Point estimation in the context of "Estimator"

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⭐ Core Definition: Point estimation

In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population mean). 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. More generally, a point estimator can be contrasted with a set estimator. Examples are given by confidence sets or credible sets. A point estimator can also be contrasted with a distribution estimator. Examples are given by confidence distributions, randomized estimators, and Bayesian posteriors.

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Point estimation in the context of Likelihood

A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model. It is constructed from the joint probability distribution of the random variable that (presumably) generated the observations. When evaluated on the actual data points, it becomes a function solely of the model parameters.

In maximum likelihood estimation, the model parameter(s) or argument that maximizes the likelihood function serves as a point estimate for the unknown parameter, while the Fisher information (often approximated by the likelihood's Hessian matrix at the maximum) gives an indication of the estimate's precision.

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LINKED FROM (PARENTS)
← Likelihood
LINKS TO (CHILDREN)
Statistics → Statistical sample → Data → Point (geometry) → Parameter space → Parameter → Population mean → Estimator → Interval estimation → Confidence interval → Frequentist inference → Credible intervals → Bayesian inference → Confidence region → Credible interval → Confidence distribution → Randomised decision rule → Bayesian statistics →