4,212 research outputs found
Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini
No full textThis paper discusses the contribution of Cerioli et al. (Stat Methods Appl, 2018), where robust monitoring based on high breakdown point estimators is proposed for multivariate data. The results follow years of development in robust diagnostic techniques. We discuss the issues of extending data monitoring to other models with complex structure, e.g. factor analysis, mixed linear models for which S- and MM-estimators exist or deviating data cells. We emphasise the importance of robust testing that is often overlooked despite robust tests being readily available once S- and MM-estimators have been defined. We mention open questions like out-of-sample inference or big data issues that would benefit from monitoring
Isotone additive latent variable models
No full textFor manifest variables with additive noise and for a given number of latent variables with an assumed distribution, we propose to nonparametrically estimate the association between latent and manifest variables. Our estimation is a two step procedure: first it employs standard factor analysis to estimate the latent variables as theoretical quantiles of the assumed distribution; second, it employs the additive models' backfitting procedure to estimate the monotone nonlinear associations between latent and manifest variables. The estimated fit may suggest a different latent distribution or point to nonlinear associations. We show on simulated data how, based on mean squared errors, the nonparametric estimation improves on factor analysis. We then employ the new estimator on real data to illustrate its use for exploratory data analysis
Robust estimation of constrained covariance matrices for Confirmatory Factor Analysis
No full textConfirmatory factor analysis (CFA) is a data analysis procedure that is widely used in social and behavioral sciences in general and other applied sciences that deal with large quantities of data (variables). The underlying model links a set latent factors, that are supposed to correspond to latent concepts, to a larger set of observed (manifest) variables through linear regression equations. With CFA, it is not necessary that all manifest variables are linked to all latent factors, and is particularly useful for the construction of so-called measurement scales like depression scales in psychology. The classical estimator (and inference) procedures are based either on the maximum likelihood (ML) or generalized least squares (GLS) approaches. Unfortunately these methods are known to be non robust to model misspecification, which in the case of factor analysis in general, and in CFA in particular, is misspecification with respect to the multivariate normal model. A natural robust estimator is obtained by first estimating the (mean and) covariance matrix of the manifest variables and then "plug-in" this statistic into the ML or GLS estimating equations. This two-stage method however doesn't fully take into account the covariance structure implied by the CFA model. In this paper, we propose an S-estimator for the parameters of the CFA model that is computed directly from the data. We derive the estimating equations and an iterative procedure. The two estimators have different asymptotic properties, in that their asymptotic covariance matrix is not the same, and they both depend on the model and the parameters values. We perform a simulation study to compare the finite sample properties of both estimators and find that the direct estimator we propose is more stable (smaller MSE) than the two-stage estimator
Robust VIF Regression with Application to Variable Selection in Large Datasets
No full textThe sophisticated and automated means of data collection used by an increasing number of institutions and companies leads to extremely large datasets. Subset selection in regression is essential when a huge number of covariates can potentially explain a response variable of interest. The recent statistical literature has seen an emergence of new selection methods that provide some type of compromise between implementation (computational speed) and statistical optimality (e.g. prediction error minimization). Global methods such as Mallows' Cp have been supplanted by sequential methods such as stepwise regression. More recently, streamwise regression, faster than the former, has emerged. A recently proposed streamwise regression approach based on the variance inflation factor (VIF) is promising but its least-squares based implementation makes it susceptible to the outliers inevitable in such large datasets. This lack of robustness can lead to poor and suboptimal feature selection. In our case, we seek to predict an individual's educational attainment using economic and demographic variables. We show how classical VIF performs this task poorly and a robust procedure is necessary for policy makers. This article proposes a robust VIF regression, based on fast robust estimators, that inherits all the good properties of classical VIF in the absence of outliers, but also continues to perform well in their presence where the classical approach fails
Bounded-Influence Robust Estimation in Generalized Linear Latent Variable Models
No full textLatent variable models are used for analyzing multivariate data. Recently, generalized linear latent variable models for categorical, metric, and mixed-type responses estimated via maximum likelihood (ML) have been proposed. Model deviations, such as data contamination, are shown analytically, using the influence function and through a simulation study, to seriously affect ML estimation. This article proposes a robust estimator that is made consistent using the basic principle of indirect inference and can be easily numerically implemented. The performance of the robust estimator is significantly better than that of the ML estimators in terms of both bias and variance. A real example from a consumption survey is used to highlight the consequences in practice of the choice of the estimator
Goodness of Fit for Generalized Linear Latent Variables Models
No full textGeneralized Linear Latent Variables Models (GLLVM) enable the modeling of relationships between manifest and latent variables, where the manifest variables are distributed according to a distribution of the exponential family (e.g. binomial or normal) and to the multinomial distribution (for ordinal manifest variables). These models are widely used in social sciences. To test the appropriateness of a particular model, one needs to define a Goodness-of-fit test statistic (GFI). In the normal case, one can use a likelihood ratio test or a modified version proposed by citeN{SaBe:01} (S&B GFI) that compares the sample covariance matrix to the estimated covariance matrix induced by the model. In the binary case, Pearson-type test statistics can be used if the number of observations is sufficiently large. In the other cases, including the case of mixed types of manifest variables, there exists GFI based on a comparison between a pseudo sample covariance and the model covariance of the manifest variables. These types of GFI are based on latent variable models that suppose that the manifest variables are themselves induced by underlying normal variables (underlying variable approach). The pseudo sample covariance matrices are then made of polychoric, tetrachoric or polyserial correlations. In this article, we propose an alternative GFI that is more generally applicable. It is based on some distance comparison between the latent scores and the original data. This GFI takes into account the nature of each manifest variable and can in principle be applied in various situations and in particular with models with ordinal, and both discrete and continuous manifest variables. To compute the value associated to our GFI, we propose a consistent resampling technique that can be viewed as a modified parametric bootstrap. A simulation study shows that our GFI has good performance in terms of empirical level and empirical power across different models with different types of manifest variables
Generalized Method of Wavelet Moments for Inertial Navigation Filter Design
No full textThe integration of observations issued from a satellite-based system (GNSS) with an inertial navigation system (INS) is usually performed through a Bayesian filter such as the extended Kalman filter (EKF). The task of designing the navigation EKF is strongly related to the inertial sensor error modeling problem. Accelerometers and gyroscopes may be corrupted by random errors of complex spectral structure. Consequently, identifying correct error-state parameters in the INS/GNSS EKF becomes difficult when several stochastic processes are superposed. In such situations, classical approaches like the Allan variance (AV) or power spectral density (PSD) analysis fail due to the difficulty of separating the error processes in the spectral domain. For this purpose, we propose applying a recently developed estimator based on the generalized method of wavelet moments (GMWM), which was proven to be consistent and asymptotically normally distributed. The GMWM estimator matches theoretical and sample-based wavelet variances (WVs), and can be computed using the method of indirect inference. This article mainly focuses on the implementation aspects related to the GMWM, and its integration within a general navigation filter alibration procedure. Regarding this, we apply the GMWM on error signals issued from MEMS-based inertial sensors by building and estimating composite stochastic processes for which classical methods cannot be used. In a first stage, we validate the resulting models using AV and PSD analyses and then, in a second stage, we study the impact of the resulting stochastic models design in terms of positioning accuracy using an emulated scenario with statically observed error signatures. We demonstrate that the GMWM-based calibration framework enables to estimate complex stochastic models in terms of the resulting navigation accuracy that are relevant for the observed structure of errors.TOP
Constrained expectation-maximization algorithm for stochastic inertial error modeling: study of feasibility
No full textStochastic modeling is a challenging task for low-cost sensors whose errors can have complex spectral structures. This makes the tuning process of the INS/GNSS Kalman filter often sensitive and difficult. For example, first-order Gauss–Markov processes are very often used in inertial sensor models. But the estimation of their parameters is a non-trivial task if the error structure is mixed with other types of noises. Such an estimation is often attempted by computing and analyzing Allan variance plots. This contribution demonstrates solving situations when the estimation of error parameters by graphical interpretation is rather difficult. The novel strategy performs direct estimation of these parameters by means of the expectation-maximization (EM) algorithm. The algorithm results are first analyzed with a critical and practical point of view using simulations with typically encountered error signals. These simulations show that the EM algorithm seems to perform better than the Allan variance and offers a procedure to estimate first-order Gauss–Markov processes mixed with other types of noises. At the same time, the conducted tests revealed limits of this approach that are related to the convergence and stability issues. Suggestions are given to circumvent or mitigate these problems when complexity of error structure is 'reasonable'. This work also highlights the fact that the suggested approach via EM algorithm and the Allan variance may not be able to estimate the parameters of complex error models reasonably well and shows the need for new estimation procedures to be developed in this context. Finally, an empirical scenario is presented to support the former findings. There, the positive effect of using the more sophisticated EM-based error modeling on a filtered trajectory is highlighted.TOP
Fast Robust Model Selection in Large Datasets
No full textLarge datasets are more and more common in many research fields. In particular, in the linear regression context, it is often the case that a huge number of potential covariates are available to explain a response variable, and the first step of a reasonable statistical analysis is to reduce the number of covariates. This can be done in a forward selection procedure that includes the selection of the variable to enter, the decision to retain it or stop the selection and estimation of the augmented model. Least squares plus t-tests can be fast, but the outcome of a forward selection might be suboptimal when there are outliers. In this paper, we propose a complete algorithm for fast robust model selection, including considerations for huge sample sizes. Since simply replacing the classical statistical criteria by robust ones is not computationally possible, we develop simplified robust estimators, selection criteria and testing procedures for linear regression. The robust estimator is a one-step weighted M-estimator that can be biased if the covariates are not orthogonal. We show that the bias can be made smaller by [...
Study of MEMS-based inertial sensors operating in dynamic conditions
No full textThis paper aims at studying the behaviour of the errors coming from inertial sensors when measured in dynamic conditions. After proposing a method for constructing the error process, the properties of these errors are estimated via the Generalized Method of Wavelets Moments methodology. The developed model parameters are compared to those obtained under static conditions. Finally an attempted is presented to find the link between the encountered dynamic of the vehicle and error-model parameters
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