@article { ISI:000280675100006,
	title = {Count data time series models based on expectation thinning},
	journal = {Stochastic Models},
	volume = {26},
	number = {3},
	year = {2010},
	pages = {PII 925211404},
	publisher = {Taylor \& Francis Inc},
	type = {article},
	abstract = {Motivated by modelling of unequally spaced count data time series, we propose the construction of a class of continuous-time first-order Markov processes based on the self-generalized expectation thinning operations. Properties of families of random variables leading to self-generalized expectation thinning operations are obtained. Characterization results are obtained for stationary marginal distributions, the innovation random variables and the infinitesimal innovation. The transition matrix and distribution of sojourn time are also derived. Particular families of self-generalized random variables are given to make the theory concrete for modelling count data that are overdispersed relative to Poisson. We also show that the self-generalizability condition is important in order to get nice properties for the Markov processes.},
	keywords = {Autoregressive, Birth-death process, Continuous-time Markov process, Expectation thinning, Generalized discrete self-decomposability, overdispersion, Self-generalizability, Sojourn time},
	issn = {1532-6349},
	doi = {10.1080/15326349.2010.498318},
	author = {Zhu, Rong and Joe, Harry}
}
@booklet {NSERC Canada; Hong Kong Polytechnic University; University of Saskatchewan},
	title = {A general family of limited information goodness-of-fit statistics for multinomial data},
	journal = {Dependence Modeling: Vine Copula Handbook},
	volume = {75},
	number = {3},
	year = {2010},
	month = {SEP},
	pages = {393-419},
	publisher = {Springer},
	type = {Article},
	chapter = {10},
	address = {Singapore},
	abstract = {Maydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009-1020, 2005; Psychometrika 71:713-732, 2006) introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are asymptotically chi-square. The new statistics need not be based on margins, and can be used for one-dimensional multinomials. We also provide theory that explains why limited information statistics have good power, regardless of sparseness. We show how quadratic-form statistics can be constructed that are more powerful than X (2) and yet, have approximate chi-square null distribution in finite samples with large models. Examples with models for truncated count data and binary item response data are used to illustrate the theory.},
	keywords = {categorical data analysis, cell-focusing, discrete data, item response theory, overdispersion, overlapping cells, Poisson models, quadratic form statistics, Rasch models, score test, sparse contingency tables, zero-inflation},
	issn = {0033-3123},
	doi = {10.1007/s11336-010-9165-5},
	url = {{http://www.worldscibooks.com/economics/7699.html doi = 10.1142/9789814299886,  @InCollectionCooke.Joe.ea2011},
	author = {Joe, Harry and Maydeu-Olivares, Alberto},
	editor = {Kurowicka, D. and Joe, H.}
}
@article { ISI:000239509800005,
	title = {Modelling count data time series with Markov processes based on binomial thinning},
	journal = {Journal of Time Series Analysis},
	volume = {27},
	number = {5},
	year = {2006},
	month = {SEP},
	pages = {725-738},
	publisher = {Blackwell Publishing},
	type = {Article},
	abstract = {We obtain new models and results for count data time series based on binomial thinning. Count data time series may have non-stationarity from trends or covariates, so we propose an extension of stationary time series based on binomial thinning such that the univariate marginal distributions are always in the same parametric family, such as negative binomial. We propose a recursive algorithm to calculate the probability mass functions for the innovation random variable associated with binomial thinning. This simplifies numerical calculations and estimation for the classes of time series models that we consider. An application with real data is used to illustrate the models.},
	keywords = {Binomial thinning, count data time series, discrete self-decomposability, higher order Markov dependence, overdispersion, time-varying mean},
	issn = {0143-9782},
	doi = {10.1111/j.1467-9892.2006.00485.x},
	author = {Zhu, Rong and Joe, Harry}
}
