A Note on the Asymptotic Properties of Constrained ML Estimators Under a Class of Local Alternatives When the Information Matrix is Singular

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This paper is concerned with hypothesis testing situations stated in terms of orthonormal constraints on the parameters involved in the distribution functions of random variables under local alternatives when the information matrix is singular. Likelihood equations are derived and existence of likelihood estimators emerging from solving these equations is demonstrated. Asymptotic properties of obtained likelihood estimators and the likelihood ratio statistic - 2log λ are developed.

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