A uniform L1L^1 law of large numbers for functions of i.i.d. random variables that are translated by a consistent estimator

We develop a new $L^1$ law of large numbers where the $i$-th summand is given by a function $h(\cdot)$ evaluated at $X_i - \theta_n$, and where $\theta_n \circeq \theta_n(X_1,X_2,\ldots,X_n)$ is an estimator converging in probability to some parameter $\theta\in \mathbb{R}$. Under broad technical conditions, the convergence is shown to hold uniformly in the set of estimators interpolating between $\theta$ and another consistent estimator $\theta_n^{\star}$. Our main contribution is the treatment of the case where $|h|$ blows up at $0$, which is not covered by standard uniform laws of large numbers.Comment: 10 pages, 1 figur

The Hellinger Correlation

In this paper, the defining properties of a valid measure of the dependence between two random variables are reviewed and complemented with two original ones, shown to be more fundamental than other usual postulates. While other popular choices are proved to violate some of these requirements, a class of dependence measures satisfying all of them is identified. One particular measure, that we call the Hellinger correlation, appears as a natural choice within that class due to both its theoretical and intuitive appeal. A simple and efficient nonparametric estimator for that quantity is proposed. Synthetic and real-data examples finally illustrate the descriptive ability of the measure, which can also be used as test statistic for exact independence testing

The Combined Effects of Mindset and Feedback on College Students’ Motivation After Experiencing Failure

The purpose of this study was to determine the effects of mindset and performance feedback on college students’ motivation after experiencing failure in a web-browser experimental study. This study was conducted with students taking a general education course in Fall 2019 (N = 74). Students completed a 3-item Growth Mindset Scale (GMS) designed to measure individuals’ beliefs about their own influence on personal ability levels. GMS can be conceptualized as a continuum ranging from a growth to a fixed mindset. After completing the GMS, participants completed a Memory for Pictures task designed to induce success. Participants received one of three manipulated feedback conditions praising ability, effort, or no praise (control). They were then given a challenging Numerical Series task designed to induce failure. Participants were asked to rate attributions for failure, make a goal orientation selection, and make a risk-aversion selection after experiencing failure. Primary analyses indicated a non-significant relationship between mindset and task persistence, as measured by total number of attempts on the Numerical Series task (r = 0.13, p = 0.26). Performance feedback conditions did not differ significantly in the number of attempts on the Numerical Series task (F = 0.40, p = 0.67). Mindset was not significantly correlated with attributions for failure, nor did the feedback conditions differ significantly on attributions for failure. A one-way ANOVA revealed that mindset made a significant difference on goal orientation (F = 8.71, p = 0.004). Specifically, growth mindset was significantly related to participants’ selecting to view information related to problem solving strategies, whereas fixed mindset was significantly related to participants’ selecting to view relative-performance feedback. Performance feedback was not significantly related to goal orientation (X 2 = 0.65, p = v 0.72). Results of a one-way ANOVA indicated no significant differences in risk-aversion based on mindset (F = 2.28, p = 0.14). A Pearson chi-square test of independence revealed no significant relationship between performance feedback and risk-aversion (X 2 = 0.61, p = 0.74). Exploratory analyses revealed marginally significant findings related to mindset, feedback and time spent on the study, as well as a significant relationship between goal orientation selection and risk aversion

A study of seven asymmetric kernels for the estimation of cumulative distribution functions

In Mombeni et al. (2019), Birnbaum-Saunders and Weibull kernel estimators were introduced for the estimation of cumulative distribution functions (c.d.f.s) supported on the half-line $[0,\infty)$. They were the first authors to use asymmetric kernels in the context of c.d.f. estimation. Their estimators were shown to perform better numerically than traditional methods such as the basic kernel method and the boundary modified version from Tenreiro (2013). In the present paper, we complement their study by introducing five new asymmetric kernel c.d.f. estimators, namely the Gamma, inverse Gamma, lognormal, inverse Gaussian and reciprocal inverse Gaussian kernel c.d.f. estimators. For these five new estimators, we prove the asymptotic normality and we find asymptotic expressions for the following quantities: bias, variance, mean squared error and mean integrated squared error. A numerical study then compares the performance of the five new c.d.f. estimators against traditional methods and the Birnbaum-Saunders and Weibull kernel c.d.f. estimators from Mombeni et al. (2019). By using the same experimental design, we show that the lognormal and Birnbaum-Saunders kernel c.d.f. estimators perform the best overall, while the other asymmetric kernel estimators are sometimes better but always at least competitive against the boundary kernel method.Comment: 38 pages, 2 tables, 9 figure

D’une politique de gestion des déchets vers une politique d’économie circulaire ?: Une mise en perspective historique par les instruments d’action publique

National audienceAs circular economy seems to lastingly take root in political agendas, the authors propose a chronological analysis of waste management policies in France. It traces the mutations of the different policy instruments which gradually operationalize the shift from an originally "waste disposal" centered policy, to a larger goal of transitioning toward a more circular economy. Even though this transition becomes a political priority, this question still remains emerging in the public policy field and the policy instruments sub-field, as well as in the communities which promote this new economic development model.Au moment où l'économie circulaire semble s'inviter durablement dans l'agenda politique, les auteurs proposent une analyse chronologique retraçant les mutations de l'instrumentation d'action publique qui accompagnent et viennent progressivement opérationnaliser le basculement d'une politique, initialement centrée sur l'élimination des déchets, à un objectif plus large de transition vers une économie circulaire; question qui reste encore émergente dans le sous-champ de l'analyse des politiques publiques par les instruments, mais aussi dans les communautés qui promeuvent ce nouveau modèle de développement, et ce alors même que sa mise en place concrète devient une priorité politique

PoweR: A Reproducible Research Tool to Ease Monte Carlo Power Simulation Studies for Goodness-of-fit Tests in R

The PoweR package aims to help obtain or verify empirical power studies for goodnessof-fit tests for independent and identically distributed data. The current version of our package is only valid for simple null hypotheses or for pivotal test statistics for which the set of critical values does not depend on a particular choice of a null distribution (and on nuisance parameters) under the non-simple null case. We also assume that the distribution of the test statistic is continuous. As a reproducible research computational tool it can be viewed as helping to simply reproducing (or detecting errors in) simulation results already published in the literature. Using our package helps also in designing new simulation studies. The empirical levels and powers for many statistical test statistics under a wide variety of alternative distributions can be obtained quickly and accurately using a C/C++ and R environment. The parallel package can be used to parallelize computations when a multicore processor is available. The results can be displayed using LATEX tables or specialized graphs, which can be directly incorporated into a report. This article gives an overview of the main design aims and principles of our package, as well as strategies for adaptation and extension. Hands-on illustrations are presented to help new users in getting started

A comprehensive empirical power comparison of univariate goodness-of-fit tests for the Laplace distribution

In this paper, we do a comprehensive survey of all univariate goodness-of-fit tests that we could find in the literature for the Laplace distribution, which amounts to a total of 45 different test statistics. After eliminating duplicates and considering parameters that yield the best power for each test, we obtain a total of 38 different test statistics. An empirical power comparison study of unmatched size is then conducted using Monte Carlo simulations, with 400 alternatives spanning over 20 families of distributions, for various sample sizes and confidence levels. A discussion of the results follows, where the best tests are selected for different classes of alternatives. A similar study was conducted for the normal distribution in Rom\~ao et al. (2010), although on a smaller scale. Our work improves significantly on Puig & Stephens (2000), which was previously the best-known reference of this kind for the Laplace distribution. All test statistics and alternatives considered here are integrated within the PoweR package for the R software.Comment: 37 pages, 1 figure, 20 table

Temporal and Spatial Independent Component Analysis for fMRI Data Sets Embedded in the AnalyzeFMRI R Package

For statistical analysis of functional magnetic resonance imaging (fMRI) data sets, we propose a data-driven approach based on independent component analysis (ICA) implemented in a new version of the AnalyzeFMRI R package. For fMRI data sets, spatial dimension being much greater than temporal dimension, spatial ICA is the computationally tractable approach generally proposed. However, for some neuroscientific applications, temporal independence of source signals can be assumed and temporal ICA becomes then an attractive exploratory technique. In this work, we use a classical linear algebra result ensuring the tractability of temporal ICA. We report several experiments on synthetic data and real MRI data sets that demonstrate the potential interest of our R package

Tests for circular symmetry of complex-valued random vectors

We propose tests for the null hypothesis that the law of a complex-valued random vector is circularly symmetric. The test criteria are formulated as $L^2$-type criteria based on empirical characteristic functions, and they are convenient from the computational point of view. Asymptotic as well as Monte-Carlo results are presented. Applications on real data are also reported. An R package called CircSymTest is available from the authors