Asymptotic behavior of the scaled mutation rate estimators

Author(s)

Pinheiro, Hildete P. ^[1] ; Kiihl, Samara F. ^[1] ; Pinheiro, Aluisio ^[1] ; dos Reis, Sergio F. ^[2]

Affiliation

^[1] Univ Estadual Campinas, Dept Stat, IMECC, BR-13083970 Campinas, SP - Brazil

^[2] Univ Estadual Campinas, Dept Parasitol, IB, BR-13083970 Campinas, SP - Brazil

• Document type: Journal article
• Source: BIOMETRICAL JOURNAL; v. 52, n. 3, p. 400-416, JUN 2010.
• Web of Science Citations: 1

Abstract

Important aspects of population evolution have been investigated using nucleotide sequences. Under the neutral Wright Fisher model, the scaled mutation rate represents twice the average number of new mutations per generations and it is one of the key parameters in population genetics. In this study, we present various methods of estimation of this parameter, analytical studies of their asymptotic behavior as well as comparisons of the distribution's behavior of these estimators through simulations. As knowledge of the genealogy is needed to estimate the maximum likelihood estimator (MLE), an application with real data is also presented, using jackknife to correct the bias of the M LE, which can be generated by the estimation of the tree. We proved analytically that the Waterson's estimator and the MLE are asymptotically equivalent with the same rate of convergence to normality. Furthermore, we showed that the MLE has a better rate of convergence than Waterson's estimator for values of the parameter greater than one and this relationship is reversed when the parameter is less than one. (AU)

• FAPESP's process: 09/14176-8 - Quasi U-statistics, wavelets and decomposability: asymptotics and applications
• Grantee: Aluísio de Souza Pinheiro
• Support Opportunities: Regular Research Grants
• FAPESP's process: 08/51097-6 - Time Series, Dependence Analysis and Applications
• Grantee: Pedro Alberto Morettin
• Support Opportunities: Research Projects - Thematic Grants