theory: Estimation, Testing, and Selection. Springer.