ANALYTICAL STATISTICS

Author: MURILLO FERNÁNDEZ ALEX.
Year: 2003.
University: GRANADA [www.ugr.es].
Place of defense: UNIVERSIDAD DE GRANADA.
Place of preparation: FACULTAD DE CIENCIAS, UNIVERSIDAD DE GRANADA.

Summary: Given a set of incentives and an array of symmetrical dissimilarities among them, Unidimensional Scaling deal with the problem of representation mediantes points in a flood. The seemingly simple fact that in general and for any metrics Minkowski, the distance between two objects in this context is the absolute deviation between them on the single axis considered, creates a serious computer problem when it comes to minimizing the role of loss . This article presents an algorithm that uses Simulated Annealing in a new way, through a strategy based on a process that uses weighted alternating permutations and translations to locate the optimal configuration for least squares, or any other absolute deviations function loss. In addition, the algorithm is extended to deal with the problem of Multidimensional Scaling, so that both the distance and for the loss of function can be used any metrics Minkowski. Using an algorithm alternating basdo in permutations and translations based on SA was revealed as the estrtegia recommended for temaños array medium and large. Finally, it is known the close relationship between the techniques Cluster Analysis and Multidimensional Scaling, having been used in a complementary manner in the literature. However, the classification is optimal in the global space while MDS provides an optimal representation in the small space. This paper presents a model using Simulated Annealing allows simultaneously perform classification and MDS.

Author: VILASECA LLOBET JOSEP M..
Year: 2004.
University: BARCELONA [www.ub.es].
Place of defense: FACULTAD DE MEDICINA.
Place of preparation: FACULTAD DE MEDICINA.

Author: JIMÉNEZ TORRES FERNANDO.
Year: 2005.
University: ZARAGOZA [www.unizar.es].
Place of defense: FACULTAD DE CIENCIAS ECONÓMICAS Y EMPRESARIALES.
Place of preparation: FACULTAD DE CIENCIAS.

Summary: The financial ratios are one of the tools most often used in economic and financial analysis accounting for comparative studies, and in particular to analyze the relative position of a company in the market in which he operates, as well as their evolution long time. Two issues have been addressed very revelantes in the analysis of financial ratios: characterization of its dynamic evolution and synthesis of information provided by a set of financial ratios. The characterization of the process of dynamic development has been based on the analysis of partial adjustment model of Wu and Ho (1997) which discriminates between effects due to shocks that affect the entire market for those who only affect the company. In this area the most significant contributions were as follows: 1) The design and implementation of estimation techniques and contrast panel data models to the analysis of the randomness and homogeneity of the factors the model, based on developments made by Swamy (1970). The methodology has been applied to data from the database BACH, finding basically, that the speed of adjustment of some of the ratios analyzed depends on the specific country where the firm is located, generally reject the assumption that all countries surveyed have identical dynamics in the process of adjusting the ratios studied. 2) The construction of a hierarchical Bayesian model that weakens the hypothesis of equal these factors taken by Wu and Ho (1997), giving greater flexibility and realism to the model. To do so, has developed an algorithm to estimate the parameters of the model based on MCMC methods for make inferences about factors without having to resort to approximations asintóticas, and the development of predictions of future developments in the value of ratio for each company taking into account the uncertainty associated with the process of estimating the model. The methodology has been applied to data from the Central Bank Balances of Spain, which is mainly observed the component error correction which has major influence in almost all ratios studied. In relation to the synthesis of information provided by a set of financial ratios on the status of a company, has created a Bayesian approach to this problem based on the work of DeSarbo and others (1999), using a model of MDS. It has developed an algorithm to estimate the parameters based on MCMC methods that has been designed for the analysis of binary information that allows, in particular, selecting the number of underlying dimensions to the problem by applying Bayesian techniques for the selection and comparison of models. Given the problems existing in this identifiability parametric model, it has also proposed a method based on the rotation process ortogonalización Gram which facilitates the interpretation of biplots made. The methodology has been applied to data from the database COMPUSTAT, finding basically four dimensions synthesize the information provided by the set of ratios analyzed.