A class of robust power spectral estimation methods based on approximative moment matching is presented. Most methods for spectral estimation are based on asymptotic results that holds when the number of data points is large. In speech processing, where the number of data points is rather small, a maximum entropy based covariance matching method is the method of choice in most applications. If there is an underlying model generating the data, and the number of data points grows large, the moment matching method can be used to identify the generating model if  it lies in the considered model class. However, for generic data the situation is different; The estimated model should be a best approximation of the true generating system, and any estimate of the moments used for the matching will have errors since the data available is limited. To deal with this practical situation an approximative moment matching method based on convex optimization has been designed. In fact, a whole class of methods based on a similar approach have been developed. The moments that are matched can be covariances and cepstrum parameters, but also generalizations of these. The level of regularization can also be controlled by choosing a design parameter.