The rescaled Pólya urn: local reinforcement and chi-squared goodness-of-fit test

Motivated by recent studies of big samples, this work aims at constructing a parametric model which is characterized the following features: (i) "local" reinforcement, i.e. reinforcement mechanism mainly based on last observations, (ii) random persistent fluctuation predictive mean, and (iii) long-term convergence empirical mean to deterministic limit, together with chi-squared goodness fit result. This triple purpose has been achieved introduction new variant Eggenberger-Polya urn, that we call "Rescaled" Polya urn. We provide complete asymptotic characterization model, pointing out that, for certain choice parameters, it properties different from ones typically exhibited other urn models in literature. Therefore, beyond possible statistical application, could be interesting those who are concerned stochastic processes reinforcement.