Generalized Method of Moments and Generalized Estimating Functions Based on Probability Generating Function for Count Models

Generalized method of moments based on probability generating function is considered. Estimation and model testing are unified using this approach which also leads to distribution free chi-square tests. The estimation methods developed are also related to estimation methods based on generalized estimating equations but with the advantage of having statistics for model testing. The methods proposed overcome numerical problems often encountered when the probability mass functions have no closed forms which prevent the use of maximum likelihood (ML) procedures and in general, ML procedures do not lead to distribution free model testing statistics.

Generalized Method of Moments and Generalized Estimating Functions Using Characteristic Function

GMM inference procedures based on the square of the modulus of the model characteristic function are developed using sample moments selected using estimating function theory and bypassing the use of empirical characteristic function of other GMM procedures in the literature. The procedures are relatively simple to implement and are less simulation-oriented than simulated methods of inferences yet have the potential of good efficiencies for models with densities without closed form. The procedures also yield better estimators than method of moment estimators for models with more than three parameters as higher order sample moments tend to be unstable.

Optimal Transportation-entropy Inequalities for Several Usual Distributions on R

In this paper, based on the recent results of Cozlan and Leonard we give optimal transportation- entropy inequalities for several usual distributions on R, such as Bernoulli, Binomial, Poisson, Gamma distributions and infinitely divisible distributions with positive or negative jumps.

Guardband Analysis for Distributed OFDMA with User Heterogeneity

This paper presents an in-depth analysis of the interference strength and required guardband width between coexistent users for distributed orthogonal frequency division multiple access （OFDMA）. In dynamic spectrum access networks, the cross-band interference between spectrally adjacent users is considered harmful with frequency guardbands inserted between spectrum blocks to eliminate the interference. However, the strength of the cross-band interference depends heavily on the user heterogeneity in different OFDM configurations. The cross-band interference due to the three user heterogeneity artifacts of power heterogeneity, sampling rate heterogeneity, and symbol length heterogeneity is investigated to determine the required guardband width. Analytical and simulation results show that the greater user heterogeneity requires larger guardbands with the sampling rate heterogeneity having the greatest effect. These results can be used to assist the design of spectrum allocation strategies.

A geometric interpretation of the transition density of a symmetric Lévy process

We study for a class of symmetric Levy processes with state space R^n the transition density pt（x） in terms of two one-parameter families of metrics, （dt）t〉o and （δt）t〉o. The first family of metrics describes the diagonal term pt （0）; it is induced by the characteristic exponent ψ of the Levy process by dr（x, y） = √tψ（x - y）. The second and new family of metrics 6t relates to √tψ through the formula exp（-δ^2t（x,y））=F[e^-tψ/pt（0）]（x-y）,where Y denotes the Fourier transform. Thus we obtain the following ＂Gaussian＂ representation of the tran- sition density： pt（x） = pt（O）e^-δ^2t（x,0） where pt（O） corresponds to a volume term related to √tψ and where an ＂exponential＂ decay is governed by 5t2. This gives a complete and new geometric, intrinsic interpretation of pt（x）.