arXiv subjects

Stephane Guerrier

Publications and source records attributed to Stephane Guerrier.

4 recordsLinked to original sources

arXiv2026

On tail-robust autocovariance matrix estimation for high-dimensional and potentially nonstationary time series

In this paper, we study the autocovariance matrix estimation and inference problems under heavy-tailedness, high-dimensionality, general nonlinear temporal dependence, and potentially nonstationarity of time series. We consider two types of tail-robust autocovariance matrix estimation methods: the element-wise Huber's $M$-estimator and a computationally more efficient element-wise truncated estimator. Both estimators are designed to achieve sharp error bounds in matrix max-norm. The nonasymptotic properties of these estimators are proved based on new variants of Bernstein-type inequalities under functional dependence for the potentially nonstationary processes which may be of independent interest. Moreover, we prove a high-dimensional Gaussian approximation result, as a limiting distribution, for our element-wise truncated autocovariance estimator. A Gaussian multiplier bootstrap result is also given to facilitate the practicality. Our theoretical results are nonasymptotic, which gives explicit error bounds in terms of the sample size, dimensionality, moments, and the strength of temporal dependence. Numerical evidence is provided to support our theoretical results. Finally, we illustrate the benefits of the proposed methodology for detecting change points in monthly macroeconomic data.

stat.ME↗

arXiv2016

Robust Inference for Time Series Models: a Wavelet-based Framework

We present a new framework for the robust estimation of latent time series models which is fairly general and, for example, covers models going from ARMA to state-space models. This approach provides estimators which are (i) consistent and asymptotically normally distributed, (ii) applicable to various classes of time series models, (iii) straightforward to implement and (iv) computationally efficient. The framework is based on the recently developed Generalized Method of Wavelet Moments (GMWM) and a new robust estimator of the wavelet variance. Compared to existing methods, the latter directly estimates the quantity of interest while performing better in finite samples and using milder conditions for its asymptotic properties to hold. Moreover, results are given showing the identifiability of the GMWM for various classes of time series models thereby allowing this method to consistently estimate many models (and combinations thereof) under mild conditions. Hence, not only does this paper provide an alternative estimator which allows to perform wavelet variance analysis when data are contaminated but also a general approach to robustly estimate the parameters of a variety of (latent) time series models. The simulation studies carried out confirm the better performance of the proposed estimators and the usefulness and broadness of the proposed methodology is shown using practical examples from the domains of economics and engineering with sample sizes up to 900,000.

stat.ME↗

arXiv2016

A Computationally Efficient Framework for Automatic Inertial Sensor Calibration

The calibration of (low-cost) inertial sensors has become increasingly important over the past years since their use has grown exponentially in many applications going from unmanned aerial vehicle navigation to 3D-animation. However, this calibration procedure is often quite problematic since the signals issued from these sensors have a complex spectral structure and the methods available to estimate the parameters of these models are either unstable, computationally intensive and/or statistically inconsistent. This paper presents a new software platform for inertial sensor calibration based on the Generalized Method of Wavelet Moments which provides a computationally efficient, flexible, user-friendly and statistically sound tool to estimate and select from a wide range of complex models. The software is developed within the open-source statistical software R and is based on C++ language allowing it to achieve high computational performance.

stat.AP↗

arXiv2015

A Prediction Divergence Criterion for Model Selection

The problem of model selection is inevitable in an increasingly large number of applications involving partial theoretical knowledge and vast amounts of information, like in medicine, biology or economics. The associated techniques are intended to determine which variables are "important" to "explain a phenomenon under investigation. The terms "important" and "explain" can have very different meanings according to the context and, in fact, model selection can be applied to any situation where one tries to balance variability with complexity. In this paper, we introduce a new class of error measures and of model selection criteria, to which many well know selection criteria belong. Moreover, this class enables us to derive a novel criterion, based on a divergence measure between the predictions produced by two nested models, called the Prediction Divergence Criterion (PDC). Our selection procedure is developed for linear regression models, but has the potential to be extended to other models. We demonstrate that, under some regularity conditions, it is asymptotically loss efficient and can also be consistent. In the linear case, the PDC is a counterpart to Mallow's Cp but with a lower asymptotic probability of overfitting. In a case study and by means of simulations, the PDC is shown to be particularly well suited in "sparse" settings with correlated covariates which we believe to be common in real applications.

stat.ME↗