  The Generalized P\'{o}lya Urn (GPU) is a popular urn model which is widely
used in many disciplines. In particular, it is extensively used in treatment
allocation schemes in clinical trials. In this paper, we propose a sequential
estimation-adjusted urn model (a nonhomogeneous GPU) which has a wide spectrum
of applications. Because the proposed urn model depends on sequential
estimations of unknown parameters, the derivation of asymptotic properties is
mathematically intricate and the corresponding results are unavailable in the
literature. We overcome these hurdles and establish the strong consistency and
asymptotic normality for both the patient allocation and the estimators of
unknown parameters, under some widely satisfied conditions. These properties
are important for statistical inferences and they are also useful for the
understanding of the urn limiting process. A superior feature of our proposed
model is its capability to yield limiting treatment proportions according to
any desired allocation target. The applicability of our model is illustrated
with a number of examples.
