Matematikostatistike

Matematikostatistike (mathematical statistics) is the branch of statistics that uses mathematical methods to study the principles and properties of statistical inference. It provides the theoretical framework for modeling randomness, designing procedures, and evaluating their performance under probabilistic assumptions.

The central problems are estimating population parameters, testing hypotheses, and making decisions under uncertainty. Mathematical statistics analyzes estimators and tests in terms of bias, variance, consistency, and efficiency, and studies how sampling distributions and probabilistic models affect the reliability of conclusions.

Common tools include point and interval estimation, maximum likelihood and Bayesian inference, and concepts of sufficiency, unbiasedness, and asymptotic efficiency. The field relies on probability theory, including limit theorems such as the law of large numbers and the central limit theorem, to derive properties of procedures as sample size grows.

Subfields cover parametric, nonparametric, and semi-parametric models, as well as decision theory, information theory, and computational methods such as bootstrap and Monte Carlo techniques to assess performance when exact analysis is difficult.

Applications span the natural and social sciences, engineering, and finance, where rigorous inference from data is essential. Matematikostatistike underpins the development of statistical methods used in data analysis, experimental design, and uncertainty quantification.