Seminari - Abstract
Conditional independence models for contingency tables: singularities and context specific restrictions
Antonio Forcina (University of Perugia)
There are independence models, even very simple ones, for whom, because of their underlying algebraic structure, the usual asymptotic approximations do not hold; in particular, the asymptotic distribution of the likelihood ratio is a mixture of chi-square variables. In the talk, after an elementary introduction to the subject and the discussion of a few examples, we outline an approach which could, intuitively, remove singularities by restricting certain conditional independence statements to hold only for a subset of the possible configurations of the conditioning variables. Without entering into the technical details required for a proof, we introduce certain conceptual tools which might be of interest on their own and be applied in other contexts, in particular: the mixed parameterisation of a discrete distribution, which combines marginal probabilities and log-linear parameters into a smooth mapping; an algorithm for the reconstruction of a joint distribution when an interaction defined in a previous marginal has to be constrained again; some basic results from the fixed point theory from numerical analysis which may be used to establish whether, under suitable conditions, an algorithm converges to a unique solution irrespective of the starting point.
Missing data Analysis: Basic Concepts and Some Theory
Issues in Missing Data Problems: Sensitivity to Assumptions
Donald Rubin (Harvard)
From the blackboard to the trading floor: how to construct and assess trading strategies using multivariate dynamic probabilistic models
Fabio Rigat (University of Warwick)
Algorithmic trading is now the main operational mode of large hedge funds, to the extent that the interaction among different semi-automatic trading strategies substantially affects the volatility of most equity markets. The exact form of the predictive models implemented by trading algorithms and the decision functions mapping predictions into trading actions are mostly unknown to the general public, for obvious strategic reasons. This talk illustrates the selection of multivariate dynamic models and score functions maximizing the cumulative returns of stock portfolios when the identity of the set of tradable stocks is fixed in advance. The main original contributions of this work consist of: 1. the formulation of different scoring functions based on one-step ahead point predictions of stock prices and on higher order moments of the one-step ahead predictive distribution; 2. the assessment of different trading strategies based on the null distribution of the cumulative portfolio returns and 3. the assessment of prediction-correction methods to improve the predictive accuracy of standard multivariate dynamic models. Having introduced the predictive models and score functions, a practical example will be illustrated in detail using weekly stock prices of seven major international pharmaceutical companies.
Ultimo aggiornamento 6 dicembre 2012.