@article{Iannario2014-,
title = {A theorem on CUB models for rank data},
author = {Maria Iannario and Domenico Piccolo},
url = {http://www.sciencedirect.com/science/article/pii/S0167715214001357},
issn = {0167-7152},
year = {2014},
date = {2014-08-31},
journal = {Statistics & Probability Letters},
volume = {91},
pages = {27-31},
publisher = { Elsevier B.V},
abstract = {We assume that m m items/objects/sentences have to be ordered by n n respondents according to a given criterion. This could refer to preference, quality, confidence, attractiveness, agreeableness, worry, concern, etc. In this case, the response of the i i th subject ( r i 1 , r i 2 , … , r i m ) , for i=1,2,…,n i = 1 , 2 , … , n , is a permutation of the first m m integers (Marden, 1995). Consequently, sample data can be considered as the realizations of a multivariate random variable ( R 1 , R 2 , … , R m ) spanned in a (m−1) ( m − 1 ) dimensional space since R 1 ...},
keywords = {CUB models, ordinal data models, Rank data},
pubstate = {published},
tppubtype = {article}
}

We assume that m m items/objects/sentences have to be ordered by n n respondents according to a given criterion. This could refer to preference, quality, confidence, attractiveness, agreeableness, worry, concern, etc. In this case, the response of the i i th subject ( r i 1 , r i 2 , … , r i m ) , for i=1,2,…,n i = 1 , 2 , … , n , is a permutation of the first m m integers (Marden, 1995). Consequently, sample data can be considered as the realizations of a multivariate random variable ( R 1 , R 2 , … , R m ) spanned in a (m−1) ( m − 1 ) dimensional space since R 1 ...

@article{Iannario2009,
title = {A comparison of preliminary estimators in a class of ordinal data models},
author = {Maria Iannario},
url = {http://www.vitaepensiero.it/scheda-articolo_digital/maria-iannario/a-comparison-of-preliminary-estimators-in-a-class-of-ordinal-data-models-999999_2009_0001_0024-151286.html},
issn = {1824-6672},
year = {2009},
date = {2009-01-01},
journal = {Statistica & Applicazioni},
volume = {VII},
number = {1},
pages = {25-44},
publisher = {Vita e Pensiero},
address = {Milan, Italy},
abstract = {In this paper, we propose several initial values for the EM algorithm of maximum likelihood estimates of the parameters in a class of models, called CUB, recently introduced for ordinal data. Specifically, we compare the algorithmic efficiency of each estimator with respect to a naive proposal through a vast simulation experiment. The results confirm a substantial gain in efficiency of the moments estimators over the whole parametric space. Then, some extensions are also discussed and several applications to real data sets are presented.},
keywords = {Maximum Likelihood Estimation, ordinal data models, Preliminary estimate},
pubstate = {published},
tppubtype = {article}
}

In this paper, we propose several initial values for the EM algorithm of maximum likelihood estimates of the parameters in a class of models, called CUB, recently introduced for ordinal data. Specifically, we compare the algorithmic efficiency of each estimator with respect to a naive proposal through a vast simulation experiment. The results confirm a substantial gain in efficiency of the moments estimators over the whole parametric space. Then, some extensions are also discussed and several applications to real data sets are presented.