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Non-fungible tokens (NFT) have recently emerged as a novel blockchain hosted financial asset class that has attracted major transaction volumes. Investment decisions rely on data and adequate preprocessing and application of analytics to them. Both owing to the non-fungible nature of the tokens and to a blockchain being the primary data source, NFT transaction data pose several challenges not commonly encountered in traditional financial data. Using data that consist of the transaction history of eight highly valued NFT collections, a selection of such challenges is illustrated. These are: price differentiation by token traits, the possible existence of lateral swaps and wash trades in the transaction history and finally, severe volatility. While this paper merely scratches the surface of how data analytics can be applied in this context, the data and challenges laid out here may present opportunities for future research on the topic.

Nonfungible tokens have recently developed into a new financial market segment notorious for wash trading activity. Wash trades are made when users swap tokens between two or more of their own wallet addresses, most often to boost asset prices and volumes artificially, or to harvest marketplace rewards. The presence of wash trades can entirely distort the apparent fair value of tokens in a collection. They should therefore be detected and excluded from further financial assessments such as token valuations and appraisals. This letter introduces three novel strategies to flag transactions for suspicious wash activity, tailored to the NFT markets.

The direpack package establishes a set of modern statistical dimensionality reduction techniques into the Python universe as a single, consistent package. Several of the methods included are only available as open source through direpack, whereas the package also offers competitive Python implementations of methods previously only available in other programming languages. In its present version, the package is structured in three subpackages for different approaches to dimensionality reduction: projection pursuit, sufficient dimension reduction and robust M estimators. As a corollary, the package also provides access to regularized regression estimators based on these reduced dimension spaces, as well as a set of classical and robust preprocessing utilities, including very recent developments such as generalized spatial signs. Finally, direpack has been written to be consistent with the scikit-learn API, such that the estimators can flawlessly be included into (statistical and/or machine) learning pipelines in that framework.(c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

As its name suggests, sufficient dimension reduction (SDR) targets to estimate a subspace from data that contains all information sufficient to explain a dependent variable. Ample approaches exist to SDR, some of the most recent of which rely on minimal to no model assumptions. These are defined according to an optimization criterion that maximizes a nonparametric measure of association. The original estimators are nonsparse, which means that all variables contribute to the model. However, in many practical applications, an SDR technique may be called for that is sparse and as such, intrinsically performs sufficient variable selection (SVS). This paper examines how such a sparse SDR estimator can be constructed. Three variants are investigated, depending on different measures of association: distance covariance, martingale difference divergence and ball covariance. A simulation study shows that each of these estimators can achieve correct variable selection in highly nonlinear contexts, yet are sensitive to outliers and computationally intensive. The study sheds light on the subtle differences between the methods. Two examples illustrate how these new estimators can be applied in practice, with a slight preference for the option based on martingale difference divergence in the bioinformatics example.

Outlier detection is an inevitable step to most statistical data analyses. However, the mere detection of an outlying case does not always answer all scientific questions associated with that data point. Outlier detection techniques, classical and robust alike, will typically flag the entire case as outlying, or attribute a specific case weight to the entire case. In practice, particularly in high dimensional data, the outlier will most likely not be outlying along all of its variables, but just along a subset of them. If so, the scientific question why the case has been flagged as an outlier becomes of interest. In this article, a fast and efficient method is proposed to detect variables that contribute most to an outlier’s outlyingness. Thereby, it helps the analyst understand in which way an outlier lies out. The approach pursued in this work is to estimate the univariate direction of maximal outlyingness. It is shown that the problem of estimating that direction can be rewritten as the normed solution of a classical least squares regression problem. Identifying the subset of variables contributing most to outlyingness, can thus be achieved by estimating the associated least squares problem in a sparse manner. From a practical perspective, sparse partial least squares (SPLS) regression, preferably by the fast sparse NIPALS (SNIPLS) algorithm, is suggested to tackle that problem. The performed method is demonstrated to perform well both on simulated data and real life examples.

In this paper, a multivariate constrained robust M‐regression method is developed to estimate shaping coefficients for electricity forward prices. An important benefit of the new method is that model arbitrage can be ruled out at an elementary level, as all shaping coefficients are treated simultaneously. Moreover, the new method is robust to outliers, such that the provided results are stable and not sensitive to isolated sparks or dips in the market. An efficient algorithm is presented to estimate all shaping coefficients at a low computational cost. To illustrate its good performance, the method is applied to German electricity prices.

Partial robust M regression (PRM), as well as its sparse counterpart sparse PRM, have been reported to be regression methods that foster a partial least squares-alike interpretation while having good robustness and efficiency properties, as well as a low computational cost. In this paper, the partial robust M discriminant analysis classifier is introduced, which consists of dimension reduction through an algorithm closely related to PRM and a consecutive robust discriminant analysis in the latent variable space. The method is further generalized to sparse partial robust M discriminant analysis by introducing a sparsity penalty on the estimated direction vectors. Thereby, an intrinsic variable selection is achieved, which yields a better graphical interpretation of the results, as well as more precise coefficient estimates, in case the data contain uninformative variables. Both methods are robust against leverage points within each class, as well as against adherence outliers (points that have been assigned a wrong class label). A simulation study investigates the effect of outliers, wrong class labels, and uninformative variables on the proposed methods and its classical PLS counterparts and corroborates the robustness and sparsity claims. The utility of the methods is demonstrated on data from mass spectrometry analysis (time-of-flight secondary ion mass spectrometry) of meteorite samples. Copyright © 2016 John Wiley & Sons, Ltd.

A new method to estimate case specific prediction uncertainty for univariate trilinear partial least squares (tri-PLS1) regression is introduced. This method is, from a theoretical point of view, the most exact finite sample approximation to true prediction uncertainty that has been reported up till now. Using the new method, different error sources can be propagated, which is an advantage that cannot be offered by data driven approaches such as the bootstrap. In a concise example, it is illustrated how the method can be applied. In the Appendix, efficient algorithms are presented to compute the estimates required.

Support vector machine (SVM) algorithms are a popular class of techniques to perform classification. However, outliers in the data can result in bad global misclassification percentages. In this paper, we propose a method to identify such outliers in the SVM framework. A specific robust classification algorithm is proposed adjusting the least squares SVM (LS-SVM). This yields better classification performance for heavily tailed data and data containing outliers. Copyright © 2009 John Wiley & Sons, Ltd.

We have developed a new user-friendly graphical interface for robust calibration with a collection of m-files, called TOMCAT (TOolbox for Multivariate CAlibration Techniques). The graphical interface and its routines are freely available and programmed in MATLAB 6.5, probably one of the most popular programming environments in the chemometrics community. The graphical interface allows a user to apply the implemented methods in an easy way and it gives a straightforward possibility to visualize the obtained results. Several useful features such as interactive numbering of the displayed objects on a plot, viewing the content of the data, easy transfer of the data between the toolbox and the MATLAB workspace and vice versa, are also implemented. Among the implemented methods there are Principal Component Analysis and its robust variant, Partial Least Squares, Continuum Power Regression, Partial Robust M-Regression, Robust Continuum Regression and Radial Basis Functions Partial Least Squares.

Sparse partial robust M regression is introduced as a new regression method. It is the first dimension reduction and regression algorithm that yields esti-mates with a partial least squares like interpretability that are sparse and robust with respect to both vertical outliers and leverage points. A simula-tion study underpins these claims. Real data examples illustrate the validity of the approach. publisher: Elsevier articletitle: Sparse partial robust M regression journaltitle: Chemometrics and Intelligent Laboratory Systems articlelink: http://dx.doi.org/10.1016/j.chemolab.2015.09.019 content_type: article copyright: Copyright © 2015 Elsevier B.V. All rights reserved. ispartof: Chemometrics and Intelligent Laboratory Systems vol:149 pages:50-59 status: published

The boostrap is a successful technique to obtain confidence limits for estimates where it is theoretically impossible to establish an exact expression thereunto. Trilinear partial least squares regression (tri-PLS) is an estimator for which this is the case; in the current paper we thus propose to apply the bootstrap in order to obtain confidence intervals for the predictions made by tri-PLS. By dint of an extensive simulation study, we show that bootstrap confidence intervals have a desirable coverage. Finally, we apply the method to an identification problem of micro-organisms and show that from the bootstrap confidence intervals, the organisms can (up to a misclassification probability of 3.5%) correctly be identified.

Two approaches are presented to perform principal component analysis (PCA) on data which contain both outlying cases and missing elements. At first an eigendecomposition of a covariance matrix which can deal with such data is proposed, but this approach is not fit for data where the number of variables exceeds the number of cases. Alternatively, an expectation robust (ER) algorithm is proposed so as to adapt the existing methodology for robust PCA to data containing missing elements. According to an extensive simulation study, the ER approach performs well for all data sizes concerned. Using simulations and an example, it is shown that by virtue of the ER algorithm, the properties of the existing methods for robust PCA carry through to data with missing elements. (C) 2007 Elsevier B.V. All rights reserved.

The aim of this study is to show the usefulness of robust multiple regression techniques implemented in the expectation maximization framework in order to model successfully data containing missing elements and outlying objects. In particular, results from a comparative study of partial least squares and partial robust M-regression models implemented in the expectation maximization algorithm are presented. The performances of the proposed approaches are illustrated on simulated data with and without outliers, containing different percentages of missing elements and on a real data set. The obtained results suggest that the proposed methodology can be used for constructing satisfactory regression models in terms of their trimmed root mean squared errors.

The PLS approach is a widely used technique to estimate path models relating various blocks of variables measured from the same population. It is frequently applied in the social sciences and in economics. In this type of applications, deviations from normality and outliers may occur, leading to an efficiency loss or even biased results. In the current paper, a robust path model estimation technique is being proposed, the partial robust M (PRM) approach. In an example its benefits are illustrated.

Projection pursuit was originally introduced to identify structures in multivariate data clouds (Huber, 1985). The idea of projecting data to a low-dimensional subspace can also be applied to multivariate statistical methods. The robustness of the methods can be achieved by applying robust estimators to the lower-dimensional space. Robust estimation in high dimensions can thus be avoided which usually results in a faster computation. Moreover, flat data sets where the number of variables is much higher than the number of observations can be easier analyzed in a robust way. We will focus on the projection pursuit approach for robust continuum regression (Serneels et al., 2005). A new algorithm is introduced and compared with the reference algorithm as well as with classical continuum regression.

The spatial sign is a multivariate extension of the concept of sign. Recently multivariate estimators of covariance structures based on spatial signs have been examined by various authors. These new estimators are found to be robust to outlying observations. From a computational point of view, estimators based on spatial sign are very easy to implement as they boil down to a transformation of the data to their spatial signs, from which the classical estimator is then computed. Hence, one can also consider the transformation to spatial signs to be a preprocessing technique, which ensures that the calibration procedure as a whole is robust. In this paper, we examine the special case of spatial sign preprocessing in combination with partial least squares regression as the latter technique is frequently applied in the context of chemical data analysis. In a simulation study, we compare the performance of the spatial sign transformation to nontransformed data as well as to two robust counterparts of partial least squares regression. It turns out that the spatial sign transform is fairly efficient but has some undesirable bias properties. The method is applied to a recently published data set in the field of quantitative structure-activity relationships, where it is seen to perform equally well as the previously described best linear model for these data.

In this article we derive an algorithm to compute the influence function for tri-PLS1 regression. Based on the influence function, we propose the squared influence diagnostic plot to assess the influence of individual samples on calibration and prediction. We illustrate the applicability of the squared influence diagnostic plot for tri-PLS1 to two different data sets which have previously been reported in literature. Finally we note that from the influence function, a new estimate of prediction variance can be obtained. Copyright © 2005 John Wiley & Sons, Ltd.

Several applications of continuum regression (CR) to non-contaminated data have shown that a significant improvement in predictive power can be obtained compared to the three standard techniques which it encompasses (ordinary least squares (OLS), principal component regression (PCR) and partial least squares (PLS)). For contaminated data continuum regression may yield aberrant estimates due to its non-robustness with respect to outliers. Also for data originating from a distribution which significantly differs from the normal distribution, continuum regression may yield very inefficient estimates. In the current paper, robust continuum regression (RCR) is proposed. To construct the estimator, an algorithm based on projection pursuit (PP) is proposed. The robustness and good efficiency properties of RCR are shown by means of a simulation study. An application to an X-ray fluorescence analysis of hydrometallurgical samples illustrates the method's applicability in practice. ispartof: Chemometrics and Intelligent Laboratory Systems vol:76 issue:2 pages:197-204 status: published

Partial Least Squares (PLS) is a standard statistical method in chemometrics. It can be considered as an incomplete, or 'partial', version of the Least Squares estimator of regression, applicable when high or perfect multicollinearity is present in the predictor variables. The Least Squares estimator is well-known to be an optimal estimator for regression, but only when the error terms are normally distributed. In the absence of normality, and in particular when outliers are in the data set, other more robust regression estimators have better properties. In this paper a 'partial' version of M-regression estimators will be defined. If an appropriate weighting scheme is chosen, partial M-estimators become entirely robust to any type of outlying points, and are called Partial Robust M-estimators. It is shown that partial robust M-regression outperforms existing methods for robust PLS regression in terms of statistical precision and computational speed, while keeping good robustness properties. The method is applied to a data set consisting of EPXMA spectra of archaeological glass vessels. This data set contains several outliers, and the advantages of partial robust M-regression are illustrated. Applying partial robust M-regression yields much smaller prediction errors for noisy calibration samples than PLS. On the other hand, if the data follow perfectly well a normal model, the loss in efficiency to be paid for is very small. ispartof: Chemometrics and Intelligent Laboratory Systems vol:79 issue:1 pages:55-64 status: published

Several algorithms to calculate the vector of regression coefficients and the Jacobian matrix for partial least squares regression have been published. Whereas many efficient algorithms to calculate the regression coefficients exist, algorithms to calculate the Jacobian matrix are inefficient. Here we introduce a new, efficient algorithm for the Jacobian matrix, thus making the calculation of prediction intervals via a local linearization of the PLS estimator more practicable. Copyright © 2004 John Wiley & Sons, Ltd.

Ventilator-associated pneumonia is one of the most lethal infections occurring in intensive care units of hospitals. In order to obtain a faster method of diagnosis, we proposed to apply the electronic nose to cultures of the relevant micro-organisms. This allowed to halve the time of the analysis. In the current paper, we focus on the application of some chemometrical tools which enhance the performance of the method. Trilinear partial least squares (tri-PLS) regression is used to perform calibration and is shown to produce satisfactory predictions. Sample specific prediction intervals are produced for each predicted value, which allows us to eliminate erroneous predictions. The method is applied to an external validation set and it is shown that only a single observation out of 22 is being wrongly classified, so that the method is acceptable for inclusion in the clinical routine.