35,373 research outputs found

    Smoothing-inspired lack-of-fit tests based on ranks

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    A rank-based test of the null hypothesis that a regressor has no effect on a response variable is proposed and analyzed. This test is identical in structure to the order selection test but with the raw data replaced by ranks. The test is nonparametric in that it is consistent against virtually any smooth alternative, and is completely distribution free for all sample sizes. The asymptotic distribution of the rank-based order selection statistic is obtained and seen to be the same as that of its raw data counterpart. Exact small sample critical values of the test statistic are provided as well. It is shown that the Pitman-Noether efficiency of the proposed rank test compares very favorably with that of the order selection test. In fact, their asymptotic relative efficiency is identical to that of the Wilcoxon signed rank and tt-tests. An example involving microarray data illustrates the usefulness of the rank test in practice.Comment: Published in at http://dx.doi.org/10.1214/193940307000000103 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

    The case of equality in the Livingstone-Wagner Theorem

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    Let G be a permutation group acting on a set Ω of size n∈ℕ and let 1≤k<(n−1)/2. Livingstone and Wagner proved that the number of orbits of G on k-subsets of Ω is less than or equal to the number of orbits on (k+1)-subsets. We investigate the cases when equality occurs

    Additive property of modal density for a composite structure Progress report

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    Additive property of modal density for composite structures in analysi

    Reference Points and the Theory of the Firm

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    In this article I argue that it has been hard to make progress on Coase's theory of the firm agenda because of the difficulty of formalizing haggling costs. I propose an approach that tries to move things forward using the idea of aggrievement costs, and apply it to the question of whether a transaction should be placed inside a firm (in-house production) or in the market place (outsourcing).

    Null form estimates for (1/2,1/2) symbols and local existence for a quasilinear Dirichlet-wave equation

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    The authors show that bilinear estimates for null forms hold for Dirichlet-wave equations outside of convex obstacle. This generalizes results for the Euclidean case of Klainerman and Machedon, and of Sogge for the variable coefficient boundaryless case. The estimates are used to prove a local existence theorem for semilinear wave equations satisfying the null condition.Comment: To appear in Annales Scientifiques L'Ecole Normale Superieur
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