About the orthogonal relations in the statistical estimation

. Let X, Y ∈ L2 (Ω, K, P) be a pair of random variables, where L2 (Ω, K, P) is the space of random variables with finite second moments. If we suppose that X is an observable random variable but Y is not, than we wish to estimate the unobservable component Y from the knowledge of observations of X using a linear or nonlinear function of them. In this paper, using some definitions and properties of the linear mean-square estimation as well as the orthogonality principle we present some implications of them in the statistical estimation.