estymatora

Estymatora is the Polish term for an estimator, the rule or function used to infer an unknown population parameter from sample data. In statistics, an estimator is typically a statistic or a mapping from the observed sample to a numerical value that serves as the best available guess for the true parameter.

Estimation can be categorized into point estimators and interval estimators. A point estimator yields a single value as the estimate of the parameter, such as the sample mean estimating the population mean. An interval estimator provides a range, such as a confidence interval, which aims to contain the true parameter with a stated probability.

Key properties used to evaluate estimators include bias, variance, and mean squared error. An unbiased estimator has an expected value equal to the true parameter. An estimator is consistent if it converges in probability to the parameter as the sample size grows. Efficiency concerns how much variance an estimator has relative to other unbiased estimators; commonly, lower variance is preferred. The mean squared error combines bias and variance: MSE = variance plus the square of the bias.

Common methods to construct estimators include maximum likelihood estimation (MLE), which uses the likelihood function to choose parameter values; the method of moments, which matches sample moments to population moments; and Bayesian estimation, which incorporates prior information.

Examples include the sample mean as an estimator of the population mean, the sample proportion as an estimator of a population proportion, and various MLEs for parameters under different distributions. Estimators are central to statistical inference but rely on model assumptions and data quality; misspecification or outliers can affect their performance.