TY  - GEN
Y1  - 2015///
TI  - Statistical Inference for Discrete-Valued Stochastic Processes
ID  - heidok19048
N2  - Statistical inference and hypothesis testing in the framework of several different models for discrete-valued stochastic processes is considered. In the case of integer-valued autoregressive (INAR) processes of the first order, underlying stochastic properties can be utilized to derive appropriate test statistics for certain scenarios. Three different tests are introduced, evaluating the deviation of  empirical measures of dispersion, generalized autocovariance and skewness of the data set from the theoretical value using the explicitly calculated asymptotic distribution of the associated estimators. For each of these test statistics, simulation studies as well as real data applications are provided, showcasing the performance in small sample sizes. 

In a more general setting, a different approach focusing on generating functions instead of moment-based estimators is pursued. The asymptotic characteristics of the resultant test statistic are derived for a very general class of Markovian models satisfying a drift condition. Furthermore, a nonparametric estimator of the stationary distribution is shown to obey a functional central limit theorem. After revealing the connections linking this approach with several methods of the preceding chapters, a simulation study highlights the strong performance of the tests in real data applications with a small number of observations.

As a further topic, one specific instance of a nonparametric estimator of the service time distribution of a discrete time GI/G/? queueing system is presented, where the given information is assumed to be limited to the counts of arriving and departing customers of the queue. It is shown that this so-called sequence of differences estimator obeys a functional central limit theorem on an appropriately chosen underlying sequence space. Finally, a moving block bootstrap method is proposed and the theoretical features of this approach are investigated.
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/19048/
AV  - public
A1  - Schweer, Sebastian
ER  -