@article{77fda05ce83e439f84c3c63f7fe3a467,
title = "On the Use of Asymptotics in Detection and Estimation",
abstract = "We illustrate the importance of a finite dimensionality assumption when using functions of asymptotic statistics. We also note that asymptotic distributions need to converge uniformly to facilitate algebraic manipulations. Finally, we point to subtleties in using detection statistics stemming from the central limit theorem and Tylor series without entering the large deviations regime.",
author = "M. Garth and Yoram Bresler",
note = "Funding Information: Proofi The proof follows directly from a simplified version of Theorem 2.5 in [2]. 0 This theorem states that the limiting distribution of the function of a random sequence is simply the function applied to the limiting distribution of the sequence itself. This theorem undermines the heuristic argument put forward in the engineering detection literature Manuscript received January 4, 1995; revised November 6, 1995. This work was supported by a Phase I1 Small Business Innovation Research contract under NOSC contract no. N66001-91-C-7017 and by NSF Grant MIP-91-57377.T he associate editor coordinating the review of this paper and approving it for publication was Dr. Roger S. Cheng. The authors are with the Coordinated Science Laboratory, Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801 USA. Publisher Item Identifier S 1053-587X(96)03050-4.",
year = "1996",
doi = "10.1109/78.502350",
language = "English (US)",
volume = "44",
pages = "1304--1307",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "5",
}