Forecasting functional time series (FTS) has arguably achieved tremendous success in recent years. Time series of curves, or functional time series, exist in many disciplines. Among the numerous existing contributions for forecasting time series, one-step-ahead functional time series forecasting, that is one-step-ahead prediction of a curve-valued time series, has been studied in several practical studies. Predominantly most traditional functional time series studies use functional (Hilbertian) autoregressive models for one-step-ahead forecast, but their application in real-world data remains a pertinent challenge due to a non-stationary behavior. Opposed to such models, several nonparametric approaches have been proposed in the recent literature for forecasting time series of curves. An analysis of the forecasting performances of such nonparametric approaches, validated empirically with a set of real experiments, is presented in this paper. While a complete understanding of these approaches remains elusive, we hope that our perspectives, discussions, and comparisons serve as a stimulus for new statistical research.

A key step to optimize the tests of semiconductors during the production process is to improve the prediction of the final yield from the defects detected on the wafers during the production process. This study investigates the link between the defects detected by a Scanning Electron Microscope (SEM) and the electrical failure of the final semiconductors, with two main objectives: (a) to identify the best layers to inspect by SEM; (b) to develop a model that predicts electrical failures of the semiconductors from the detected defects. The first objective has been reached by a model based on Odds Ratio that gave a (ranked) list of the layers that best predict the final yield. This allows process engineers to concentrate inspections on a few important layers. For the second objective, a regression/classification model based on Gradient Boosting has been developed. As a by-product, this latter model confirmed the results obtained by Odds Ratio analysis. Both models take account of the high lacunarity of the data and have been validated on two distinct datasets from STMicroelectronics.

Clustering univariate functional data is mostly based on projecting the curves onto an adequate basis and applying some distance or similarity models on the coefficients. The basis functions should be chosen depending on features of the function being estimated. Commonly used are Fourier, polynomial and splines, but these may not be well suited for curves that exhibit inhomogeneous behavior. Wavelets on the contrary are well suited for identifying highly discriminant local time and scale features, and are able to adapt to the data smoothness. In recent years, few methods, relying on wavelet-based similarity measures, have been proposed for clustering curves, observed on equidistant points. In this work, we present a non-equidistant design wavelet based method for non-parametrically estimating and clustering a large number of curves. The method consists of several crucial stages: fitting functional data by non-equispaced design wavelet regression, screening out nearly flat curves, denoising the remaining curves with wavelet thresholding, and finally clustering the denoised curves. Simulation studies compare our proposed method with some other functional clustering methods. The method is applied for clustering some real functional data profiles.

Nowadays, Predictive Maintenance is a mandatory tool to reduce the cost of production in the semiconductor industry. This paper considers as a case study a critical part of the electrochemical deposition system, namely, the four Pins that hold a wafer inside a chamber. The aim of the study is to replace the schedule of replacement of Pins presently based on fixed timing (Preventive Maintenance) with a Hardware/Software system that monitors the conditions of the Pins and signals possible conditions of failure (Predictive Maintenance). The system is composed of optical sensors endowed with an image processing methodology. The prototype built for this study includes one optical camera that simultaneously takes images of the four Pins on a roughly daily basis. Image processing includes a pre-processing phase where images taken by the camera at different times are coregistered and equalized to reduce variations in time due to movements of the system and to different lighting conditions. Then, some indicators are introduced based on statistical arguments that detect outlier conditions of each Pin. Such indicators are pixel-wise to identify small artifacts. Finally, criteria are indicated to distinguish artifacts due to normal operations in the chamber from issues prone to a failure of the Pin. An application (PINapp) with a user friendly interface has been developed that guides industry experts in monitoring the system and alerting in case of potential issues. The system has been validated on a plant at STMicroelctronics in Catania (Italy). The study allowed for understanding the mechanism that gives rise to the rupture of the Pins and to increase the time of replacement of the Pins by a factor at least 2, thus reducing downtime.

This paper concerns the study of a non-smooth logistic regression function. The focus is on a high-dimensional binary response case by penalizing the decomposition of the unknown logit regression function on a wavelet basis of functions evaluated on the sampling design. Sample sizes are arbitrary (not necessarily dyadic) and we consider general designs. We study separable wavelet estimators, exploiting sparsity of wavelet decompositions for signals belonging to homogeneous Besov spaces, and using efficient iterative proximal gradient descent algorithms. We also discuss a level by level block wavelet penalization technique, leading to a type of regularization in multiple logistic regression with grouped predictors. Theoretical and numerical properties of the proposed estimators are investigated. A simulation study examines the empirical performance of the proposed procedures, and real data applications demonstrate their effectiveness.

Nonparametric univariate regression via wavelets is usually implemented under the assumptions of dyadic sample size, equally spaced fixed sample points, and i.i.d. normal errors. In this work, we propose, study and compare some wavelet based nonparametric estimation methods designed to recover a one-dimensional regression function for data that not necessary possess the above requirements. These methods use appropriate regularizations by penalizing the decomposition of the unknown regression function on a wavelet basis of functions evaluated on the sampling design. Exploiting the sparsity of wavelet decompositions for signals belonging to homogeneous Besov spaces, we use some efficient proximal gradient descent algorithms, available in recent literature, for computing the estimates with fast computation times. Our wavelet based procedures, in both the standard and the robust regression case have favorable theoretical properties, thanks in large part to the separability nature of the (non convex) regularization they are based on. We establish asymptotic global optimal rates of convergence under weak conditions. It is known that such rates are, in general, unattainable by smoothing splines or other linear nonparametric smoothers. Lastly, we present several experiments to examine the empirical performance of our procedures and their comparisons with other proposals available in the literature. An interesting regression analysis of some real data applications using these procedures unambiguously demonstrate their effectiveness.

This article studies M-type estimators for fitting robust additive models in the presence of anomalous data. The components in the additive model are allowed to have different degrees of smoothness. We introduce a new class of wavelet-based robust M-type estimators for performing simultaneous additive component estimation and variable selection in such inhomogeneous additive models. Each additive component is approximated by a truncated series expansion of wavelet bases, making it feasible to apply the method to nonequispaced data and sample sizes that are not necessarily a power of 2. Sparsity of the additive components together with sparsity of the wavelet coefficients within each component (group), results into a bi-level group variable selection problem. In this framework, we discuss robust estimation and variable selection. A two-stage computational algorithm, consisting of a fast accelerated proximal gradient algorithm of coordinate descend type, and thresholding, is proposed. When using nonconvex redescending loss functions, and appropriate nonconvex penalty functions at the group level, we establish optimal convergence rates of the estimates. We prove variable selection consistency under a weak compatibility condition for sparse additive models. The theoretical results are complemented with some simulations and real data analysis, as well as a comparison to other existing methods.

We introduce a new class of robust M-estimators for performing simultaneous parameter estimation and variable selection in high-dimensional regression models. We first explain the motivations for the key ingredient of our procedures which are inspired by regularization methods used in wavelet thresholding in noisy signal processing. The derived penalized estimation procedures are shown to enjoy theoretically the oracle property both in the classical finite dimensional case as well as the high-dimensional case when the number of variables p is not fixed but can grow with the sample size n, and to achieve optimal asymptotic rates of convergence. A fast accelerated proximal gradient algorithm, of coordinate descent type, is proposed and implemented for computing the estimates and appears to be surprisingly efficient in solving the corresponding regularization problems including the case for ultra high-dimensional data where p>> n. Finally, a very extensive simulation study and some real data analysis, compare several recent existing M-estimation procedures with the ones proposed in the paper, and demonstrate their utility and their advantages.

Short-Term Load Forecasting (STLF) is a fundamental instrument in the efficient operational management and planning of electric utilities. Emerging smart grid technologies pose new challenges and opportunities. Although load forecasting at the aggregate level has been extensively studied, electrical load forecasting at fine-grained geographical scales of households is more challenging. Among existing approaches, semi-parametric generalized additive models (GAM) have been increasingly popular due to their accuracy, flexibility, and interpretability. Their applicability is justified when forecasting is addressed at higher levels of aggregation, since the aggregated load pattern contains relatively smooth additive components. High resolution data are highly volatile, forecasting the average load using GAM models with smooth components does not provide meaningful information about the future demand. Instead, we need to incorporate irregular and volatile effects to enhance the forecast accuracy. We focus on the analysis of such hybrid additive models applied on smart meters data and show that it leads to improvement of the forecasting performances of classical additive models at low aggregation levels. (C) 2020 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

Wavelet methods are known to be very competitive in terms of denoising and compression, due to the simultaneous localization property of a function in time and frequency. However, boundary assumptions, such as periodicity or symmetry, generate bias and artificial wiggles which degrade overall accuracy. We present and compare some nonparametric estimation methods (wavelet and/or spline-based) designed to recover a one-dimensional piecewise-smooth regression function in both a fixed equidistant or not equidistant design regression model and a random design model.

We introduce a multi-platform portable implementation of the NonLocal Means methodology aimed at noise removal from remotely sensed images. It is particularly suited for hyperspectral sensors for which real-time applications are not possible with only CPU based algorithms. In the last decades computational devices have usually been a compound of cross-vendor sets of specifications (heterogeneous system architecture) that bring together integrated central processing (CPUs) and graphics processor (GPUs) units. However, the lack of standardization resulted in most implementations being too specific to a given architecture, eliminating (or making extremely difficult) code re-usability across different platforms. In order to address this issue, we implement a multi option NonLocal Means algorithm developed using the Open Computing Language (OpenCL) applied to Hyperion hyperspectral images. Experimental results demonstrate the dramatic speed-up reached by the algorithm on GPU with respect to conventional serial algorithms on CPU and portability across different platforms. This makes accurate real time denoising of hyperspectral images feasible.

A Round Robin exercise was implemented by ESA to compare different classification methods in detecting clouds from images taken by the PROBA-V sensor. A high-quality dataset of 1350 reflectances and Clear/Cloudy corresponding labels had been prepared by ESA in the framework of the exercise. Motivated by both the experience acquired by one of the authors in this exercise and the availability of such a reliable annotated dataset, we present a full assessment of the methodology proposed therein. Our objective is also to investigate specific issues related to cloud detection when remotely sensed images comprise only a few spectral bands in the visible and near-infrared. For this purpose, we consider a bunch of well-known classification methods. First, we demonstrate the feasibility of using a training dataset semi-automatically obtained from other accurate algorithms. In addition, we investigate the effect of ancillary information, e.g., surface type or climate, on accuracy. Then we compare the different classification methods using the same training dataset under different configurations. We also perform a consensus analysis aimed at estimating the degree of mutual agreement among classification methods in detecting Clear or Cloudy sky conditions.

Service literature has recognized the important role of customers' characteristics for successful innovation and is increasingly emphasizing the contribution of lead users. However, few studies have analyzed this issue with reference to advertising and other creative services, especially because of the difficulties in defining innovation in these industries, by capturing its complex nature. Through a large-scale survey on European advertising agencies, we provide empirical evidence of a multidimensional nature of innovation in these services, which can be better promoted by clients embodying some attributes rather than others. Indeed, our results identify three clusters, which differ for the clients' innovation enabling characteristics and their potential roles in promoting agency's innovation: the Dominant lead users; the Expert lead users; the Ordinary clients. We acknowledge the role of lead users in advertising and contribute to literature highlighting when they can be conducive to agency's innovation or be detrimental to it.

Cloud detection is a critical issue for satellite optical remote sensing, since potential errors in cloud masking can be translated directly into significant uncertainty in the retrieved downstream geophysical products. The problem is particularly challenging when only of a limited number of spectral bands is available, and thermal infrared bands are lacking. This is the case of Proba-V instrument, for which the European Space Agency (ESA) carried out a dedicated Round Robin exercise, aimed at intercomparing several cloud detection algorithms to better understand their advantages and drawbacks for various clouds and surface conditions, and to learn lessons on cloud detection in the VNIR and SWIR domain for land and coastal water remote sensing. The present contribution is aimed at a thorough quality assessment of the results of the cloud detection approach we proposed, based on Cumulative Discriminant Analysis. Such a statistical method relies on the empirical cumulative distribution function of the measured reflectance in clear and cloudy conditions to produce a decision rule. It can be adapted to the user's requirements in terms of preferred levels for both type I and type II errors. In order to obtain a fully automatic procedure, we choose as a training dataset a subset of the full Proba-V scenes for which a cloud mask is estimated by a consolidated algorithm (silver standard), that is from either SEVIRI, MODIS or both sensors. Within this training set, different subsets have been setup according to the different types of surface underlying scenes (water, vegetation, bare land, urban, and snow/ice). We present the analysis of the cloud classification errors for a range of such test scenes to yield important inferences on the efficiency and accuracy of the proposed methodology when applied to different types of surfaces.

The theoretical understanding of Gartner's "hype curve" is an interesting open question in deciding the strategic actions to adopt in presence of an incoming technology. In order to describe the hype behaviour quantitatively, we propose a mathematical approach based on a rate equation, similar to that used to describe quantum level transitions. The model is able to describe the hype curve evolution in many relevant conditions, which can be associated to various market parameters. Different hype curves, describing the time evolution of a new technology market penetration, are then obtained within a single coherent mathematical approach. We have also used our theoretical model to describe the time evolution of the number of scientific publications in different fields of scientific research. Data are well described by our model, so we present a statistical analysis and forecasting potentiality of our approach. We note that the hype peak of inflated expectations is very smooth in the case of scientific publications, probably due to the high level of awareness and the deep preliminary understanding which is necessary to carry on a research project. Our model is anyway flexible enough to describe many patterns of increasing interest on a new idea, leading to a hype behaviour or other time evolution.

A critical issue in image restoration is noise removal, whose state-of-art algorithm, NonLocal Means, is highly demanding in terms of computational time. Aim of the present paper is to boost its performance by an efficient algorithm tailored to GPU hardware architectures. This algorithm adapts itself to several variants of the methodologies in terms of different strategies for estimating the involved filtering parameter, type of noise affecting data, multicomponent signals, spatial dimension of the images. Numerical experiments on brain Magnetic Resonance images are provided.

Even though the Hartley-entropy-based contrast function guarantees an unmixing local minimum, the reported nonsmooth optimization techniques that minimize this nondifferentiable function encounter computational bottlenecks. Toward this, Powell's derivative-free optimization method has been extended to a Riemannian manifold, namely, oblique manifold, for the recovery of quasi-correlated sources by minimizing this contrast function. The proposed scheme has been demonstrated to converge faster than the related algorithms in the literature, besides the impressive source separation results in simulations involving synthetic sources having finite-support distributions and correlated images.

We study sparse high dimensional additive model fitting via penalization with sparsity-smoothness penalties. We review several existing algorithms that have been developed for this problem in the recent literature, highlighting the connections between them, and present some computationally efficient algorithms for fitting such models. Furthermore, using reasonable assumptions and exploiting recent results on group LASSO-like procedures, we take advantage of several oracle results which yield asymptotic optimality of estimators for high-dimensional but sparse additive models. Finally, variable selection procedures are compared with some high-dimensional testing procedures available in the literature for testing the presence of additive components.

First asymptotic relations of Voronovskaya-type for rational operators of Shepard-type are shown. A positive answer in some senses to a problem on the pointwise approximation power of linear operators on equidistant nodes posed by Gavrea, Gonska and Kacs is given. Direct and converse results, computational aspects and Gruss-type inequalities are also proved. Finally an application to images compression is discussed, showing the outperformance of such operators in some senses.

The accurate segmentation of the optic disc (OD) offers an important cue to extract other retinal features in an automated diagnostic system, which in turn will assist ophthalmologists to track many retinopathy conditions such as glaucoma. Research contributions regarding the OD segmentation is on the rise, since the design of a robust automated system would help prevent blindness, for instance, by diagnosing glaucoma at an early stage and a condition known as ocular hypertension. Among the evaluated OD segmentation schemes, the active contour models (ACMs) have often been preferred by researchers, because ACMs are endowed with several attractive properties. To this end, we designed an OD segmentation scheme to infer how the performance of the well-known gradient vector flow (GVF) model compares with nine popular/recent ACM algorithms by supplying them with the initial OD contour derived from the circular Hough transform. The findings would hopefully equip a diagnostic system designer with an empirical support to ratify the choice of a specific model as we are bereft of such a comparative study. A dataset comprising 169 diverse retinal images was tested, and the segmentation results were assessed by a gold standard derived from the annotations of five domain experts. The segmented ODs from the GVF-based ACM coincide to a greater degree with those of the experts in 94% of the cases as predicted by the least overall Hausdorff distance value (33.49 +/- 18.21). Additionally, the decrease in the segmentation error due to the suggested ACM has been confirmed to be statistically significant in view of the p values (<= 1.49e-09) from the Wilcoxon signed-rank test. The mean computational time taken by the investigated approaches has also been reported. (C) 2014 Elsevier Ltd. All rights reserved.