arXiv subjects

Lionel Truquet

Publications and source records attributed to Lionel Truquet.

23 records · Page 2Linked to original sources

arXiv2017

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.

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arXiv2016

Parameter stability and semiparametric inference in time-varying ARCH models

In this paper, we develop a complete methodology for detecting time-varying/non time-varying parameters in ARCH processes. For this purpose, we estimate and test various semiparametric versions of the time-varying ARCH model (tv-ARCH) which include two well known non stationary ARCH type models introduced in the econometric literature. Using kernel estimation, we show that non time-varying parameters can be estimated at the usual parametric rate of convergence and for a Gaussian noise, we construct estimates that are asymptotically efficient in a semiparametric sense. Then we introduce two statistical tests which can be used for detecting non time-varying parameters or for testing the second order dynamic. An information criterion for selecting the number of lags is also provided. We illustrate our methodology with several real data sets.

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arXiv2016

Root-n consistent estimation of the marginal density in some time series models

In this paper, we consider the problem of estimating the marginal density in some nonlinear autoregressive time series models for which the conditional mean and variance have a parametric specification. Under some regularity conditions, we show that a kernel type estimate based on the residuals can be root-n consistent even if the noise density is unknown. Our results, which are shown to be valid for classical time series models such as ARMA or GARCH processes, extend substantially the existing results obtained for some homoscedatic time series models. Asymptotic expansion of our estimator is obtained by combining some martingale type arguments and a coupling method for time series which is of independent interest. We also study the uniform convergence of our estimator on compact intervals.

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arXiv2016

Local stationarity and time-inhomogeneous Markov chains

In this paper, we study a notion of local stationarity for discrete time Markov chains which is useful for applications in statistics. In the spirit of some locally stationary processes introduced in the literature, we consider triangular arrays of time-inhomogeneous Markov chains, defined by some families of contracting Markov kernels. Using the Dobrushin's contraction coefficients for various metrics, we show that the distribution of such Markov chains can be approximated locally with the distribution of ergodic Markov chains and we also study some mixing properties. From our approximation results in Wasserstein metrics, we recover several properties obtained for autoregressive processes. Moreover, using the total variation distance or more generally some distances induced by a drift function, we consider new models, such as finite state space Markov chains with time-varying transition matrices or some time-varying versions of integer-valued autoregressive processes. For these two examples, nonparametric kernel estimation of the transition matrix is discussed. \end{abstract}

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arXiv2016

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.

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