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The purpose of this paper is to introduce sequential investment strategies that guarantee an optimal rate of growth of the capital, under minimal assumptions on the behavior of the market. The new strategies are analyzed both theoretically and empirically. The theoretical results show that the asymptotic rate of growth matches the optimal one that one could(More)
In recent years optimal portfolio selection strategies for sequential investment have been shown to exist. Although their asymptotical optimality is well established, finite sample properties do need the adjustment of parameters that depend on dimensionality and scale. In this paper we introduce some nearest neighbor based portfolio selectors that solve(More)
We study the behavior of random geometric graphs in high dimensions. We show that as the dimension grows, the graph becomes similar to an Erd˝ os-Rényi random graph. We pay particular attention to the clique number of such graphs and show that it is very close to that of the corresponding Erd˝ os-Rényi graph when the dimension is larger than log 3 n where n(More)
BACKGROUND Boundaries that prevent cell movement allow groups of cells to maintain their identity and follow independent developmental trajectories without the need for ongoing instructive signals from surrounding tissues. This is the case of vertebrate rhombomeric boundaries. Analysis in the developing chick hindbrain provided the first evidence that(More)
Although the histogram is the most widely used density estimator, it is well{known that the appearance of a constructed histogram for a given bin width can change markedly for diierent choices of anchor position. In this paper we construct a stability index G that assesses the potential changes in the appearance of histograms for a given data set and bin(More)
A tool for user choice of the local bandwidth function for a kernel density estimate is developed using KDE, a graphical object-oriented package for interactive kernel density estimation written in LISP-STAT. The bandwidth function is a cubic spline, whose knots are manipulated by the user in one window, while the resulting estimate appears in another(More)
We continue the development of a method for the selection of a bandwidth or a number of design parameters in density estimation. We provide explicit non-asymptotic density-free inequalities that relate the L 1 error of the selected estimate with that of the best possible estimate, and study in particular the connection between the richness of the class of(More)
We analyze and discuss how a generic software to produce biplot graphs should be designed. We describe a data structure appropriate to include the biplot description and we specify the algorithm(s) to be used for several biplot types. We discuss the options the software should offer to the user in two different environments. In a highly interactive(More)
In recent years optimal portfolio selection strategies for sequential investment have been shown to exist. Although their asymptotical optimality is well established, finite sample properties do need to be tested in practice. In this paper we present some experiments based on real data form financial markets. We show that these methods show very good(More)