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Separable models occur frequently in spectral analysis, array processing, radar imaging and astronomy applications. Statistical inference methods for these models can be categorized in three large classes: parametric, nonparametric (also called “dense”) and semiparametric (also called “sparse”). We begin by discussing the advantages and disadvantages of each class. Then we go on to introduce a new semiparametric/sparse method called SPICE (a semiparametric/sparse iterative covariance-based estimation method). SPICE is computationally quite efficient, enjoys global convergence properties, can be readily used in the case of replicated measurements and, unlike most other sparse estimation methods, does not require any subtle choices of user parameters. We illustrate the statistical performance of SPICE by means of a line-spectrum estimation study for irregularly sampled data.