Large Deviation Local Limit Theorems for Ratio Statistics

Let {T„, n \u3e 1} be an arbitrary sequence of non-lattice random variables and {Sn, n \u3e 1} be another sequence of positive non-lattice random variables. Let the two sequences be independent. Let Ø1n and Ø2n be the moment genereating functions of {Tn, n \u3e 1} and { Sn,n \u3e 1} respectively. Let {an} be a sequence of real numbers such that an —»• oo

Comparison of CART and discriminant analysis of morphometric data in foraminiferal taxonomy

Paleontologists use statistical methods for prediction and classification of taxa. Over the years, the statistical analyses of morphometric data are carried out under the assumption of multivariate normality. In an earlier study, three closely resembling species of a biostratigraphically important genus Nummulites were discriminated by multi-group discrimination. Two discriminant functions that used diameter and thickness of the tests and height and length of chambers in the final whorl accounted for nearly 100% discrimination. In this paper Classification and Regression Tree (CART), a non-parametric method, is used for classification and prediction of the same data set. In all 111 iterations of CART methodology are performed by splitting the data set of 55 observations into training, validation and test data sets in varying proportions. In the validation data sets 40% of the iterations are correctly classified and only one case of misclassification in 49% of the iterations is noted. As regards test data sets, nearly 70% contain no misclassification cases whereas in about 25% test data sets only one case of misclassification is found. The results suggest that the method is highly successful in assigning an individual to a particular species. The key variables on the basis of which tree models are built are combinations of thickness of the test (T), height of the chambers in the final whorl (HL) and diameter of the test (D). Both discriminant analysis and CART thus appear to be comparable in discriminating the three species. However, CART reduces the number of requisite variables without increasing the misclassification error. The method is very useful for professional geologists for quick identification of species