Statistics and Operation Research Seminars 2000, Department of Economics, Pompeu Fabra University

• October 26, 17:30, Room 20.179, Jaume I. Peter J. Rousseeuw (Department of Mathematics and Computer Science, Universitaire Instelling Antwerpen, Belgium) The Deepest Regression Method
  Abstract: Deepest regression (DR) is a method for linear regression introduced by Rousseeuw and Hubert (1999). The DR method is defined as the fit with largest regression depth relative to the data. We will show that DR is a robust method, with breakdown value that converges almost surely to 1/3 in any dimension. We construct an approximate algorithm for fast computation of the DR in more than two dimensions. From the distribution of the regression depth we derive tests for the true unknown parameters in the linear regression model. Moreover, we construct confidence regions based on bootstrapped estimates. For bivariate datasets we use the maximal regression depth to construct a test for linearity versus convexity/concavity. We also extend the DR to polynomial regression. Finally, DR is applied to the Michaelis-Menten model of enzyme kinetics, where it resolves a long-standing ambiguity.
• Friday, November 3, 12:00, room 20.237, Jaume I. Karl Joreskog, University of Uppsala Factor Analysis of ordinal variables
  Abstract Theory and methodology or exploratory actor analysis have been well developed or continuous variables In practice, observed or measured variables are of ten ordinal How-ever, ordinality is most of ten ignored and numbers such as 1, 2, 3, 4, representing ordered categories, are treated as numbers having metric properties, a procedure which is incorrect in several ways In this paper we describe our approaches to actor analysis of ordinal variables which take proper account of ordinality and compare three of them with respect to parameter estimates and fit The comparison is made both in terms of their relative methodological advantages and in terms of an empirical data example and two generated data examples In particular, we discuss the issue of how to test the model and to measure model fit.
• Friday, November 10, 17:00, room 20.201, Jaume I. Anna Torres (UPF) A Note on the Dual Scaling of Dominance Data and its Relationship to Correspondence Analysis
  Abstract: Dual scaling of a subjects-by-objects table of dominance data (preferences, paired comparisons and successive categories data) has been contrasted with correspondence analysis, as if the two techniques were somehow different. In this note we show that dual scaling of dominance data is equivalent to the correspondence analysis of a table which is doubled with respect to subjects. We also show that the results of both methods can be recovered from a principal components analysis of the undoubled dominance table which is centred with respect to subject means.
• Thursday, January 18, 17:30, room 20.023, Jaume I. Michael Wolf (Univesidad Carlos III) Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection
  Abstract: This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our shrinkage estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multi-factor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing estimators, including multi-factor models.
• Thursday, May 31, 17:30, room 20.137 F. Udina (UPF) Estimating parliamentary composition through electoral polls (joint work with Pedro Delicado, UPC)
  ABSTRACT: Any electoral system has an electoral formula that converts vote proportions into parliamentary seats. Pre-electoral polls usually focus on estimating vote proportions and then applying the electoral formula to give a forecast of the parliament's composition. We here describe the problems arising from this approach: there is always a bias in the forecast. We study the origin of the bias and some methods to evaluate and to reduce it. We propose some rules to compute the sample size required for a given forecast accuracy. We show by Monte Carlo simulation the performance of the proposed methods using data from Spanish elections in last years. We also propose graphical methods to visualize how electoral formulae and parliament forecasts work (or fail).
• Friday, June 15, 10:00, room 20.237 Andreas Gottschling (Washington State University), Christian Haeffke (UPF), and Halbert White (UCSD) Closed form integration of artificial neural networks with some applications to finance
  Abstract: Many economic and econometric applications require the integration of functions lacking a closed form antiderivative, which is therefore a task that can only be solved by numerical methods. We propose a new family of probability densities that can be used as substitutes and have the property of closed form integrability. This is especially advantageous in cases where either the complexity of a problem makes numerical function evaluations very costly, or fast information extraction is required for time-varying environments. Our approach allows generally for nonparametric maximum likelihood density estimation and may thus find a variety of applications, two of which are illustrated briefly: *) Estimation of Value at Risk based on approximations to the density of stock returns. *) Recovering risk neutral densities for the valuation of options from the option price -- strike price relation.