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Given a univariate probabilty density function depending on a set of parameters, is there a generic method to estimate these parameters approximately without having to run the full (numerical) maximization of the likelihood given a dataset ?

In the simple case of estimating the mean and standard deviation of a Gaussian distribution, one can calculate the estimators for mean and standard deviation from the 'moments' of the dataset. Is there a generalization to arbitrary PDFs ? Are there methods based on basis function expansion (e.g. Fourier transform, Wavelet transform) to achieve this ?

(The original problem is to perform maximum likelihood parameter estimates with a large number of datasets with the same PDF. Computing coefficients related to the PDF only can therefore be expensive because they only have to be done once but computation of coefficients for each dataset should be fast)

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