Abstract: | A new definition of asymptotic quasi-score sequence of estimating functions is given and studied. The relationship between asymptotic quasi-likelihood and quasi-likelihood estimates is investigated. A new practical approach for obtaining a good estimate of θ in the model y t = ft (θ) + mt without any prior knowledge on the nature of E ( m 2 t |F t −1) is suggested, where ft is a predictable process and mt is a martingale difference process. Two examples are used to show that the approach is practicable. |