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- 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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| 2. |
- 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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| 3. |
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| 4. |
- Srivastava, Muni S., et al.
(författare)
-
Testing Some Covariance Structures under a Growth Curve Model in High Dimension
- 2015
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- fIn 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. or both structures (a) and (b), we modify the MLE for the mean to n 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 or each structure (a) and (b) the attained signicance 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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