Subgeometric ergodicity of Markov chains

The goal of this paper is to give a short and self contained proof of general bounds for subgeometric rates of convergence, under practical conditions. The main result whose proof, based on coupling, provides an intuitive understanding of the results of Nummelin and Tuominen (1983) and Tuominen and Tweedie (1994). To obtain practical rates, a very general drift condition, recently introduced in Douc et al (2004) is used

Practical drift conditions for subgeometric rates of convergence

We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a \psi-irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by Jarner and Roberts [Ann. Appl. Probab. 12 (2002) 224-247] for polynomial convergence rates, turns out to be very convenient to prove subgeometric rates of convergence. Several applications are presented including nonlinear autoregressive models, stochastic unit root models and multidimensional random walk Hastings-Metropolis algorithms

Estimating long memory in volatility

We consider semiparametric estimation of the memory parameter in a model which includes as special cases both the long-memory stochastic volatility (LMSV) and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long-memory signal and a white noise. We consider periodogram-based estimators which explicitly account for the noise term in a local Whittle criterion function. We allow the optional inclusion of an additional term to allow for a correlation between the signal and noise processes, as would occur in the FIEGARCH model. We also allow for potential nonstationarity in volatility, by allowing the signal process to have a memory parameter d 1=2. We show that the local Whittle estimator is consistent for d 2 (0; 1). We also show that a modi ed version of the local Whittle estimator is asymptotically normal for d 2 (0; 3=4), and essentially recovers the optimal semiparametric rate of convergence for this problem. In particular if the spectral density of the short memory component of the signal is suficiently smooth, a convergence rate of n2=5-δ for d 2 (0; 3=4) can be attained, where n is the sample size and δ > 0 is arbitrarily small. This represents a strong improvement over the performance of existing semiparametric estimators of persistence in volatility. We also prove that the standard Gaussian semiparametric estimator is asymptotically normal if d = 0. This yields a test for long memory in volatility.Statistics Working Papers Serie

Contribution of ecotoxicological tests in the evaluation of soil bioremediation efficiency

Clean-up of contaminated soils became a high priority only recently. Several techniques have been developed forthis purpose such as chemical, physical, thermic or microbiological methods. Efficiency of the remediation can be estimated using two approaches : a chemical specific approach and a toxicity-based approach. So far, the efficiency of the decontamination process was based essentially on chemical analyses which does not integrale the toxicity of all the soil contaminants and does not give a response on effects caused by the bioavailable fraction of these contaminants äs the toxicity-based approach. In the present study, bioremediation efficiency of a soil contaminated by 4-chlorobiphenyl was evaluated using chemical and biological analyses. Experiments were carried out in microcosms contaminated at a rate of 1 g/kg. Control microcosms without specific degrader were performed simultaneously. Acute toxicity to earthworms and inhibition of growth of barley roots were selected, from previous work, äs relevant ecotoxicological test

Fonctionnelles non-linéaires du périodogramme

- Deux théorèmes de limite centrale sont énoncés pour des tableaux triangulaires de fonctionnelles non-linéaires du périodogramme. Le premier concerne un bruit i.i.d. Il s'obtient par une méthode de moments, évalués par des développements d'Edgeworth. Le second théorème, concernant les signaux linéaires, est une généralisation de résultats obtenus précédemment pour des signaux gaussiens (voir Chen et Hannan 1980, von Sachs 1994, Janas et von Sachs 1995). Il dérive du premier théorème et de la décomposition de Bartlett. Des applications à l'estimation spectrale non-paramétrique robuste et à l'estimation de paramètres par régression sur le log-periodogramme sont présentées

Estimating long memory in volatility

We consider semiparametric estimation of the memory parameter in a model which includes as special cases both the long-memory stochastic volatility (LMSV) and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long-memory signal and a white noise. We consider periodogram-based estimators which explicitly account for the noise term in a local Whittle criterion function. We allow the optional inclusion of an additional term to allow for a correlation between the signal and noise processes, as would occur in the FIEGARCH model. We also allow for potential nonstationarity in volatility, by allowing the signal process to have a memory parameter d 1=2. We show that the local Whittle estimator is consistent for d 2 (0; 1). We also show that a modi ed version of the local Whittle estimator is asymptotically normal for d 2 (0; 3=4), and essentially recovers the optimal semiparametric rate of convergence for this problem. In particular if the spectral density of the short memory component of the signal is suficiently smooth, a convergence rate of n2=5-δ for d 2 (0; 3=4) can be attained, where n is the sample size and δ > 0 is arbitrarily small. This represents a strong improvement over the performance of existing semiparametric estimators of persistence in volatility. We also prove that the standard Gaussian semiparametric estimator is asymptotically normal if d = 0. This yields a test for long memory in volatility.Statistics Working Papers Serie

Fault Diagnosis in Fuzzy Discrete Event System: Incomplete Models and Learning

Nowadays, determining faults in non-stationary environment and that can deal with the problems of fuzziness impreciseness and subjectivity is a challenging task in complex systems such as nuclear center, or wind turbines, etc. Our objective in this paper is to develop models based on fuzzy finite state automaton with fuzzy variables describing the industrial process in order to detect anomalies in real time and possibly in anticipation. A diagnosis method has for goal to alert actors responsible for managing operations and resources, able to adapt to the emergence of new procedures or improvisation in the case of unexpected situations. The diagnoser module use the outputs events and membership values of each active state of the model as input events

Hepatitis C virus cell-cell transmission and resistance to direct-acting antiviral agents

Hepatitis C virus (HCV) is transmitted between hepatocytes via classical cell entry but also uses direct cell-cell transfer to infect neighboring hepatocytes. Viral cell-cell transmission has been shown to play an important role in viral persistence allowing evasion from neutralizing antibodies. In contrast, the role of HCV cell-cell transmission for antiviral resistance is unknown. Aiming to address this question we investigated the phenotype of HCV strains exhibiting resistance to direct-acting antivirals (DAAs) in state-of-the-art model systems for cell-cell transmission and spread. Using HCV genotype 2 as a model virus, we show that cell-cell transmission is the main route of viral spread of DAA-resistant HCV. Cell-cell transmission of DAA-resistant viruses results in viral persistence and thus hampers viral eradication. We also show that blocking cell-cell transmission using host-targeting entry inhibitors (HTEIs) was highly effective in inhibiting viral dissemination of resistant genotype 2 viruses. Combining HTEIs with DAAs prevented antiviral resistance and led to rapid elimination of the virus in cell culture model. In conclusion, our work provides evidence that cell-cell transmission plays an important role in dissemination and maintenance of resistant variants in cell culture models. Blocking virus cell-cell transmission prevents emergence of drug resistance in persistent viral infection including resistance to HCV DAAs