| 1. |
- Ahmad, M. Rauf, et al.
(författare)
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A U-statistics Based Approach to Mean Testing for High Dimensional Multivariate Data Under Non-normality
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p large, and under mild assumptions, the statistic is shown to asymptotically follow a normal distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of well-known Box's approximation, under high-dimensional set up.
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| 2. |
- Ahmad, M. Rauf, et al.
(författare)
-
Some Tests of Covariance Matrices for High Dimensional Multivariate Data
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Using the asymptotic theory of U-statistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces of the unknown covariance matrix. Neither any relationship between n and p is assumed. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. The validity of the commonly used assumptions for high-dimensional set up is also briefly discussed.
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| 3. |
- Ohlson, Martin, 1977-, et al.
(författare)
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More on the Kronecker Structured Covariance Matrix
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper the multivariate normal distribution with a Kronecker product structured covariance matrix is studied. Particularly, estimation of a Kronecker structured covariance matrix of order three, the so called double separable covariance matrix. The estimation procedure, suggested in this paper, is a generalization of the procedure derived by Srivastava et al. (2008), for a separable covariance matrix. Furthermore, the restrictions imposed by separability and double separability are discussed.
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| 4. |
- Ohlson, Martin, et al.
(författare)
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The Multilinear Normal Distribution:Introduction and Some Basic Properties
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, the multilinear normal distribution is introduced as an extension of the matrix-variate normal distribution. Basic properties such as marginal and conditional distributions, moments, and the characteristic function, are also presented. The estimation of parameters using a flip-flop algorithm is also briefy discussed.
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