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.

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.

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.

Error estimates of pointwise approximation, that are not possible by polynomials, are obtained by simple rational operators based on exponential-type meshes, improving previous results. Rational curves deduced from such operators are analyzed by Discrete Fourier Transform and a CAGD modeling technique for Shepard-type curves by truncated DFT and the PIA algorithm is developed.

A stochastic scheme, namely, PLM-Lap, has recently been propounded, which relies on the profile likelihood (PL) constructed with a Laplace distribution for estimating muscle activation onsets (MAOs) in surface electromyographic (sEMG) data. The MAO detection accuracy and robustness of the PLM-Lap have been empirically shown to be better than those of several state-of-the-art approaches. The algorithm designates the data point index associated with the maximum of the PL function as an onset occurrence by regarding every sEMG data point as a candidate onset and hence exhaustively evaluating the objective function. This article concerns an expedient and faster approach premised on the discrete Fibonacci search (DFS) to locate the maximum of the discrete PL function. The experimental results support that both the exhaustive and DFS procedures are equivalent in a statistical sense, whereas the latter offers impressive computational savings by a factor of approximately 90. Owing to the speed-up, the accuracy of MAO estimation may further be enhanced by modeling the sEMG data with a set of PL functions, each one built using a suitable probability distribution, and picking the estimate from the best model. Three statistical criteria, i.e., Kolmogorov-Smirnov, Lilliefors, and Anderson-Darling test, for choosing the probability distribution are recommended. A freely downloadable MATLAB package, namely PROLIFIC, meant for sEMG onset detection is available on MATLAB File Exchange from the following link: https://www.mathworks.com/matlabcentral/fileexchange/76495-prolific-profile-likelihoodbased-on-fibonacci-search.

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.

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.

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.

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.

In a previous work, we have presented an innovative theoretical model to describe the evolution of the life cycle of a new technology. We have proposed 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 with various external parameters. In this article, we apply this model to describe the evolution of the number of publications in some different research fields that are very current and extremely advanced in terms of social impact. The applications have been chosen in the fields of biomolecular chemistry, genetics and superconducting nanoelectronics.

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.

Direct and converse approximation error estimates for generalized Shepard operators are given, improving analogous inequalities for well-known Shepard operators. As application in CAGD, generalized degree elevation algorithms for modeling the shape of Shepard-type curves are presented, improving previous techniques.

A Gupta-type variant of Shepard operators is introduced and convergence results and pointwise and uniform direct and converse approximation results are given. An application to image compression improving a previous algorithm is also discussed.

Surface electromyographic (sEMG) data impart valuable information concerning muscle function and neuromuscular diseases especially under human movement conditions. However, they are subject to trial-wise and subject-wise variations, which would pose challenges for investigators engaged in precisely estimating the onset of muscle activation. To this end, we posited two unsupervised statistical approaches-scree-plot elbow detection (SPE) heavily relying on the threshold choice and the more robust profile likelihood maximization (PLM) that obviates parameter tuning-for accurately detecting muscle activation onsets (MAOs). The performance of these algorithms was evaluated using the sEMG dataset provided in the article by Tenanet al. and the simulated sEMG created as explained therein. These sEMG signals are reported to have been collected from the biceps brachii and vastus lateralis of 18 participants while performing a biceps curl or knee extension, respectively. The acquired sEMG signals were first preconditioned with the Teager-Kaiser energy operator, and then, either supplied to the SPE or to the PLM or to a state-of-the-art algorithm. The mean and median errors, between the MAO time in milliseconds estimated by each of the algorithms and the gold standard onset time, were computed. The outcome of a PLM variant, namely, PLM-Laplacian, has been found to have good agreement with the gold standard, i.e., an absolute median error of 9 and 21 ms in the simulated and the actual sEMG data, respectively; whereas, the errors produced by the other algorithms are statistically significantly larger than that incurred by the PLM-Laplacian according to Wilcoxon rank-sum test. In addition, the advocated approach does not necessitate parameter settings, lending itself to be flexible and adaptable to any application, which is a unique advantage over several other methods. Research is underway to further validate this technique by imposing various experimental conditions.

Shepard-type rational operators based on q-integers are studied and convergence results and pointwise approximation error estimates improving previous statements are obtained. Influence of choice of q on the error estimates is also discussed. Techniques in CAGD for shape modeling of rational curves based on above operators are also presented and numerical examples are given.

Uniform approximation error estimates for weighted Shepard-type operators more flexible than the unweighted analogues are given. Error estimates for a linear combination of their iterates faster converging than previous ones are also showed. The results are applied in CAGD to construct Shepard-type curves useful in modeling and a weighted progressive iterative approximation technique exponentially converging.

In this paper we study sparse high dimensional additive partial linear models with nonparametric additive components of heterogeneous smoothness. We review several existing algo- rithms that have been developed for this problem in the recent literature, highlighting the connec- tions between them, and present some computationally efficient algorithms for fitting such models. To achieve optimal rates in large sample situations we use hybrid P-splines and block wavelet penal- isation techniques combined with adaptive (group) LASSO-like procedures for selecting the additive components in the nonparametric part of the models. Hence, the component selection and estimation in the nonparametric part may be viewed as a functional version of estimation and grouped variable selection. This allows to take advantage of several oracle results which yield asymptotic optimality of estimators in high-dimensional but sparse additive models. Numerical implementations of our procedures for proximal like algorithms are discussed. Large sample properties of the estimates and of the model selection are presented and the results are illustrated with simulated examples and a real data analysis.

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.

First parametric curves of Shepard-type are studied, which overcome some of the original Shepard operator's drawbacks, have some advantages with respect to the Bezier case and are optimal in some sense. Bounds for the deviation and approximation results for Shepard-type operators faster converging than the original one are proved. As an application a weighted progressive iterative approximation technique interesting in CAGD and an extension to tensor product surfaces case are given.