For 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.
The 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 data sets. This lack of robustness can lead to poor and suboptimal feature selection. 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. The analysis of two real data sets shows the necessity of a robust approach for policy makers.
This paper presents a new estimation method for the parameters of a model generating times series. Given some conditions on the form of the power spectral density associated to the process, it is possible to indirectly recover pa- rameter estimates from wavelet variances (WV) associated to the process. We propose an optimization criterion based on a standardized distance between the sample WV estimates and the model based WV, as is done e.g. with the generalized method of moments and therefore call the new estimator the generalized method of Wavelet Moments (GMWM) estimator. Moreover, it can be computed using simulations, so that it is very straightforward to implement in practice, since the only specification that is needed for a given model, is the data generating process. We derive its asymptotic properties for inference and perform a simulation study to compare the GMWM estimator to the MLE and another estimator with different models. We also use it to estimate the the stochastic error's parameters in accelerometer and gyroscopes composing inertial navigation systems by means of a sample of over 8000000 measurements, for which no other estimation method can be used.
This research presents methods for detecting and isolating faults in multiple MEMS-IMU configurations. First, geometric configurations with n sensor triads are investigated. It is proofed that the relative orientation between sensor triads is irrelevant to system optimality in the absence of failures. Then, the impact of sensor failure or decreased performance is investigated. Three FDI approaches (i.e. the parity space method, Mahalanobis distance method and its direct robustification) are reviewed theoretically and in the context of experiments using reference signals. It is shown that in the presence of multiple outliers the best performing detection algorithm is the robust version of the Mahalanobis distance.
