Doctor of Philosophy / Department of Statistics / Paul Nelson / Panels of judges are often used to estimate consumer preferences for m items such as food products. Judges can either evaluate each item on several ordinal scales and indirectly produce an overall ranking, or directly report a ranking of the items. A complete ranking orders all the items from best to worst. A partial ranking, as we use the term, only reports rankings of the best q out of m items. Direct ranking, the subject of this report, does not require the widespread but questionable practice of treating ordinal measurement as though they were on ratio or interval scales. Here, we develop and study segmentation models in which the panel may consist of relatively homogeneous subgroups, the segments. Judges within a subgroup will tend to agree among themselves and differ from judges in the other subgroups. We develop and study the statistical analysis of mixture models where it is not known to which segment a judge belongs or in some cases how many segments there are. Viewing segment membership indicator variables as latent data, an E-M algorithm was used to find the maximum likelihood estimators of the parameters specifying a mixture of Mallow’s (1957) distance models for complete and partial rankings. A simulation study was conducted to evaluate the behavior of the E-M algorithm in terms of such issues as the fraction of data sets for which the algorithm fails to converge and the sensitivity of initial values to the convergence rate and the performance of the maximum likelihood estimators in terms of bias and mean square error, where applicable. A Bayesian approach was developed and credible set estimators was constructed. Simulation was used to evaluate the performance of these credible sets as confidence sets. A method for predicting segment membership from covariates measured on a judge was derived using a logistic model applied to a mixture of Mallows probability distance models. The effects of covariates on segment membership were assessed. Likelihood sets for parameters specifying mixtures of Mallows distance models were constructed and explored.

Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide.

Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide.

De nos jours, les propriétés sensorielles des matériaux font l'objet d'une attention croissante tant au point de vue hédonique qu'utilitaire. Notre thèse s'inscrit dans une recherche visant à établir les bases d'une approche métrologique instrumentale permettant la caractérisation des similarités visuelles entre textures «de même nature». Notre objectif spécifique a été de faire le lien entre une évaluation métrologique instrumentale des textures «lumineuses» produites par des surfaces texturées colorées et une évaluation basée sur des tests psychophysiques réalisés par des observateurs humains. Ces tests psychophysiques ont consisté en des épreuves de classement d'images texturées colorées biphasées suivant un critère de contraste visuel. Les données de classement collectées ont été analysées à l'aide de deux approches statistiques. La première considère l'ajustement d'un modèle factoriel à effets fixes aux statistiques des rangs moyens. La seconde approche est basée sur l'ajustement aux données d'une extension du modèle de Mallows-Bradley-Terry (MBT), sous-classe du modèle de Babington Smith. L'estimation des paramètres des modèles de MBT par le maximum de vraisemblance a été résolue à l'aide d'algorithmes MM et une évaluation par une méthode MCMC du vecteur des scores. Un test d'hypothèse basé sur une statistique du rapport de vraisemblance évaluée par une méthode de Monte Carlo a été proposé pour décider entre l'hypothèse de discernabilité perceptive des textures et celle de non discernabilité. Les résultats obtenus par les deux approches montrent que la qualité sensorielle de contraste visuel se présente bien comme un continuum sensoriel que l'on peut quantifier en construisant perceptivement une échelle de discernabilité.