Nonparametric maximum likelihood estimation of general mixture models pioneered by the work of Kiefer and Wolfowitz (1956) has been recently reformulated as an exponential family regression spline problem in Efron (2016). Both approaches yield a low dimensional estimate of the mixing distribution, g-modeling in the terminology of Efron. Some casual empiricism suggests that the Efron approach is preferable when the mixing distribution has a smooth density, while Kiefer-Wolfowitz is preferable for discrete mixing settings. In the classical Gaussian deconvolution problem both maximum likelihood methods appear to be preferable to (Fourier) kernel methods. Kernel smoothing of the Kiefer-Wolfowitz estimator appears to be competitive with the Efron procedure for smooth alternatives.
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