Abstract

Recently there has been a growing interest in joint estimation of the location and scale parameters using combined estimation functions. Combined estimating functions had been studied in Liang et al. (2011) for models with finite variance errors  and in Thavaneswaran et al. (2013) for models with infinite variance
stable errors. In this paper, first a theorem on recursive estimation based on estimating functions is extended to multi-parameter setup and it is shown that the unified approach can be used to estimate the location parameter recursively for models with finite variance/infinite variance  errors. The method is applied for the joint estimation of the location and scale parameters for regression models with ARCH errors and RCA models with GARCH errors.

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