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  • 1.
    Ahmad, M. Rauf
    Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics. Uppsala Univ, Dept Stat, Uppsala, Sweden.
    On Testing Sphericity and Identity of a Covariance Matrix with Large Dimensions2016In: Mathematical Methods of Statistics, ISSN 1066-5307, E-ISSN 1934-8045, Vol. 25, no 2, p. 121-132Article in journal (Refereed)
    Abstract [en]

    Tests for certain covariance structures, including sphericity, are presented when the data may be high-dimensional but not necessarily normal. The tests are formulated as functions of location-invariant estimators defined as U-statistics of higher order kernels. Under a few mild assumptions, the limit distributions of the tests are shown to be normal. The accuracy of the tests is demonstrated by simulations.

  • 2.
    Wiklund, Tilo
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
    The Deficiency Introduced by Resampling2018In: Mathematical Methods of Statistics, ISSN 1066-5307, E-ISSN 1934-8045, Vol. 27, no 2, p. 145-161Article in journal (Refereed)
    Abstract [en]

    When the classical nonparametric bootstrap is implemented by a Monte-Carlo procedure one resamples values from a sequence of, typically, independent and identically distributed ones. But what happens when a decision has to be taken based on such resampled values? One way to quantify the loss of information due to this resampling step is to consider the deficiency distance, in the sense of Le Cam, between a statistical experiment of n independent and identically distributed observations and the one consisting of m observations taken from the original n by resampling with replacement. By comparing with an experiment where only subsamplingwith a random subsampling size has been performed one can bound the deficiency in terms of the amount of information contained in additional observations. It follows for certain experiments that the deficiency distance is proportional to the expected fraction of observations missed when resampling.

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