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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" or "best estimate" of 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: such interval estimates are typically either confidence intervals in the case of frequentist inference, or credible intervals in the case of Bayesian inference.

- minimum-variance mean-unbiased estimator (MVUE), minimizes the risk (expected loss) of the squared-error loss-function.
- minimum mean squared error (MMSE)
- median-unbiased estimator, minimizes the risk of the absolute-error loss function
- maximum likelihood (ML)
- method of moments, generalized method of moments

Bayesian inference is 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:

- Posterior mean, which minimizes the (posterior)
*risk*(expected loss) for a squared-error loss function; in Bayesian estimation, the risk is defined in terms of the posterior distribution. - Posterior median, which minimizes the posterior risk for the absolute-value loss function.
- maximum a posteriori (
*MAP*), which finds a maximum of the posterior distribution; for a uniform prior probability, the MAP estimator coincides with the maximum-likelihood estimator;

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.^{[1]}^{[2]}^{[3]} Bayesian estimators are admissible, by Wald's theorem.^{[4]}^{[2]}

Special cases of Bayesian estimators are important:

Several methods of computational statistics have close connections with Bayesian analysis:

- Predictive inference
- Induction (philosophy)
- Philosophy of statistics
- Algorithmic inference
- Interval estimation

**^**Ferguson, Thomas S (1996).*A course in large sample theory*. Chapman & Hall. ISBN 0-412-04371-8.- ^
^{a}^{b}Le Cam, Lucien (1986).*Asymptotic methods in statistical decision theory*. Springer-Verlag. ISBN 0-387-96307-3. **^**Ferguson, Thomas S. (1982). "An inconsistent maximum likelihood estimate".*Journal of the American Statistical Association***77**(380): 831–834. doi:10.1080/01621459.1982.10477894. JSTOR 2287314.**^**Lehmann, E.L.; Casella, G. (1998).*Theory of Point Estimation, 2nd ed*. Springer. ISBN 0-387-98502-6.

- 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.