41,906 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).

    The density of eigenvalues in thin circular conical shells

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    Resonant frequencies in thin circular conical shell

    Modal density of thin circular cylinders

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    Vibration modal response of thin cylindrical shell

    The impact of four weeks of high intensity interval training oncardiac autonomic function in physically inactive males and females

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    Introduction: Physical inactivity is the fourth largest risk factor of premature mortality, responsible for 6% of deaths each year worldwide. Autonomic dysfunction has shown to be an indicator of cardiovascular diseases. High intensity interval training has shown to reduce traditional cardiovascular risk factors in less time than traditional aerobic exercise training. However, the adaptations following a high intensity interval training programme to the cardiac autonomic nervous system have not yet been fully researched. Method: Using an independent-measures design, 45 physically inactive males and females (22.8 ± 2.7 years) were placed into either a high intensity interval training or control group. The subjects in the high intensity interval training group completed 3 x 30 seconds all out maximal cycle sprints, 3 times a week on a Wattbike cycle ergometer at a resistance of 7.5% of their body weight, with two minutes of active recovery between bouts, for four weeks. Cardiac autonomic function was measured using the task force monitor. Results: This study found that four weeks of high intensity interval training led to resting heart rate significantly reducing (65.59 ± 10.15 to 63.05 ± 13.42 b.min-1; p < 0.05) and significant improvements in total power spectrum density (498.8 ± 239.8 ms2; p < 0.05) and high frequency power (389.4 ± 123 ms2; p < 0.01) against the control group. There was a nonsignificant increase in low frequency power (189.7 ± 91.2 ms2) and no significant reduction in LF/HF ratio compared to the control group
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