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Fitting multidimensional parametric models in frequency domain using non-parametric noise models is considered in this paper. A non-parametric estimate of the noise statistics is obtained from a finite number of independent data sets. The estimated noise model is then substituted for the true noise covariance matrix in the maximum likelihood loss function to obtain suboptimal parameter estimates. Goal here is to present an analysis of the resulting estimates. Sufficient conditions for consistency are derived, and an asymptotic accuracy analysis is carried out. The first and second order statistics of the cost function at the global minimum point are also explored, which can be used for model validation. The analytical findings are validated using numerical simulation results.