Efficient semiparametric estimation in time-varying regression models

We study semiparametric inference in some linear regression models with time-varying coefficients, dependent regressors and dependent errors. This problem, which has been considered recently by Zhang and Wu (2012) under the functional dependence measure, is interesting for parsimony reasons or for testing stability of some coefficients in a linear regression model. In this paper, we propose a different procedure for estimating non time-varying parameters at the rate root n, in the spirit of the method introduced by Robinson (1988) for partially linear models. When the errors in the model are martingale differences, this approach can lead to more effcient estimates than the method considered in Zhang and Wu (2012). For a time-varying AR process with exogenous covariates and conditionally Gaussian errors, we derive a notion of efficient information matrix from a convolution theorem adapted to triangular arrays. For independent but non identically distributed Gaussian errors, we construct an asymptotically efficient estimator in a semiparametric sense

A perturbation analysis of some Markov chains models with time-varying parameters

We study some regularity properties in locally stationary Markov models which are fundamental for controlling the bias of nonparametric kernel estimators. In particular, we provide an alternative to the standard notion of derivative process developed in the literature and that can be used for studying a wide class of Markov processes. To this end, for some families of V-geometrically ergodic Markov kernels indexed by a real parameter u, we give conditions under which the invariant probability distribution is differentiable with respect to u, in the sense of signed measures. Our results also complete the existing literature for the perturbation analysis of Markov chains, in particular when exponential moments are not finite. Our conditions are checked on several original examples of locally stationary processes such as integer-valued autoregressive processes, categorical time series or threshold autoregressive processes

A new smoothed QMLE for AR processes with LARCH errors

We introduce a smoothed version of the quasi maximum likelihood estimator (QMLE) in order to fit heteroschedastic time series with possibly vanishing conditional variance. We apply this procedure to a finite-order autoregressive process with linear ARCH errors. We prove both the almost sure consistency and the asymptotic normality of our estimator. This estimator is more robust that QMLE with the same type of assumptions. A numerical study confirms the qualities of our procedure

A nonparametric test for Cox processes

In a functional setting, we propose two test statistics to highlight the Poisson nature of a Cox process when n copies of the process are available. Our approach involves a comparison of the empirical mean and the empirical variance of the functional data and can be seen as an extended version of a classical overdispersion test for counting data. The limiting distributions of our statistics are derived using a functional central limit theorem for c`adl`ag martingales. We also study the asymptotic power of our tests under some local alternatives. Our procedure is easily implementable and does not require any knowledge of covariates. A numerical study reveals the good performances of the method. We also present two applications of our tests to real data sets

Weakly dependent random fields with infinite interactions - paru sous le titre "A fixed point approach to model random fields"

http://alea.impa.br/articles/v3/03-05.pdfWe introduce new models of stationary random fields, solutions of Xt =

An integer-valued bilinear type model

A integer-valued bilinear type model is proposed. It can take positive as well as negative values. The existence of the process is established in Lm. In fact, this process is the unique causal solution to an equation that is similar to a classical bilinear type model equation. For the estimation of the parameters, we suggest a quasi-maximum likelihood approach. The estimator is strongly consistent and asymptotically normal

Modélisation autorégressive à coefficients aléatoires

National audienceNous présenterons les différents modèles autorégressifs à valeurs entières positives introduits dans la littérature, leur structure de covariance, leur propriété de prévision ainsi les méthodes principales d'inférence