Deterministic Noises that can be Statistically Distinguished from the Random Ones
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Empirical measures generated by random sequences with deterministic and random noises have same asymptotic distributions provided that the noises have same asymptotic distributions (cf., Davydov and Zitikis, 2004, Proc. Am. Math. Soc. 132, 1203–1210). This phenomenon has raised an intriguing question about the possibility of distinguishing the two types of noises based only on their asymptotic distributions. In the present paper we suggest an answer to the question by considering asymptotic variances, and distributions, of the appropriately centered and normalized empirical measures and processes.
KeywordsEmpirical measures empirical processes weak convergence asymptotic normality deterministic noise random noise white noise
AMS Mathematics Subject Classifications 2000Primary 60F05 60H40 Secondary 62G10 62G20
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