APPLICATION OF TYPES OF CONVERGENCE OF RANDOM VARIABLES IN STATISTICAL ESTIMATION THEORY

This paper studies various types of convergence of sequences of random variables and their applications in mathematical statistics, particularly in the theory of statistical estimation. The concepts of convergence in probability, mean square convergence, and convergence in distribution are analyzed in relation to the consistency of estimators, the law of large numbers, and the central limit theorem. The practical importance of convergence theory in statistical methods is also discussed.