What is "mathematical statistics"

n. (context statistics English) The study of statistics from a purely mathematical standpoint, using probability theory, measure theory, linear algebra and analysis.

Mathematical statistics is the application of mathematics to statistics, which was originally conceived as the science of the state — the collection and analysis of facts about a country: its economy, land, military, population, and so forth. Mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure-theoretic probability theory.