We face an indeterminate parameters problem when there are two sets of parameters such that the null hypothesis on a set of parameters makes the likelihood independ¬ent of the other. 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 so that a Wald-type test statistic can be used. 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 con¬sistent and asymptotically normally distributed with variance-covariance matrix approxi¬mated by the Moore-Penrose pseudoinverse of the information matrix. These properties allow one to construct a Wald-type test statistic useful for inferential purposes.
Inference in the indeterminate parameters problem / M.Barnabani. - In: STATISTICA. - ISSN 0390-590X. - STAMPA. - 1:(2006), pp. 59-75.
Inference in the indeterminate parameters problem
BARNABANI, MARCO
2006
Abstract
We face an indeterminate parameters problem when there are two sets of parameters such that the null hypothesis on a set of parameters makes the likelihood independ¬ent of the other. 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 so that a Wald-type test statistic can be used. 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 con¬sistent and asymptotically normally distributed with variance-covariance matrix approxi¬mated by the Moore-Penrose pseudoinverse of the information matrix. These properties allow one to construct a Wald-type test statistic useful for inferential purposes.File | Dimensione | Formato | |
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