Summary
In the paper we propose a way to test the null hypothesis h(θ)=0 when the information matrix is singular. The approach is based on the introduction of a quadratic penalty log-likelihood function with the penalty parameter close to zero (but not zero). This slight change of the log-likelihood allows to obtain a consistent estimator close to the maximum likelihood estimator and whose limiting distribution is Normal with variance-covariance matrix given by the Moore-Penrose pseudoinverse of the information matrix. This result allows to obtain an asymptoticx 2-distribution that may be used in hypothesis testing when the infonnation matrix is singular.
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Barnabani, M. Hypothesis testing when the information matrix is singular. J. Ital. Statist. Soc. 6, 23–35 (1997). https://doi.org/10.1007/BF03178899
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DOI: https://doi.org/10.1007/BF03178899