Estimatsioon

Estimatsioon is the process of inferring a population parameter from sample data. A parameter may describe the population mean, proportion, variance, or other characteristics. An estimation procedure yields an estimator, a rule that assigns a numerical value to data. Estimators can be point estimators, giving a single value, or interval estimators, which express uncertainty as a range (confidence intervals or credible intervals).

In statistics, common estimation methods include maximum likelihood estimation (MLE), method of moments, and Bayesian estimation. Least squares estimation is widely used in regression and related models. Estimation relies on sampling assumptions and models, and results depend on data quality and the correctness of the chosen model.

Key properties of good estimators include unbiasedness (the expected value equals the true parameter), consistency (estimates converge to the parameter as sample size grows), and efficiency (achieving the smallest possible variance). The Cramér-Rao bound provides a lower limit on the variance of unbiased estimators. In Bayesian estimation, uncertainty is represented by a posterior distribution rather than a single point value.

Examples include estimating the population mean with the sample mean, or estimating a proportion with the sample proportion, and constructing confidence or credible intervals to express uncertainty.

Estimatsioon is central to scientific research, data analysis, quality control, economics, and forecasting. It supports decision making under uncertainty but is subject to limitations: sampling error, potential bias, model misspecification, outliers, and small sample sizes can distort results. Good practice involves model checking, sensitivity analysis, and transparent reporting of methods and uncertainty.