On the High-SNR Conditional Maximum-Likelihood Estimator Full Statistical Characterization

Abstract

In the field of asymptotic performance characterization of Conditional Maximum Likelihood (CML) estimator, asymptotic generally refers to either the number of samples or the Signal to Noise Ratio (SNR) value. The first case has been already fully characterized although the second case has been only partially investigated. Therefore, this correspondence aims to provide a sound proof of a result, i.e. asymptotic (in SNR) Gaussianity and efficiency of the CML estimator in the multiple parameters case, generally regarded as trivial but not so far demonstrated. Index TermsMaximum Likelihood, statistical efficiency, high Signal to Noise Ratio, array processing.

Conditional Maximum Likelihood of Three-Phase Phasor Estimation for μPMU in Active Distribution Networks

“…The minimum value isû = g, where g is the eigenvector corresponding to the minimum eigenvalue of the sample covariance matrixR [18].…”

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

“…The CRLB is not achieved asymptotically unless the used estimator is asymptotically efficient. For example, the maximum likelihood estimator (MLE) in [13] (with deterministic signals) asymptotically achieves the CRLB whereas the MLE in [14] (with random signals and finite snapshots) and the Capon algorithm in [15] do not achieve it.…”

Statistical resolution limit for the multidimensional harmonic retrieval model: hypothesis test and Cramér-Rao Bound approaches

“…In the following, CRB(δ) denotes the CRB for the parameter δ where the unknown vector parameter is given by [δ ϑ T ] T . Consequently, assuming that CRB(δ) exists (under H 0 and H 1 ), is well defined (see section "MSRL closed-form expression" for the necessary e and sufficient conditions) and is a tight bound (i.e., achievable under quite general/weak conditions [36,37]), thus the noncentral parameter '(P fa , P d ) is given by [[35], p. 239]…”