Inference in the indeterminate parameters problem
We face an indeterminate parameters problem when there are two sets of parameters, x and g, say, such that the null hypothesis H0:x=x0 makes the likelihood independent of g. A consequence of indeterminacy is the singularity of the information matrix. For this problem the standard results, such as th...
| Published in: | Statistica |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
University of Bologna
2013-03-01
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| Online Access: | http://rivista-statistica.unibo.it/article/view/448 |
| Summary: | We face an indeterminate parameters problem when there are two sets of parameters, x and g, say, such that the null hypothesis H0:x=x0 makes the likelihood independent of g. A consequence of indeterminacy is the singularity of the information matrix. For this problem the standard results, such as the asymptotic chi-squared distribution of the Wald test statistic, are generally false. In the paper we propose an estimator of the parameters of interest, x, so that a Wald-type test statistic can be used for testing H0. Such an estimator is obtained through the maximization of a modified (penalized) log-likelihood function. We show that a solution to the (penalized) likelihood equation is consistent and asymptotically normally distributed with variance-covariance matrix approximated by the Moore-Penrose pseudoinverse of the information matrix. These properties allow one to construct a Wald-type test statistic useful for inferential purposes. |
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| ISSN: | 0390-590X 1973-2201 |