Asymptotic Properties of Least-Squares Estimates for Regression Coefficients

The asymptotic normality of least-squares estimates for the coefficients of a linear combination of stochastic functions is verified, along with the existence and convergence of the moments of the estimates. Estimates are formulated from observations of stochastic functions and a linear combination with additive “noise”. The stochastic functions and “noise” are assumed to be independent Gaussian processes.