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 log N)1/2.

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Journal Sankhya A
Farrell, P, Ehsanes Saleh, A.K.M. (A. K. Md.), & Zhang, Z. (Zhengmin). (2011). Methods of moments estimation in finite mixtures. Sankhya A, 73(2), 218–230. doi:10.1007/s13171-011-0011-3