Point estimation

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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.

Point estimators[edit]

Bayesian point-estimation[edit]

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:

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:

Properties of point estimates[edit]

See also[edit]

Notes[edit]

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

Bibliography[edit]