Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions

This paper studies the Minimum Divergence (MD) class of estimators for econometric models specified through moment restrictions. We show that MD estimators can be obtained as solutions to a computationally tractable optimization problem. This problem is similar to the one solved by the Generalized Empirical Likelihood estimators of Newey and Smith (2004), but it is equivalent to it only for a subclass of divergences. The MD framework provides a coherent testing theory: tests for overidentification and parametric restrictions in this framework can be interpreted as semiparametric versions of Pearson-type goodness of fit tests. The higher order properties of MD estimators are also studied and it is shown that MD estimators that have the same higher order bias as the Empirical Likelihood (EL) estimator also share the same higher order Mean Square Error and are all higher order efficient. We identify members of the MD class that are not only higher order efficient, but, unlike the EL estimator, well behaved when the moment restrictions are misspecified.Minimum divergence; GMM; Generalized empirical likelihood; Higher order efficiency; Misspecified models

Bayesian Likelihoods for Moment Condition Models

Bayesian inference in moment condition models is difficult to implement. For these models, a posterior distribution cannot be calculated because the likelihood function has not been fully specified. In this paper, we obtain a class of likelihoods by formal Bayesian calculations that take into account the semiparametric nature of the problem. The likelihoods are derived by integrating out the nuisance parameters with respect to a maximum entropy tilted prior on the space of distribution. The result is a unification that uncovers a mapping between priors and likelihood functions. We show that there exist priors such that the likelihoods are closely connected to Generalized Empirical Likelihood (GEL) methods.Moment condition; GMM; GEL; Likelihood functions; Bayesian inference

Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term

We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type L u + V u= 0, where L is a linear second order hypoelliptic operator and V belongs to a class of functions of Stummel-Kato type. We also obtain the existence of a Green function and an uniqueness result for the Cauchy-Dirichlet problem

Predicting loss in magnetic steels under arbitrary induction waveform and with minor hysteresis loops

We have studied ways of predicting power losses in soft magnetic laminations for generic time dependence of the periodic magnetic polarization J(t). We found that, whatever the frequency and the induction waveform, the loss behavior can be quantitatively assessed within the theoretical framework of the statistical loss model. The prediction requires a limited set of preemptive experimental data, depending on whether or not the arbitrary J(t) waveform is endowed with local slope inversions (i.e., minor hysteresis loops) in its periodic time behavior. In the absence of minor loops, such data reduce, for any peak polarization value Jp, to the loss figures obtained under sinusoidal J(t) at two different frequency values. In the presence of minor loops of semiamplitude Jm, the two-frequency loss experiment should be carried out for both peak polarization values Jp and Jm. Additional knowledge of the quasi-static major loop, to be used for modeling hysteresis loss, does improve the accuracy of the prediction method. A more general approach to loss in soft magnetic laminations is obtained in this way, the only limitation apparently being the onset of skin effect at high frequencie