In statistics, a confidence region is a multi-dimensional generalization of a confidence interval. For a bivariate normal distribution, it is an ellipse, also known as the error ellipse. More generally, it is a set of points in an n-dimensional space, often represented as a hyperellipsoid around a point which is an estimated solution to a problem, although other shapes can occur.
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Confidence region in the context of 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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