The contrast of fraud in international trade is a crucial task of modern economic regulations. We develop statistical tools for the detection of frauds in customs declarations that rely on the Newcomb–Benford law for significant digits. Our first contribution is to show the features, in the context of a European Union market, of the traders for which the law should hold in the absence of fraudulent data manipulation. Our results shed light on a relevant and debated question, since no general known theory can exactly predict validity of the law for genuine empirical data. We also provide approximations to the distribution of test statistics when the Newcomb–Benford law does not hold. These approximations open the door to the development of modified goodness-of-fit procedures with wide applicability and good inferential properties.

The Newcomb-Benford law for digit sequences has recently attracted interest in antifraud analysis. However, most of its applications rely either on diagnostic checks of the data, or on informal decision rules. We suggest a new way of testing the Newcomb-Benford law that turns out to be particularly attractive for the detection of frauds in customs data collected from international trade. Our approach has two major advantages. The first one is that we control the rate of false rejections at each stage of the procedure, as required in antifraud applications. The second improvement is that our testing procedure leads to exact significance levels and does not rely on large-sample approximations. Another contribution of our work is the derivation of a simple expression for the digit distribution when the Newcomb-Benford law is violated, and a bound for a chi-squared type of distance between the actual digit distribution and the Newcomb-Benford one.

Robust methods are little applied (although much studied by statisticians). We monitor very robust regression by looking at the behaviour of residuals and test statistics as we smoothly change the robustness of parameter estimation from a breakdown point of 50% to non-robust least squares. The resulting procedure provides insight into the structure of the data including outliers and the presence of more than one population. Monitoring overcomes the hindrances to the routine adoption of robust methods, being informative about the choice between the various robust procedures. Methods tuned to give nominal high efficiency fail with our most complicated example. We find that the most informative analyses come from S estimates combined with Tukey’s biweight or with the optimal $\rho$ functions. For our major example with 1,949 observations and 13 explanatory variables, we combine robust S estimation with regression using the forward search, so obtaining an understanding of the importance of individual observations, which is missing from standard robust procedures. We discover that the data come from two different populations. They also contain six outliers. Our analyses are accompanied by numerous graphs. Algebraic results are contained in two appendices, the second of which provides useful new results on the absolute odd moments of elliptically truncated multivariate normal random variables.

A news article's online audience provides useful insights about the article's identity. However, fake news classifiers using such information risk relying on profiling. In response to the rising demand for ethical AI, we present a profiling-avoiding algorithm that leverages Twitter users during model optimisation while excluding them when an article's veracity is evaluated. For this, we take inspiration from the social sciences and introduce two objective functions that maximise correlation between the article and its spreaders, and among those spreaders. We applied our profiling-avoiding algorithm to three popular neural classifiers and obtained results on fake news data discussing a variety of news topics. The positive impact on prediction performance demonstrates the soundness of the proposed objective functions to integrate social context in text-based classifiers. Moreover, statistical visualisation and dimension reduction techniques show that the user-inspired classifiers better discriminate between unseen fake and true news in their latent spaces. Our study serves as a stepping stone to resolve the underexplored issue of profiling-dependent decision-making in user-informed fake news detection.

Tempered distributions have received considerable attention, both from a theoretical point of view and in several important application fields. The most popular choice is perhaps the Tweedie model, which is obtained by tempering the Positive Stable distribution. Through tempering, we suggest a very flexible four-parameter family of distributions that generalizes the Tweedie model and that could be applied to data sets of non-negative observations with complex (and difficult to accommodate) features. We derive the main theoretical properties of our proposal, through which we show its wide application potential. We also embed our proposal within the theory of Lévy processes, thus providing a strengthened probabilistic motivation for its introduction. Furthermore, we derive a series expansion for the probability density function which allows us to develop algorithms for fitting the distribution to data. We finally provide applications to challenging real-world examples taken from international trade.