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Conditional behavior of confidence intervals

1994
Journal Articles

Résumé

This paper studies conditional properties of equivariant confidence intervals of a location parameter. The probability of covering the true value of the location parameter conditional on the location-and-scale configuration is computed. Also, the asymptotic distribution of this coverage probability is derived. Finally, the resulting expressions are applied to various confidence bounds such as the Wilcoxon, the Student $t$ and the Cauchy likelihood bound.

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1994
Journal Articles

Résumé

Source officielle

Concepts associés (32)

Statistical parameter

In statistics, as opposed to its general use in mathematics, a parameter is any measured quantity of a statistical population that summarises or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution, for example the normal distribution, then a small set of parameters can be measured which completely describes the population, and can be considered to define a probability distribution for the purposes of extracting samples from this population.

Credible interval

In Bayesian statistics, a credible interval is an interval within which an unobserved parameter value falls with a particular probability. It is an interval in the domain of a posterior probability distribution or a predictive distribution. The generalisation to multivariate problems is the credible region. Credible intervals are analogous to confidence intervals and confidence regions in frequentist statistics, although they differ on a philosophical basis: Bayesian intervals treat their bounds as fixed and the estimated parameter as a random variable, whereas frequentist confidence intervals treat their bounds as random variables and the parameter as a fixed value.

Coverage probability

In statistics, the coverage probability, or coverage for short, is the probability that a confidence interval or confidence region will include the true value (parameter) of interest. It can be defined as the proportion of instances where the interval surrounds the true value as assessed by long-run frequency. The fixed degree of certainty pre-specified by the analyst, referred to as the confidence level or confidence coefficient of the constructed interval, is effectively the nominal coverage probability of the procedure for constructing confidence intervals.

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Publications associées (2)

Conditional behavior of confidence intervals

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