| 1. |
- Ohlson, Martin, 1977-, et al.
(författare)
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Profile Analysis for a Growth Curve Model
- 2011
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- In this talk, we consider profile analysis of several groups where subvectors of the mean vectors are equal. This leads to a profile analysis in a growth curve model. The likelihood ratio statistics are given for the three hypotheses known in literature as parallelism, level hypothesis and flatness. Furthermore, exact and asymptotic distributions are given in the relevant cases.
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| 2. |
- Ohlson, Martin, 1977-, et al.
(författare)
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Profile Analysis for a Growth Curve Model
- 2010
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Ingår i: Journal of the Japan Statistical Society. - 1882-2754 .- 1348-6365. ; 40:1, s. 1-21
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider profile analysis of several groups where the groups have partly equal means. This leads to a profile analysis for a growth curve model. The likelihood ratio statistics are given for the three hypotheses known in literature as parallelism, level hypothesis and flatness. Furthermore, exact and asymptotic distributions are given in the relevant cases.
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| 3. |
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| 4. |
- Srivastava, Muni S., et al.
(författare)
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Estimation in General Multivariate Linear Models with Kronecker Product Covariance Structure
- 2008
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this article models based on pq-dimensional normally distributed random vectors x are studied with a mean vec(ABC), where A and Care known matrices, and a separable covariance matrix $\psi\otimes \Sigma$, where both $\Psi$ and $\Sigma$ are positive definite and except the estimability condition $\psi_{qq} = 1$, unknown. The model may among others be applied when spatial-temporal relationships exist. On the basis of n independent observations on the random vector x, we wish to estimate the parameters of the model. In the paper estimation equations for obtaining maximum likelihood estimators are presented. It is shown that there exist only one solution to these equations. Likelihood equations are also considered when $FBG = 0$, with F and G known. Moreover, the likelihood ratio test for testing $FBG = 0$ against $FBG\neq = 0$ is considered.
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| 6. |
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| 7. |
- Srivastava, Muni S., et al.
(författare)
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Models with a Kronecker Product Covariance Structure: Estimation and Testing
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this article we consider a $pq$-dimensional random vector $x$ distributed normally with mean vector $\theta$ and the covariance matrix $\Lambda$, assumed to be positive definite. On the basis of $N$ independent observations on the random vector $x$, we wish to estimate parameters and test the hypothesis $H: \Lambda=\Psi\otimes\Sigma$, where $\Psi = (\psi_{ij}) : q\times q$ and $\Sigma = (\sigma_{ij}) : p\times p$, and $\Lambda =(\psi_{ij}\Sigma)$, the Kronecker product of $\Psi$ and $\Sigma$. That is instead of $\frac{1}{2}pq(pq+1)$ parameters, it has only $\frac{1}{2}p(p + 1) + \frac{1}{2}q(q + 1) - 1$ parameters. When this model holds, we test the hypothesis that $\Psi$ is an identity matrix, a diagonal matrix or of intraclass correlation structure. The maximum likelihood estimators (MLE) are obtained under the hypothesis as well as under the alternatives. Using these estimators the likelihood ratio tests (LRT) are obtained. Moreover, it is shown that the estimators are unique.
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| 8. |
- Srivastava, Muni S., et al.
(författare)
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Profile Analysis with Random-Effects Covariance Structure
- 2012
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Ingår i: Journal of the Japan Statistical Society. - : The Japan Statistical Society. - 1882-2754 .- 1348-6365. ; 42:2, s. 145-164
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider a parallel profile model for several groups. Given the parallel profile model we construct tests based on the likelihood ratio, without any restrictions on the parameter space, testing the covariance matrix for random-effects structure or sphericity. Furthermore, given both the parallel profile and random- effects covariance structure the level hypothesis is tested. The attained significance levels and the empirical powers for the given tests in this paper are compared with the tests given by Yokoyama and Fujikoshi (1993) and Yokoyama (1995).
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| 9. |
- Srivastava, Muni S., et al.
(författare)
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Test for the mean matrix in a Growth Curve model for high dimensions
- 2017
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 46:13, s. 6668-6683
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider the problem of testing (a) sphericity and (b) intraclass covariance structure under a Growth Curve model. The maximum likelihood estimator (MLE) for the mean in a Growth Curve model is a weighted estimator with the inverse of the sample covariance matrix which is unstable for large p close to N and singular for p larger than N. The MLE for the covariance matrix is based on the MLE for the mean, which can be very poor for p close to N. For both structures (a) and (b), we modify the MLE for the mean to an unweighted estimator and based on this estimator we propose a new estimator for the covariance matrix. This new estimator leads to new tests for (a) and (b). We also propose two other tests for each structure, which are just based on the sample covariance matrix.To compare the performance of all four tests we compute for each structure (a) and (b) the attained significance level and the empirical power. We show that one of the tests based on the sample covariance matrix is better than the likelihood ratio test based on the MLE.
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