On Recursive Parametric Estimation Theory
by Teo Sharia
Abstract:
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.