Statistics of Statistical Experiments
Dmitri Koroliouk · 2020
This chapter examines two main problems of mathematical statistics: parameter estimation and hypothesis verification for the dynamic processes of statistical experiments. The statistical estimation of the drift parameter under additional conditions of statistical experiment wide-sense stationarity, is carried out in terms of covariances of two-component processes. The hypothesis verification for the dynamic statistical experiment process is reduced to statistical experiment classification, determined by the values of the drift parameter and the equilibria. The statistics of one-dimensional stationary statistical experiments is generalized on the MSE. The chapter considers the classification of evolutionary processes and demonstrates the analysis of complexity of the MSEs. It also considers the model of ternary statistical experiments with persistent linear regression and the presence of equilibrium states in terms of the main factor dynamics. The ternary model is considered in a deeper scheme of multivariate discrete stationary Markov diffusion.