Comparing the performance of baseball players : a multiple output approach

This article extends ideas from the economics literature on multiple output production and efficiency to develop methods for comparing baseball players that take into account the many dimensions to batting performance. A key part of this approach is the output aggregator. The weights in this output aggregator can be selected a priori (as is done with batting or slugging averages) or can be estimated statistically based on the performance of the best players in baseball. Once the output aggregator is obtained, an individual player can then be measured relative to the best, and a number between 0 and 1 characterizes his performance as a fraction of the best. The methods are applied to hitters using data from 1995-1999 on all regular players in baseball's major leagues

New bounds for the free energy of directed polymers in dimension 1+1 and 1+2

We study the free energy of the directed polymer in random environment in dimension 1+1 and 1+2. For dimension 1, we improve the statement of Comets and Vargas concerning very strong disorder by giving sharp estimates on the free energy at high temperature. In dimension 2, we prove that very strong disorder holds at all temperatures, thus solving a long standing conjecture in the field.Comment: 31 pages, 4 figures, final version, accepted for publication in Communications in Mathematical Physic

Staircase polygons: moments of diagonal lengths and column heights

We consider staircase polygons, counted by perimeter and sums of k-th powers of their diagonal lengths, k being a positive integer. We derive limit distributions for these parameters in the limit of large perimeter and compare the results to Monte-Carlo simulations of self-avoiding polygons. We also analyse staircase polygons, counted by width and sums of powers of their column heights, and we apply our methods to related models of directed walks.Comment: 24 pages, 7 figures; to appear in proceedings of Counting Complexity: An International Workshop On Statistical Mechanics And Combinatorics, 10-15 July 2005, Queensland, Australi

Total time on test function principal components

A Fourier analytic development of the total time on test function (TTT) provides principal components that are scale free, and which provide criteria for lack of fit. Aggregated values of the squares of these principal components yield a decomposition of the squared coefficient of variation, and a discrete version of the Anderson-Darling type test statistic.Exponential Gini index Goodness of fit Principal component Normalized spacing Total time on test

Subsampling quantile estimator majorization inequalities

A Lorenz partial order majorization inequality is obtained for the Kaigh--Lachenbruch (KL), Harrell--Davis (HD), and Kaigh--Cheng (KC) subsampling quantile estimators developed in Kaigh and Cheng (1991a,b). Bernstein polynomial approximation schemes yield continuous quantile function estimators which are also Lorenz ordered according to their respective inputs.Bernstein polynomial Lorenz curve majorization quantile

Creation or deletion of a drift on a Brownian trajectory

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