arXiv subjects

Stéphane Guerrier

Publications and source records attributed to Stéphane Guerrier.

33 records · Page 2Linked to original sources

arXiv2020

Prevalence Estimation from Random Samples and Census Data with Participation Bias

Countries officially record the number of COVID-19 cases based on medical tests of a subset of the population with unknown participation bias. For prevalence estimation, the official information is typically discarded and, instead, small random survey samples are taken. We derive (maximum likelihood and method of moment) prevalence estimators, based on a survey sample, that additionally utilize the official information, and that are substantially more accurate than the simple sample proportion of positive cases. Put differently, using our estimators, the same level of precision can be obtained with substantially smaller survey samples. We take into account the possibility of measurement errors due to the sensitivity and specificity of the medical testing procedure. The proposed estimators and associated confidence intervals are implemented in the companion open source R package cape.

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arXiv2020

A General Approach for Simulation-based Bias Correction in High Dimensional Settings

An important challenge in statistical analysis lies in controlling the bias of estimators due to the ever-increasing data size and model complexity. Approximate numerical methods and data features like censoring and misclassification often result in analytical and/or computational challenges when implementing standard estimators. As a consequence, consistent estimators may be difficult to obtain, especially in complex and/or high dimensional settings. In this paper, we study the properties of a general simulation-based estimation framework that allows to construct bias corrected consistent estimators. We show that the considered approach leads, under more general conditions, to stronger bias correction properties compared to alternative methods. Besides its bias correction advantages, the considered method can be used as a simple strategy to construct consistent estimators in settings where alternative methods may be challenging to apply. Moreover, the considered framework can be easily implemented and is computationally efficient. These theoretical results are highlighted with simulation studies of various commonly used models, including the negative binomial regression (with and without censoring) and the logistic regression (with and without misclassification errors). Additional numerical illustrations are provided in the supplementary materials.

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arXiv2020

Asymptotically Optimal Bias Reduction for Parametric Models

An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. This problem is magnified in high-dimensional settings where the number of variables $p$ diverges with the sample size $n$, as well as for nonlinear models and/or models with discrete data. For these complex settings, we propose to use a general simulation-based approach and show that the resulting estimator has a bias of order $\mathcal{O}(0)$, hence providing an asymptotically optimal bias reduction. It is based on an initial estimator that can be slightly asymptotically biased, making the approach very generally applicable. This is particularly relevant when classical estimators, such as the maximum likelihood estimator, can only be (numerically) approximated. We show that the iterative bootstrap of Kuk (1995) provides a computationally efficient approach to compute this bias reduced estimator. We illustrate our theoretical results in simulation studies for which we develop new bias reduced estimators for the logistic regression, with and without random effects. These estimators enjoy additional properties such as robustness to data contamination and to the problem of separability.

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arXiv2020

Robust Two-Step Wavelet-Based Inference for Time Series Models

Complex time series models such as (the sum of) ARMA$(p,q)$ models with additional noise, random walks, rounding errors and/or drifts are increasingly used for data analysis in fields such as biology, ecology, engineering and economics where the length of the observed signals can be extremely large. Performing inference on and/or prediction from these models can be highly challenging for several reasons: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when models include more than just a few parameters and/or the time series are large; (iii) model building and/or selection adds another layer of (computational) complexity to the previous task; and (iv) solutions that address (i), (ii) and (iii) simultaneously do not exist in practice. For this reason, this paper aims at jointly addressing these challenges by proposing a general framework for robust two-step estimation based on a bounded influence M-estimator of the wavelet variance. In this perspective, we first develop the conditions for the joint asymptotic normality of the latter estimator thereby providing the necessary tools to perform (direct) inference for scale-based analysis of signals. Taking advantage of the model-independent weights of this first-step estimator that are computed only once, we then develop the asymptotic properties of two-step robust estimators using the framework of the Generalized Method of Wavelet Moments (GMWM), hence defining the Robust GMWM (RGMWM) that we then use for robust model estimation and inference in a computationally efficient manner even for large time series. Simulation studies illustrate the good finite sample performance of the RGMWM estimator and applied examples highlight the practical relevance of the proposed approach.

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arXiv2019

Wavelet-Based Moment-Matching Techniques for Inertial Sensor Calibration

The task of inertial sensor calibration has required the development of various techniques to take into account the sources of measurement error coming from such devices. The calibration of the stochastic errors of these sensors has been the focus of increasing amount of research in which the method of reference has been the so-called "Allan variance slope method" which, in addition to not having appropriate statistical properties, requires a subjective input which makes it prone to mistakes. To overcome this, recent research has started proposing "automatic" approaches where the parameters of the probabilistic models underlying the error signals are estimated by matching functions of the Allan variance or Wavelet Variance with their model-implied counterparts. However, given the increased use of such techniques, there has been no study or clear direction for practitioners on which approach is optimal for the purpose of sensor calibration. This paper formally defines the class of estimators based on this technique and puts forward theoretical and applied results that, comparing with estimators in this class, suggest the use of the Generalized Method of Wavelet Moments as an optimal choice.

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arXiv2019

Phase Transition Unbiased Estimation in High Dimensional Settings

An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is typically magnified in high-dimensional settings where the number of variables $p$ is allowed to diverge with the sample size $n$. However, it is generally difficult to establish whether an estimator is unbiased and therefore its asymptotic order is a common approach used (in low-dimensional settings) to quantify the magnitude of the bias. As an alternative, we introduce a new and stronger property, possibly for high-dimensional settings, called phase transition unbiasedness. An estimator satisfying this property is unbiased for all $n$ greater than a finite sample size $n^\ast$. Moreover, we propose a phase transition unbiased estimator built upon the idea of matching an initial estimator computed on the sample and on simulated data. It is not required for this initial estimator to be consistent and thus it can be chosen for its computational efficiency and/or for other desirable properties such as robustness. This estimator can be computed using a suitable simulation based algorithm, namely the iterative bootstrap, which is shown to converge exponentially fast. In addition, we demonstrate the consistency and the limiting distribution of this estimator in high-dimensional settings. Finally, as an illustration, we use our approach to develop new estimators for the logistic regression model, with and without random effects, that also enjoy other properties such as robustness to data contamination and are also not affected by the problem of separability. In a simulation exercise, the theoretical results are confirmed in settings where the sample size is relatively small compared to the model dimension.

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arXiv2019

Multivariate Signal Modelling with Applications to Inertial Sensor Calibration

The common approach to inertial sensor calibration for navigation purposes has been to model the stochastic error signals of individual sensors independently, whether as components of a single inertial measurement unit (IMU) in different directions or arrayed in the same direction for redundancy. These signals usually have an extremely complex spectral structure that is often described using latent (or composite) models composed by a sum of underlying models. A large amount of research in this domain has been focused on the latter aspect through the proposal of various methods that have been able to improve the estimation of these models both from a computational and a statistical point of view. However, the separate calibration of the individual sensors is still unable to take into account the dependence between each of them which can have an important impact on the precision of the navigation systems. In this paper, we develop a new approach to simultaneously model both the individual signals and the dependence between them by studying the quantity called Wavelet Cross-Covariance and using it to extend the application of the Generalized Method of Wavelet Moments. This new method can be used in other settings for time series modeling, especially in cases where the dependence among signals may be hard to detect. Moreover, in the field of inertial sensor calibration, this approach can deliver important contributions among which the possibility to test dependence between sensors, integrate their dependence within the navigation filter and construct an optimal virtual sensor that can be used to simplify and improve navigation accuracy. The advantages of this method and its usefulness for inertial sensor calibration are highlighted through a simulation study and an applied example with a small array of XSens MTi-G IMUs.

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arXiv2019

A simple recipe for making accurate parametric inference in finite sample

Constructing tests or confidence regions that control over the error rates in the long-run is probably one of the most important problem in statistics. Yet, the theoretical justification for most methods in statistics is asymptotic. The bootstrap for example, despite its simplicity and its widespread usage, is an asymptotic method. There are in general no claim about the exactness of inferential procedures in finite sample. In this paper, we propose an alternative to the parametric bootstrap. We setup general conditions to demonstrate theoretically that accurate inference can be claimed in finite sample.

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arXiv2018

On the Properties of Simulation-based Estimators in High Dimensions

Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase with the sample size bringing standard inferential procedures to incur significant loss in terms of performance. Moreover, the complexity of statistical models is also increasing thereby entailing important computational challenges in constructing new estimators or in implementing classical ones. A trade-off between numerical complexity and statistical properties is often accepted. However, numerically efficient estimators that are altogether unbiased, consistent and asymptotically normal in high dimensional problems would generally be ideal. In this paper, we set a general framework from which such estimators can easily be derived for wide classes of models. This framework is based on the concepts that underlie simulation-based estimation methods such as indirect inference. The approach allows various extensions compared to previous results as it is adapted to possibly inconsistent estimators and is applicable to discrete models and/or models with a large number of parameters. We consider an algorithm, namely the Iterative Bootstrap (IB), to efficiently compute simulation-based estimators by showing its convergence properties. Within this framework we also prove the properties of simulation-based estimators, more specifically the unbiasedness, consistency and asymptotic normality when the number of parameters is allowed to increase with the sample size. Therefore, an important implication of the proposed approach is that it allows to obtain unbiased estimators in finite samples. Finally, we study this approach when applied to three common models, namely logistic regression, negative binomial regression and lasso regression.

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arXiv2017

A Study of the Allan Variance for Constant-Mean Non-Stationary Processes

The Allan Variance (AV) is a widely used quantity in areas focusing on error measurement as well as in the general analysis of variance for autocorrelated processes in domains such as engineering and, more specifically, metrology. The form of this quantity is widely used to detect noise patterns and indications of stability within signals. However, the properties of this quantity are not known for commonly occurring processes whose covariance structure is non-stationary and, in these cases, an erroneous interpretation of the AV could lead to misleading conclusions. This paper generalizes the theoretical form of the AV to some non-stationary processes while at the same time being valid also for weakly stationary processes. Some simulation examples show how this new form can help to understand the processes for which the AV is able to distinguish these from the stationary cases and hence allow for a better interpretation of this quantity in applied cases.

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arXiv2016

Wavelet Variance for Random Fields: an M-Estimation Framework

We present a general M-estimation framework for inference on the wavelet variance. This framework generalizes the results on the scale-wise properties of the standard estimator and extends them to deliver the joint asymptotic properties of the estimated wavelet variance vector. Moreover, this is achieved by extending the estimation of the wavelet variance to multidimensional random fields and by stating the necessary conditions for these properties to hold when the size of the wavelet variance vector goes to infinity with the sample size. Finally, these results generally hold when using bounded estimating functions thereby delivering a robust framework for the estimation of this quantity which improves over existing methods both in terms of asymptotic properties and in terms of its finite sample performance. The proposed estimator is investigated in simulation studies and different applications highlighting its good properties.

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arXiv2016

Fast and Robust Parametric Estimation for Time Series and Spatial Models

We present a new framework for robust estimation and inference on second-order stationary time series and random fields. This framework is based on the Generalized Method of Wavelet Moments which uses the wavelet variance to achieve parameter estimation for complex models. Using an M-estimator of the wavelet variance, this method can be made robust therefore allowing to estimate the parameters of a wide range of time series and spatial models when the data suffers from outliers or different forms of contamination. The paper presents a series of simulation studies as well as a range of applications where this new approach can be considered as a computationally efficient, numerically stable and robust method which performs at least as well as existing methods in bounding the influence of outliers on the estimation procedure.

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arXiv2016

On the Identifiability of Latent Models for Dependent Data

The condition of parameter identifiability is essential for the consistency of all estimators and is often challenging to prove. As a consequence, this condition is often assumed for simplicity although this may not be straightforward to assume for a variety of model settings. In this paper we deal with a particular class of models that we refer to as "latent" models which can be defined as models made by the sum of underlying models, such as a variety of linear state-space models for time series. These models are of great importance in many fields, from ecology to engineering, and in this paper we prove the identifiability of a wide class of (second-order stationary) latent time series and spatial models and discuss what this implies for some extremum estimators, thereby reducing the conditions for their consistency to some very basic regularity conditions. Finally, a specific focus is given to the Generalized Method of Wavelet Moments estimator which is also able to estimate intrinsically second-order stationary models.

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arXiv2016

The gmwm R package: a comprehensive tool for time series analysis from state-space models to robustness

The gmwm R package for inference on time series models is mainly based on the quantity called wavelet variance which is derived from a wavelet decomposition of a time series. This quantity provides a means to summarize and graphically represent the features of time series in order to identify possible models. Moreover, it is used as a moment condition for model estimation through the generalized method of wavelet moments. Based on the latter method, this package not only provides an alternative method to estimate classical ARMA models but also delivers a general framework for the robust estimation of many time series models as well as a quick and efficient estimation of many linear state-space models.

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arXiv2015

A Paradigmatic Regression Algorithm for Gene Selection Problems

Motivation: Gene selection has become a common task in most gene expression studies. The objective of such research is often to identify the smallest possible set of genes that can still achieve good predictive performance. The problem of assigning tumours to a known class is a particularly important example that has received considerable attention in the last ten years. Many of the classification methods proposed recently require some form of dimension-reduction of the problem. These methods provide a single model as an output and, in most cases, rely on the likelihood function in order to achieve variable selection. Results: We propose a prediction-based objective function that can be tailored to the requirements of practitioners and can be used to assess and interpret a given problem. The direct optimization of such a function can be very difficult because the problem is potentially discontinuous and nonconvex. We therefore propose a general procedure for variable selection that resembles importance sampling to explore the feature space. Our proposal compares favorably with competing alternatives when applied to two cancer data sets in that smaller models are obtained for better or at least comparable classification errors. Furthermore by providing a set of selected models instead of a single one, we construct a network of possible models for a target prediction accuracy level.

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