On Recursive Parametric Estimation Theory

The classical non-recursive methods to estimate unknown parameters of the model, such as the maximum likelihood method, the method of least squares etc. eventually require maximization procedures. These methods are often difficult to implement, especially for non i.i.d. models. If for every sample size n, when new data are acquired, an estimator has to be computed afresh, and if a numerical method is needed to do so, it generally becomes very laborious. Therefore, it is important to consider recursive estimation procedures which are appealing from the computational point of view. Recursive procedures are those which at each step allow one to re-estimate values of unknown parameters based on the values already obtained at the previous step together with new information. We propose a wide class of recursive estimation procedures for the general statistical model and study convergence, the rate of convergence, and the local asymptotic linearity. Also, we demonstrate the use of the results on some examples.