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In statistics, interval estimation is the use of sample data to estimate an interval of possible values of a parameter of interest. This is in contrast to point estimation, which gives a single value. [1] The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method). [2]
In statistics, a nuisance parameter is any parameter which is unspecified [1] but which must be accounted for in the hypothesis testing of the parameters which are of interest. The classic example of a nuisance parameter comes from the normal distribution , a member of the location–scale family .
A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean). Thus a "statistical parameter" can be more ...
In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. [1] For example, the sample mean is a commonly used estimator of the population mean. There are point and interval ...
In statistical estimation theory, 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.
When the theoretical distribution of a statistic of interest is complicated or unknown. Since the bootstrapping procedure is distribution-independent it provides an indirect method to assess the properties of the distribution underlying the sample and the parameters of interest that are derived from this distribution.
Conceptually, a confidence distribution is no different from a point estimator or an interval estimator (confidence interval), but it uses a sample-dependent distribution function on the parameter space (instead of a point or an interval) to estimate the parameter of interest. A simple example of a confidence distribution, that has been broadly ...