Angel Rodolfo Baigorri

arXiv2016

A New Approach to Inverse Local Times

In 1981 F. Knight published an article with a partial solution to a problem proposed by Ito-McKean see [Ito,[p.217]]. In this paper Knight, see [Knight], characterized the Levy measures of gap diffusions also known as quasi-diffusions. The proof is very elegant but it uses quite a lot functional analysis, more specifically spectral Krein Theory. We present a new proof of Knight's Theorem, defined at the beginning of the Introduction as well as the new proof of the same theorem referred as Theorem 2.6 in Section 2.

math.ST↗

arXiv2012

Non Asymptotic Performance of Some Markov Chains Order Estimators

In what follows we study non asymptotic behavior of different well known estimators AIC(\cite{Tong}), BIC(\cite{Schwarz}) and EDC(\cite{Zhao,Dorea}) in contrast with the Markov chain order estimator, named as Global Depency Level - GDL(\cite{Baigorri}). The estimator GDL, is based on a different principle which makes it behave in a quite different form. It is strongly consistent and more efficient than AIC(inconsistent), outperforming the well established and consistent BIC and EDC, mainly on relatively small samples. The estimators mentioned above mainly consist in the evaluation of the Markov chain's sample by different multivariate deterministic functions. The log likelihood approach or the GDL approach, shall be analysed exhibiting different structural properties. It will become clear the intimate differences existing between the variance of both estimators, which induce quite dissimilar performance, mainly for samples of moderated sizes.

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