Besides the different approaches suggested in the literature, accurate estimation of the order of a Markov chain from a given symbol sequence is an open issue, especially when the order is moderately large. Here, parametric significance tests of conditional mutual information (CMI) of increasing order m, Ic(m), on a symbol sequence are conducted for increasing orders m in order to estimate the ...

The transition density of a diffusion process does not admit an explicit expression in general, which prevents the full maximum likelihood estimation (MLE) based on discretely observed sample paths. Aı̈t-Sahalia (1999, 2002) proposed asymptotic expansions to the transition densities of diffusion processes, which lead to an approximate maximum likelihood estimation (AMLE) for parameters. Built on...

We propose a new model for multivariate Markov chains of order one or higher based on the mixture transition distribution (MTD) model. We call it the MTD-Probit. The proposed model presents two attractive features: it is completely free of constraints, thereby facilitating the estimation procedure, and it is more precise at estimating the transition probabilities of a multivariate or higher-ord...

Segmentation of images in the context of model based stochasUc techniques is connected with high, very often unpracticle computational complexity. The objective with this thesis is to take the models used in model based image processing, simplify and use them in suboptimal. but not computationally demanding algorithms. Algorithms that are essentially one-dimensional, and their extensions to two...

This paper derives a model for the profitability of credit cards, which allow lenders to find the optimal dynamic credit limit policy. The model is a Markov decision process, where the states of the system are based on the borrower’s behavioural score and the decisions are what credit limit to give the borrower each period. In determining the Markov chain which best describes the borrower’s per...

In this work, we propose to improve the neighboring relationship ability of the Hidden Markov Chain (HMC) model, by extending the memory lengthes of both the Markov chain process and the data-driven densities arising in the model. The new model is able to learn more complex noise structures, with respect to the configuration of several previous states and observations. Model parameters estimati...

Because the evaluation of the stochastic complexity is difficult for most of the models, various approximations have been proposed during the last two decades. In this article, we focus on two approximations that rely on the Fisher information, and we revisit some recent results that demonstrate the estimation performances of the two formulae in solving the following problems: order selection f...

Abstract. We find upper bounds for the probability of underestimation and overestimation errors in penalized likelihood context tree estimation. The bounds are explicit and applies to processes of not necessarily finite memory. We allow for general penalizing terms and we give conditions over the maximal depth of the estimated trees in order to get strongly consistent estimates. This generalize...