n Annual Proceedings of the South African Statistical Association Conference - Asymptotic relative efficiency of empirical characteristic function estimators with normal weighting

Volume 2018 Number Congress 1
  • ISSN :


Estimation of parameters based on the empirical characteristic function (ECF) is a popular method when the likelihood function of a distribution is not analytically tractable. An example is the estimation of the parameters of the stable law. However, the choice of weight function has a large impact on the efficiency of the estimators obtained, which will be measured by the asymptotic efficiency, relative to maximum likelihood estimators (ARE). In this paper we analyse the ARE of ECF estimators using a weight function that is either a normal density or a mixture of two normal densities. The ECF method is applied to estimate the index parameter of a standard symmetric stable law. Our results indicate that the ARE is sensitive with respect to the choice of weight function. We also show that the ARE can be optimised by choosing a normal density as aweight function, centered around the origin with a small standard deviation.

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