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Maximum Likelihood Estimator Under a Misspecified Model With High Signal-to-Noise Ratio

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2 Author(s)
Quan Ding ; Dept. of Electr., Comput. & Biomed ical Eng., Univ. of Rhode Island, Kingston, RI, USA ; Steven Kay

It is well known that the maximum-likelihood estimator (MLE) under a misspecified model converges to a well defined limit and it is asymptotically Gaussian as the sample size goes to infinity. In this correspondence, we consider a misspecified model with deterministic signal embedded in Gaussian noise and fully characterize the asymptotic performance of the MLE under this misspecified model with high signal-to-noise (SNR). We see that under some regularity conditions, it converges to a well defined limit and is asymptotically Gaussian with high SNR.

Published in:

IEEE Transactions on Signal Processing  (Volume:59 ,  Issue: 8 )