Approximation of statistics distribution by convolutions of generalized Poisson measures

This article considers goodness-of-fit tests for bivariate INAR and bivariate Poisson autoregression models. The test statistics are based on an L2-type distance between two estimators of the probability generating function of the observations: one being entirely nonparametric and the second one being semiparametric computed under the corresponding null hypothesis. The asymptotic distribution of the proposed tests statistics both under the null hypotheses as well as under alternatives is derived and consistency is proved. The case of testing bivariate generalized Poisson autoregression and extension of the methods to dimension higher than two are also discussed. The finite-sample performance of a parametric bootstrap version of the tests is illustrated via a series of Monte Carlo experiments. The article concludes with applications on real data sets and discussion.

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Global existence of large solutions for the generalized Poisson–Nernst–Planck equations

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2021.124943 ◽

2021 ◽

Vol 498 (1) ◽

pp. 124943

Author(s):

Jihong Zhao

Keyword(s):

Global Existence ◽

Generalized Poisson ◽

Large Solutions

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On improvements of the order of approximation in the Poisson limit theorem

Journal of Applied Probability ◽

10.1017/s0021900200103808 ◽

1996 ◽

Vol 33 (01) ◽

pp. 146-155 ◽

Cited By ~ 1

Author(s):

K. Borovkov ◽

D. Pfeifer

Keyword(s):

Limit Theorem ◽

Random Variables ◽

Poisson Approximation ◽

Order Of Approximation ◽

Operator Semigroups ◽

Bernoulli Random Variables ◽

Usual Rate ◽

Poisson Limit ◽

Poisson Measures ◽

Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

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Asymptotic Expansions in the Exponent: a Compound Poisson Approach

Advances in Applied Probability ◽

10.1017/s0001867800028044 ◽

1997 ◽

Vol 29 (02) ◽

pp. 374-387 ◽

Cited By ~ 1

Author(s):

V. Čekanavičius

Keyword(s):

Asymptotic Expansion ◽

Large Deviations ◽

Poisson Distribution ◽

Asymptotic Expansions ◽

Compound Poisson ◽

Poisson Measures ◽

Poisson Approximations

The accuracy of the Normal or Poisson approximations can be significantly improved by adding part of an asymptotic expansion in the exponent. The signed-compound-Poisson measures obtained in this manner can be of the same structure as the Poisson distribution. For large deviations we prove that signed-compound-Poisson measures enlarge the zone of equivalence for tails.

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