Emprical distribution for linear system identification
George Yin, Ben G Fitzpatrick, Kexin Yin · Stochastic Analysis and Applications · 1999
Asymptotic properties of empirical distributions of approximate errors for least squares identification are developed in this work. As a preparation, it is first shown that a law of large numbers type of result holds for the empirical distribution. Then a scaled sequence is proved to converge to a Gaussian process with a Brownian bridge component. These results are useful for carrying out statistical inference tasks, goodness of fit tests, and related matters