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Register a new userPoisson limit of an inhomogeneous nearly critical INAR(1) model
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An inhomogeneous first--order integer--valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound Poisson distribution.
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In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence in total variation distance, (ii) convergence of arbitrary moments, and (iii) pointwise convergence of Laplace transforms. Hence the nonparametric model P_d has similar properties as parametric models such as, for instance, the family of all d-variate Gaussian distributions.
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