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" 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

  • minimum-variance mean-unbiased estimator (MVUE), minimizes the risk (expected loss) of the squared-error loss-function.
  • best linear unbiased estimator (BLUE)
  • 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 point-estimation

    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:

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