In this paper, we study the method of moments estimation in a finite mixture where the mixing distribution is supported on [0; 1], and the number of support points is fixed. We prove the validity of the modification method proposed by Lindsay (1989). Further, we demonstrate that the modified estimator is weakly consistent and that its convergence rate is N -1/2 (log logN) 1/2.

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Keywords Convergence rate, Finite mixture, Method of moments, Mod-ification, Weak consistency
Journal Sankhya: The Indian Journal of Statistics
Farrell, P, Ehsanes Saleh, M.A.K. (Md A.K.), & Zhang, Z. (Zhengmin). (2011). Methods of moments estimation in finite mixtures. Sankhya: The Indian Journal of Statistics, 73(2 A), 218–230.