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Identifiability of a model for discrete frequency distributions with a multidimensional parameter space. (English) Zbl 1360.62112

The main aims of this paper are twofold. In the first part the authors shortly describe the problem of identifiability of a model for discrete frequency distributions with a multidimensional parameter space using the so-called CUB (combination of shifted binomial and discrete uniform variables) mixture models introduced recently by M. Iannario [Metron 68, No. 1, 87–94 (2010; Zbl 1301.62017)].
In the second part, being the most important contribution of this paper, a general approach described previously is applied to investigate the identifiability of nonlinear CUB (NLCUB) models. While CUB models fit rating and/or ranking data by means of a mixture of uniform and shifted binomial random variables, the main innovation of NLCUB models is that they can be used to model rating data with a non-constant intensity probabilities, i.e. probabilities moving from one rating to the next during the decision process. First, the authors discuss issues of parameter estimation of NLCUB models. Later, the conditions under which the models are identifiable are given. A short numerical study is included and several open issues are concisely discussed.

MSC:

62F99 Parametric inference
62E10 Characterization and structure theory of statistical distributions
62F10 Point estimation
62-07 Data analysis (statistics) (MSC2010)

Citations:

Zbl 1301.62017

Software:

CUB; catdata
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References:

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