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This paper presents a novel method for noise-compensated autoregressive estimation founded on the maximum-likelihood of the spectral samples. This framework yields a nonlinear optimization problem that can be revamped as a reweighted least-square problem. The resulting spectral weighting function turns out to be the square of the Wiener filter, this meaning that spectral regions with higher signal-to-noise ratio are more relevant in the estimation. Furthermore, this frequency-selective scenario allows us to interpret this problem as one of incomplete samples. From that perspective, an approximate accuracy bound for autoregressive analysis in noise is deduced. Simulated experiments prove the validity of the method foundations, showing as well the excellent performance of the numerical algorithm versus state-of-the-art techniques.