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This paper introduces reduced rank statistical processing to residual error linear predictive source coding. A reduced rank predictive weight vector is generated using the reduced order correlation kernel estimation technique (ROCKET). The results illustrate a significant reduction in the reconstruction error of a reduced rank filter when the residual error is corrupted by noise. The noise may be due to either quantization noise or channel noise. The analysis shows that a filter's impulse response determines the impact of noise on its signal reconstruction and it is the ability of the predictive filter to alter its impulse response as a function of rank, which improves its performance. The results are demonstrated on recorded speech data and compared with the conventional Levinson-Durbin algorithm. Finally it is interesting to note that the reason for this reduced rank performance gain is not related to limited training data for the predictive filter.