| 1. |
- Ahmad, M. Rauf, et al.
(författare)
-
A note on mean testing for high dimensional multivariate data under non-normality
- 2013
-
Ingår i: Statistica Neerlandica. - : Wiley. - 0039-0402 .- 1467-9574. ; 67:1, s. 81-99
-
Tidskriftsartikel (refereegranskat)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?8, and under mild assumptions, but without assuming any relationship between n and p, the statistic is shown to asymptotically follow a chi-square distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of the well-known Box's approximation, under high-dimensional set up. Using a classical limit theorem, the approximation is further extended to an asymptotic normal limit under the same high dimensional set up. The simulation results, generated under different parameter settings, are used to show the accuracy of the approximation for moderate n and large p.
|
|
| 2. |
- Ahmad, M. Rauf, et al.
(författare)
-
A U-statistics Based Approach to Mean Testing for High Dimensional Multivariate Data Under Non-normality
- 2011
-
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.
|
|
| 3. |
- Ahmad, M. Rauf, et al.
(författare)
-
Some Tests of Covariance Matrices for High Dimensional Multivariate Data
- 2011
-
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.
|
|
| 4. |
- Ahmad, M. Rauf, et al.
(författare)
-
Tests for high-dimensional covariance matrices using the theory of U-statistics
- 2015
-
Ingår i: Journal of Statistical Computation and Simulation. - : Informa UK Limited. - 0094-9655 .- 1563-5163. ; 85:13, s. 2619-2631
-
Tidskriftsartikel (refereegranskat)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. Under certain mild conditions mainly on the traces of the unknown covariance matrix, and 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 accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. A real data set is used to illustrate the application of the proposed test statistics.
|
|
| 5. |
- Ahmad, M. Rauf, et al.
(författare)
-
Tests of Covariance Matrices for High Dimensional Multivariate Data Under Non Normality
- 2015
-
Ingår i: Communications in Statistics - Theory and Methods. - : Informa UK Limited. - 0361-0926 .- 1532-415X. ; 44:7, s. 1387-1398
-
Tidskriftsartikel (refereegranskat)abstract
- Ahmad et al. (in press) presented test statistics for sphericity and identity of the covariance matrix of a multivariate normal distribution when the dimension, p, exceeds the sample size, n. In this note, we show that their statistics are robust to normality assumption, when normality is replaced with certain mild assumptions on the traces of the covariance matrix. Under such assumptions, the test statistics are shown to follow the same asymptotic normal distribution as under normality for large p, also whenp >> n. The asymptotic normality is proved using the theory of U-statistics, and is based on very general conditions, particularly avoiding any relationship between n and p.
|
|
| 6. |
- Ohlson, Martin, 1977-, et al.
(författare)
-
More on the Kronecker Structured Covariance Matrix
- 2012
-
Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 41:13-14, s. 2512-2523
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper, the multivariate normal distribution with a Kronecker product structured covariance matrix is studied. Particularly focused is the estimation of a Kronecker structured covariance matrix of order three, the so called double separable covariance matrix. The suggested estimation generalizes the procedure proposed by Srivastava et al. (2008) for a separable covariance matrix. The restrictions imposed by separability and double separability are also discussed.
|
|
| 7. |
- Ohlson, Martin, 1977-, et al.
(författare)
-
More on the Kronecker Structured Covariance Matrix
- 2011
-
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.
|
|
| 8. |
- Ohlson, Martin, et al.
(författare)
-
The Multilinear Normal Distribution:Introduction and Some Basic Properties
- 2011
-
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.
|
|
| 9. |
- Ohlson, Martin, 1977-, et al.
(författare)
-
The Multilinear Normal Distribution: Introduction and Some Basic Properties
- 2013
-
Ingår i: Journal of Multivariate Analysis. - Maryland Heights, MO, United States : Academic Press. - 0047-259X .- 1095-7243. ; 113:S1, s. 37-47
-
Tidskriftsartikel (refereegranskat)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 briefly discussed.
|
|
