Nonparametric Measures Research Articles

Integrating Data Across Misaligned Spatial Units

AbstractTheoretical units of interest often do not align with the spatial units at which data are available. This problem is pervasive in political science, particularly in subnational empirical research that requires integrating data across incompatible geographic units (e.g., administrative areas, electoral constituencies, and grid cells). Overcoming this challenge requires researchers not only to align the scale of empirical and theoretical units, but also to understand the consequences of this change of support for measurement error and statistical inference. We show how the accuracy of transformed values and the estimation of regression coefficients depend on the degree of nesting (i.e., whether units fall completely and neatly inside each other) and on the relative scale of source and destination units (i.e., aggregation, disaggregation, and hybrid). We introduce simple, nonparametric measures of relative nesting and scale, asex anteindicators of spatial transformation complexity and error susceptibility. Using election data and Monte Carlo simulations, we show that these measures are strongly predictive of transformation quality across multiple change-of-support methods. We propose several validation procedures and provide open-source software to make transformation options more accessible, customizable, and intuitive.

Nonparametric tests for market timing ability using daily mutual fund returns

When using daily mutual fund returns to study market timing ability, heavy tails and heteroscedasticity significantly challenge the existing methods. We propose a weighted nonparametric measure and test for market timing. The test finds different results from the traditional parametric inference concerning timing. By examining the holding characteristics of the funds with different levels of timing ability, we find that funds with positive timing ability hold stocks with lower trading frictions. We find evidence of a tradeoff between market timing ability and stock picking skill after excluding funds with zero timing ability, which is robust to different benchmark models.

Indications of an Achaea sp. caterpillar outbreak disrupting fruiting of an ectomycorrhizal tropical tree in Central African rainforest

Background and aims – Where one or several tree species come to dominate patches of tropical forest, as many masting ectomycorrhizal legumes do in Central Africa, ecological theory predicts they may be prone to herbivory, which might alter their reproductive output. This was indirectly investigated in lowland rainforest in Cameroon for Tetraberlinia korupensis, whose crowns were attacked in 2008 by an outbreaking black caterpillar—identified as an Achaea sp., probably A. catocaloides—in Korup National Park. Material and methods – Field-collected data on tree-level seed and fruit (pod) production of T. korupensis in its 2008 masting event were compared with that of its two co-dominant neighbours (T. bifoliolata, Microberlinia bisulcata), whose populations masted in 2007 (and 2010). To do this, bivariate regression models (linear, polynomial, ZiG [zero-inflated gamma model]), contingency table analysis, and non-parametric measures of dispersion were used. Key results – Assuming T. korupensis is prone to Achaea caterpillar attacks, empirical data support the hypothesized lower proportion of adults participating in its masting (54% in 2008) than for either masting population of M. bisulcata (98% in 2007, 89% in 2010) or T. bifoliolata (96% in 2007, 78% in 2010). These fruiting T. korupensis trees were about one-third larger in stem diameter than conspecific non-fruiters and produced as many pods and seeds per capita as T. bifoliolata. However, regressions only modestly support the hypothesis that the positive tree size–fecundity relationship for T. korupensis was weaker (i.e. lower adj. R2) than for M. bisulcata (whose leaves are morphologically similar) or T. bifoliolata, with mostly similar dispersion about the median among these species. Conclusion – Altogether, the findings suggest a role for tolerance in nutrient-poor forests. It is postulated that instead of conferring resistance to herbivores, the ectomycorrhizas associated with these trees may enable them to more quickly recover from potential yet unpredictable insect outbreaks.

A nonparametric measure of noise in x-ray diagnostic images—mammography

Objective. In x-ray diagnostics, modern image reconstruction or image processing methods may render established methods of image quality assessment inadequate. Task specific quality assessment by using model observers has the disadvantage of being very labour-intensive. Therefore, it appears highly desirable to develop novel image quality parameters that neither rely on the linearity and the shift-invariace of the imaging system nor require the acquisition of hundreds of images as is necessary for the application of model observers, and which can be derived directly from diagnostic images. Approach. A new measure for the noise based on non-maximum-suppression images is defined and its properties are explored using simulated images before it is applied to an exposure series of mammograms of a homogeneous phantom and a 3D-printed breast phantom to demonstrate its usefulness under realistic conditions. Main results. The new noise parameter cannot only be derived from images with a homogeneous background but it can be extracted directly from images containing anatomic structures and is proportional to the standard deviation of the noise. At present, the applicability is restricted to mammography, which satisfies the assumption of short covariance length of the noise. Significance. The new measure of the noise is but a first step of the development of a set of parameters that are required to quantify image quality directly from diagnostic images without relying on the assumption of a linear, shift-invariant system, e.g. by providing measures of sharpness, contrast and structural complexity, in addition to the noise measure. For mammography, a convenient method is now available to quantify noise in processed diagnostic images.

Rest-Activity Rhythm Characteristics Associated With Depression Symptoms in Stroke Survivors

ObjectiveTo examine which 24-hour rest-activity rhythm (RAR) characteristics are associated with depression symptoms in stroke survivors. DesignCross-sectional observational study examining associations of RAR characteristics with the presence of depression symptoms adjusting for age, sex, race, and medical comorbidity. SettingCommunity setting. ParticipantsStroke survivors: (1) recruited locally (N women=35, N men=28) and (2) a nationally representative probability sample (the National Health and Nutrition Examination Survey [NHANES]; N women=156, N men=124). InterventionsNone. MeasurementsObjective RAR characteristics derived from accelerometer recordings including activity onset/offset times and non-parametric measures of RAR strength (relative amplitude), stability (interdaily stability), and fragmentation (intradaily variability). The presence of depression symptoms was categorized using Patient Health Questionnaire scores. ResultsIn both samples, the only RAR characteristic associated with depression symptoms was intradaily variability (fragmentation): local sample, odds ratio=1.96 [95% confidence interval=1.05-3.63]; NHANES sample, odds ratio=1.34, [95% confidence interval=1.01-1.78]). In the NHANES sample, which included both mild and moderate/severe depression, the association between 24-hour sleep-wake fragmentation and depression symptoms was driven by moderate-to-severe cases. ConclusionsStroke survivors with higher levels of RAR fragmentation were more likely to have depression symptoms in both samples. These findings have implications, given prior studies in general samples linking RAR fragmentation with future depression and dementia risk. Research is needed to establish the potential consequences, mechanisms, and modifiability of RAR fragmentation in stroke survivors.

Elucidation of G×E interactions by AMMI, BLUP and nonparametric measures of Wheat genotypes evaluated in NWPZ

Elucidation of G×E interactions by AMMI, BLUP and nonparametric measures of Wheat genotypes evaluated in NWPZ

Bone Mineral Density and Serum Bone Turnover Markers among Post-Menarchal Girls from Rural South India.

The data on the bone mineral density (BMD) and bone turnover markers (BTMs) in Indian adolescents are limited. To assess BMD at lumbar spine (LS, L1-L4) and femoral neck (FN) in South Indian post-menarchal girls and correlate it with dietary calcium intake (mg/day), physical activity score and post-menarchal years. The study also assessed serum BTMs and their correlation with chronological age in the study population. This cross-sectional study included apparently healthy post-menarchal adolescent girls aged 12-16 years randomly selected from the community. Participants with vitamin D deficiency were excluded. The data on calcium intake and physical activity were obtained using validated questionnaires. All participants were evaluated with serum calcium, 25-hydroxy vitamin D, parathyroid hormone, N-terminal propeptide of type 1 collagen (P1NP) and Beta-CrossLaps (CTx) and BMD at LS and FN using dual X-ray absorptiometry (DXA). EpiData version 3.1 was used for the data entry. The data analysis was done using Statistical Package for Social Sciences (SPSS) version 21. Continuous variables were expressed as mean ± SD. Pearson's correlation coefficient (r) was calculated, and two-tailed Kendall's tau-b test was used for assessing correlation of all nonparametric measures. A total of 103 participants were screened, and data from 77 were analysed. There was a significant positive correlation of BMD at LS with chronological age (r: +0.235, P = 0.036), but not at FN. Positive correlation of BMD with increase in post-menarchal years was also noted at LS (r: +0.276, P = 0.015). There was no significant association of BMD with calcium intake and physical activity scores at both sites. There was a significant negative correlation of serum BTMs with age CTx (r: -0.596, P = 0.0001) and P1NP (r: -0.505, P = 0.0001). This study provides insight into the reference BMD range at LS spine and FN in South Indian rural post-menarchal adolescent girls. BMD positively correlated, whereas BTMs negatively correlated with age. The study also provides the first Indian reference range for serum BTMs in this age group.

НЕПАРАМЕТРИЧНИЙ ПIДХIД ДО ПОЯСНЮВАЛЬНОГО ШТУЧНОГО IНТЕЛЕКТУ ТА ЙОГО ЗАСТОСУВАННЯ В МЕДИЦИНI

The paper proposes a non-parametrical approach to explainable artificial intelligence based on the compactness postulate, which states that objects of one class in the feature space are, as a rule, located closer to each other than to objects of other classes. Objects are considered similar if they are located close to each other in the feature space. Meanwhile, the properties of objects in real life are often random values. Such objects are not described by a vector of features, but by a random sample or several samples of features, and the postulate of compactness should be replaced by the postulate of statistical homogeneity. Objects are considered statistically homogeneous if their features obey the same distributions. The paper describes a non-parametric measure of homogeneity and an illustration of its use in medical applications, in particular for the diagnosis of breast cancer within the framework of similarity-based explainable artificial intelligence.For comparison, the results of diagnostics of the same data set using deep learning of an artificial neural network are given. We formulate new statistical postulates of machine learning and propose to consider a machine learning algorithm as explanatory and interpretable if it satisfies these postulates.

A simulation study of the finite-sample performance of the sample scale curve as an estimator of its population counterpart

The depth-based scale curves have broad applications in nonparametric multivariate statistics. Many nonparametric multivariate measures and procedures are based on the scale curves. In this article, we study the finite-sample performance of the sample scale curve as an estimator of its population counterpart by simulation. It is found that the sample scale curve tends to underestimate its population counterpart and that the discrepancy increases quickly as dimension increases. The effect of data shape characterized by kurtosis on the performance is also studied. Compared with the effect of dimension, the effect of kurtosis is minor. The root cause of the issue is explored and some suggestions for improvement are provided.

Low Rates of Reproductive Counseling Documentation in Women With Interstitial Pneumonia With Autoimmune Features.

Women with interstitial pneumonia with autoimmune features (IPAFs), a subset of interstitial lung disease (ILD), are at risk for pregnancy complications. Family planning discussions improve pregnancy outcomes in women with ILD. The objective of this study was to evaluate the documentation of reproductive counseling in IPAF female patients of childbearing age by pulmonary and rheumatology providers at an academic medical center. We conducted a medical record review study of pulmonary and rheumatology encounters in reproductive-aged women with IPAF to evaluate documentation of family planning discussions and contraceptive use. We used nonparametric measures of association and logistic regression to evaluate the relationship between patient characteristics and the presence of reproductive counseling documentation by providers. Thirty-one women met IPAF classification and were ≤50 years at initial ILD clinic visit. Twenty-five (81%) of these women had risk factors for adverse pregnancy outcomes. Ten women (32%) had a record of reproductive counseling during any visit with their pulmonary provider. Of the 21 patients who also saw a rheumatology provider, 12 (57%) women had a record of reproductive counseling during any visit with their rheumatology provider. No baseline characteristics were associated with odds of reproductive counseling documentation. Neither pulmonary nor rheumatology providers consistently discussed family planning/contraceptive use with reproductive-aged women with IPAF. There was a trend for rheumatology providers to discuss reproductive issues with IPAF patients more frequently than pulmonary providers. Efforts should focus on educating providers about the need for reproductive counseling in women with IPAF of childbearing age.

The impact of Twitter-based sentiment on US sectoral returns

This paper scrutinizes the effect of Twitter-based sentiment on US sectoral returns using data from between 21 June 2010 and 13 April 2020. We apply causality in quantiles as a non-parametric measure, followed by a rolling window wavelet correlation. The former measures the manifestation of causality directed from Twitter-based sentiment towards US sectoral returns, whereas the latter measures the correlation of returns across decomposed series that correspond to different time horizons. Our results highlight symmetric changes in US sectoral returns that vary across different sectors. The healthcare, communications, materials, consumer discretionary, energy, staples, and information technology sectors are more sensitive to changes in Twitter-based sentiment across all quantiles. Our findings from the rolling window wavelet correlation point to low correlation values for all decomposed series (i.e., long-, medium-, and short-run). Our findings have value for investors in the US sectoral market because they may be helpful for constructing and rebalancing portfolios based on varying levels of correlation across different quantile distributions and investment periods.

Physical Activity Among Adults in Rural Western North Carolina During the COVID-19 Pandemic.

During the COVID-19 pandemic, measures implemented to protect community health may have influenced how and where people engaged in physical activity. In rural communities, access to resources, the environment, and socioeconomic status could play a role in how adults are physically active. Our study examined locations where rural residents of a county in western North Carolina engaged in physical activity early in the COVID-19 pandemic, their reasons for being physically active, and their perceptions of benefits and barriers related to engaging in physical activity. Rural adults (N =297) completed an online survey from August 3 through September 15, 2020, describing their physical activity during the summer of 2020. Data were analyzed using nonparametric measures. Survey respondents frequently engaged in physical activity in the home (57.8%), at parks or on trails (45.3%), and around their neighborhood (39.4%). The most common types of physical activities at parks or on trails were walking and hiking (99.5%). Across all locations, the most frequently reported reasons for engaging in physical activity were getting out of the house, maintaining fitness and mental health, and exercising. Our study showed many locations where rural residents were physically active and their reasons for participating in physical activity during the pandemic. Data about perceived benefits of and barriers to physical activity during the pandemic can assist in meeting the current need to increase physical activity levels in rural communities.

Treatment Outcomes of Childhood Picalm:MLLT10+ Acute Leukemias: An International Retrospective Study

Introduction: Acute leukemia with translocation t(10;11)(p12-13;q14-21) results in generation of the PICALM:MLLT10 fusion gene, and is distinct from t(10;11)(p11-13;q23) which gives rise to KMT2A (formerly MLL) gene rearrangement. Defective PICALM function leads to aberrant hematopoiesis, while defective MLLT10 function impairs chromatin-mediated gene regulation. The PICALM:MLLT10 gene has been reported in patients with Acute Myeloid Leukemia (AML), Acute Lymphoblastic Leukemia (ALL) predominantly T-cell, Acute Undifferentiated Leukemia (AUL) and Mixed Phenotype Acute Leukemia (MPAL). MLLT10 interacts directly with DOT1L in a complex that regulates the methylation of H3K79. MLLT10 fusions are thought to misdirect DOT1L to the promoters of HOXA genes, leading to hypermethylation of H3K79. This hypermethylation causes constitutive activation of HOXA activity and prevents cell maturation and differentiation. The clinico-biological characteristics, response to conventional treatments, and survival outcomes of childhood PICALM:MLLT10+ leukemias are poorly understood. Methods: This was an international, multicenter, retrospective cohort study. Data were submitted by ten International-BFM (I-BFM) study Group-AML and ALL committees and by the Children`s Oncology Group (COG)-AML Study committee. For study inclusions, patients were required to be ≤ 21 years of age at diagnosis, diagnosed between January 1995 and December 2019 with de novo ALL, AML, AUL or MPAL and PICALM:MLLT10 fusion-positive. Patients with KMT2A-rearranged leukemia or acute promyelocytic leukemia were excluded. Kaplan Meier curves were employed for survival analysis with Cox proportional hazard modelling to compare effect of AML vs ALL therapy, and receipt of hematopoietic stem cell transplant (HSCT) vs no HSCT, on survival. Pearson's Chi Squared was employed as a non-parametric measure to determine the effect of end of induction-1 (EIO-1) MRD positive vs negative status on incidence of relapse. P value cut-off for data to reach statistical significance was <0.05. Results: Ninety-eight children with acute leukemia were included, 60 were males. Median age at diagnosis was 12 years (IQR:9-14.8 years) and median initial white cell count was 40.5 x 109/L (IQR:13.8-168.9). Fifty-five (55.6%) patients were diagnosed with T-ALL, 39 (39.4%) with AML, while precursor-B ALL, AUL and MPAL were each diagnosed in single patients; 1 subtype diagnosis was unknown. Ten (10.1%) patients presented with CNS disease and 13 (13.1%) presented with non-CNS extramedullary manifestations. Of 66 with cytogenetic/molecular data available, 33 (50%) had additional cytogenetic-molecular aberrations; NOTCH1, WT1 and RAS pathway mutations predominated. Most patients received an initial chemotherapy regimen guided by their disease immunophenotype: 58/98 (58.6%) received an ALL-like chemotherapy regimen upfront, 38 (38.4%) received an AML-like regimen, 1 (1.0%) a hybrid regimen, 1 initial chemotherapy regimen was unknown. Five-year event-free survival (EFS) was 50.4% (CI 39.1-64.9). For AML patients, 5-year EFS was 22.5% (CI 9.75-52.0) and for ALL 67.7% (CI 54.2-84.7), p=<0.001. Five-year overall survival (OS) was 56.3% (CI 46.3-68.5). For AML patients, 5-year OS was 26.7% (CI 13.3-53.6) and for ALL 75.7% (CI 64.6-88.8), p=<0.001. Thirty-eight patients died, 22 (57.9%) deaths were disease-related, 4 (10.5%) treatment-related. Patients who received HSCT in CR1, demonstrated a trend towards an inferior 5-year EFS (23.7% vs 56.5%) and OS (42.6% vs 64.5%) than those who did not; however, analysis was limited by small sample size. Four (22.2%) HSCT recipients had ALL but most, 14 (77.8%), had AML, which may account for the unfavourable outcomes associated with HSCT. There was no statistically significant difference in rate of relapse in the EOI-1 MRD-positive compared with MRD-negative patients (p=0.49). Of those who relapsed, 25 (75.8%) had an isolated bone marrow relapse, 3 (9.1%) isolated CNS, 3 (9.1%) other sites and, for 2 patients, site of relapse was unknown. Conclusions: Children with PICALM:MLLT10+ AML have inferior 5-year EFS and OS outcomes compared to their T-ALL counterparts. MRD status at EOI-1 was not predictive of relapse. Targeted therapies with DOT1L inhibitors or DNA demethylating agents should be explored, particularly for patients with AML.

Measuring association with Wasserstein distances

Let π∈Π(μ,ν) be a coupling between two probability measures μ and ν on a Polish space. In this article we propose and study a class of nonparametric measures of association between μ and ν, which we call Wasserstein correlation coefficients. These coefficients are based on the Wasserstein distance between ν and the disintegration πx1 of π with respect to the first coordinate. We also establish basic statistical properties of this new class of measures: we develop a statistical theory for strongly consistent estimators and determine their convergence rate in the case of compactly supported measures μ and ν. Throughout our analysis we make use of the so-called adapted/bicausal Wasserstein distance, in particular we rely on results established in [Backhoff, Bartl, Beiglböck, Wiesel. Estimating processes in adapted Wasserstein distance. 2020]. Our approach applies to probability laws on general Polish spaces.

New nonparametric measures for instantaneous and granger-causality tail co-dependence

ABSTRACT We propose a new methodology to asses risk spillovers in a time-series framework. Firstly, we introduce an explicit nonparametric measure of cross-sectional conditional tail co-movement, which is intuitively comparable to the Conditional Value-at-Risk (CoVaR). We show that nonlinear CoVaR (NCoVaR) is able to capture even highly nonlinear dependence structures. Secondly, for the purpose of potential contagion analysis, we adapt the measure to be informative about the causality direction between the variables in the Granger causality sense. By showing that the natural estimators of the two metrics are U-statistics, we construct formal nonparametric tests for independence and Granger non-causality. Numerical simulations confirm that in common situations the nonparametric tests have better size and power properties than their parametric counterparts. The methodology is illustrated empirically by assessing risk transmissions between sovereigns and banking sectors in the euro area, which observed highly irregular co-movements between asset prices after the global financial crisis. The new measures seem to be less susceptible to these irregularities than their parametric analogues, providing a clearer overview of the underlying sovereign-bank risk feedback loops.

Cardiometabolic Risk after SARS-CoV-2 Virus Infection: A Retrospective Exploratory Analysis.

The aim of this study is to characterize the cardiometabolic risk of individuals who were infected with the SARS-CoV-2 virus and subsequently admitted to a hospital in a major city in mainland Portugal. This is a retrospective exploratory study using a sample of 102 patients, with data analysis including descriptive statistics, nonparametric measures of association between variables based on Spearman's rank-order correlation, a logistic regression model for predicting the likelihood that an individual might eventually pass away, and a multiple linear regression model to predict a likely increase in the number of days an infected patient remained in the hospital. About 62.7% of the individuals required intensive care on the second day of hospitalization, remaining 14.2 days in the intensive care unit (ICU) on average. The likelihood that an individual might eventually pass away due to SARS-CoV-2 virus infection increases for the older than younger ones and increases even more if he/she suffers from cardiometabolic disorders such as obesity, especially cardiovascular disease. Older individuals and those with obesity and hypertension remained more days in the ICU. A later age and the prevalence of cardiometabolic disorders severely affect the care pathway of individuals infected with the SARS-CoV-2 virus.

Redefine carbon footprint performance with the total factor productivity: A case from a regional food production system

By observing the disturbance of indicators, models, and samples variability to the robustness of low carbon performance evaluation, the importance of random errors and heterogeneity of sample data is clarified. The carbon footprint joint total factor productivity conceptual framework is proposed in this study, then we apply it to a food production system in a region of China to reasonably judge the carbon footprint performance level of peasant households. With regard to the single-output production frontier, the internal method changes did not cause significant changes in the level of crop production technical efficiency in the deterministic and stochastic estimation strategies respectively. Although the results of partial low-carbon economic technical efficiency are consistent in the two estimation strategies, a significant difference is obvious for the low-carbon technical efficiency; The total low-carbon economic technical efficiency is significantly different between deterministic non-parametric slacks-based measure and parameterized random distance function estimation strategies under the framework of the multi-output production frontier; Ultimately, the total factor productivity including the carbon footprint of the food system in our research area close to the technical level of the industry, as well as the technical efficiency of the sample is at an efficient level.

Quantifying ethnic segregation in cities through random walks

Socioeconomic segregation has an important role in the emergence of large-scale inequalities in urban areas. Most of the available measures of spatial segregation depend on the scale and size of the system under study, or neglect large-scale spatial correlations, or rely on ad-hoc parameters, making it hard to compare different systems on equal grounds. We propose here a family of non-parametric measures for spatial distributions, based on the statistics of the trajectories of random walks on graphs associated to a spatial system. These quantities provide a consistent estimation of segregation in synthetic spatial patterns, and we use them to analyse the ethnic segregation of metropolitan areas in the US and the UK. We show that the spatial diversity of ethnic distributions, as measured through diffusion on graphs, allow us to compare the ethnic segregation of urban areas having different size, shape, or peculiar microscopic characteristics, and exhibits a strong association with socio-economic deprivation.

Morphologic and Functional Changes of Macula and Optic Nerve Head in Adult Kidney Transplant Recipient

To assess macular and optic nerve head characteristics in patients after kidney transplantation using noninvasive optical coherence tomography (OCT) imaging. The study had a prospective character and was performed during period from November 2019 to November 2020 at the University Clinical Center Tuzla, Tuzla, Bosnia and Herzegovina, and included 59 patients with renal graft who underwent OCT. The obtained OCT images, pathologic changes on the fundus, including macula and optic nerve, were analyzed by reviewing nonparametric measures such as scanning laser ophthalmoscope, B-scan, 3D display, as well as parametric measurements such as central macular thickness, optic nerve head excavation, and retinal nerve thickness fiber (RNFL). There is a statistically significant difference in RNFL values (P=0.031) and cup to disc (P=0.002) ratio in relation to duration of graft. The highest average values of RNFL was in patients with creatinine clearance <30 mL/min, while average cup to disc ratio was lowest in patients with creatinine clearance >60 mL/min. Optic nerve head edema was bilateral in 9 and unilateral in 5 patients. Fundus examination also revealed changes on posterior segment, including retinal detachment (1 patient), bilateral macular edema (9 patients), unilateral macular edema (3 patients), central serous chorioretinopathy (2 patients), and macular pseudo hole (3 patients). Different retinal pathology is present in high incidence in patients secondary to renal transplant. Immunosuppressive therapy, older age, and comorbidities are the usual causes of these changes.

TCMI: a non-parametric mutual-dependence estimator for multivariate continuous distributions

The identification of relevant features, i.e., the driving variables that determine a process or the properties of a system, is an essential part of the analysis of data sets with a large number of variables. A mathematical rigorous approach to quantifying the relevance of these features is mutual information. Mutual information determines the relevance of features in terms of their joint mutual dependence to the property of interest. However, mutual information requires as input probability distributions, which cannot be reliably estimated from continuous distributions such as physical quantities like lengths or energies. Here, we introduce total cumulative mutual information (TCMI), a measure of the relevance of mutual dependences that extends mutual information to random variables of continuous distribution based on cumulative probability distributions. TCMI is a non-parametric, robust, and deterministic measure that facilitates comparisons and rankings between feature sets with different cardinality. The ranking induced by TCMI allows for feature selection, i.e., the identification of variable sets that are nonlinear statistically related to a property of interest, taking into account the number of data samples as well as the cardinality of the set of variables. We evaluate the performance of our measure with simulated data, compare its performance with similar multivariate-dependence measures, and demonstrate the effectiveness of our feature-selection method on a set of standard data sets and a typical scenario in materials science.