A new kind of asymptotic quasi-score estimating function

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 f or obtaining a good estimate of theta in the model y(t) = f(t)(theta) + m(t ) without any prior knowledge on the nature of E(m(r)(2)\Ft-1) is suggested , where f(t) is a predictable process and m(t) is a martingale difference p rocess. Two examples are used to show that the approach is practicable.