An urn model with local reinforcement: a theoretical framework for a chi-squared goodness of fit test with a big sample

by   Giacomo Aletti, et al.

Motivated by recent studies of big samples, this work aims at constructing a parametric model which is characterized by the following features: (i) a "local" reinforcement, i.e. a reinforcement mechanism mainly based on the last observations, (ii) a random fluctuation of the conditional probabilities, and (iii) a long-term convergence of the empirical mean to a deterministic limit, together with a chi-squared goodness of fit result. This triple purpose has been achieved by the introduction of a new variant of the Eggenberger-Polya urn, that we call the "Rescaled" Polya urn. We provide a complete asymptotic characterization of this model and we underline that, for a certain choice of the parameters, it has properties different from the ones typically exhibited from the other urn models in the literature. As a byproduct, we also provide a Central Limit Theorem for a class of linear functionals of non-Harris Markov chains, where the asymptotic covariance matrix is explicitly given in linear form, and not in the usual form of a series.


page 1

page 2

page 3

page 4


The Rescaled Polya Urn and the Wright-Fisher process with mutation

In [arXiv:1906.10951 (forthcoming on Advances in Applied Probability),ar...

Generalized Rescaled Pólya urn and its statistical applications

We introduce the Generalized Rescaled Pólya (GRP) urn. In particular, th...

On Linear Stochastic Approximation: Fine-grained Polyak-Ruppert and Non-Asymptotic Concentration

We undertake a precise study of the asymptotic and non-asymptotic proper...

Geometric ergodicity of trans-dimensional Markov chain Monte Carlo algorithms

This article studies the convergence properties of trans-dimensional MCM...

A Central Limit Theorem for L_p transportation cost with applications to Fairness Assessment in Machine Learning

We provide a Central Limit Theorem for the Monge-Kantorovich distance be...

Fully Modified Least Squares Cointegrating Parameter Estimation in Multicointegrated Systems

Multicointegration is traditionally defined as a particular long run rel...

Please sign up or login with your details

Forgot password? Click here to reset