Empirical Distributions in Least Squares Estimation for Distributed Parameter Systems
نویسنده
چکیده
We consider the estimation of error distributions in least squares identiication of distributed parameter systems. Asymptotic properties of approximate error sequences are developed. In particular, we examine consistency and asymptotic normality of empirical estimates of the error distribution. The consistency obtained is analogous to the Glivenko-Cantelli theorem. For asymptotic normality, we establish that the normalized sequence of empirical distributions converges to a Gaussian random element, which is the sum of a stretched Brownian bridge plus another Gaussian process.
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