Nonparametric Tests Of Independence Research Articles

Beyond Pearson’s Correlation: Modern Nonparametric Independence Tests for Psychological Research

When examining whether two continuous variables are associated, tests based on Pearson’s, Kendall’s, and Spearman’s correlation coefficients are typically used. This paper explores modern nonparametric independence tests as an alternative, which, unlike traditional tests, have the ability to potentially detect any type of relationship. In addition to existing modern nonparametric independence tests, we developed and considered two novel variants of existing tests, most notably the Heller-Heller-Gorfine-Pearson (HHG-Pearson) test. We conducted a simulation study to compare traditional independence tests, such as Pearson’s correlation, and the modern nonparametric independence tests in situations commonly encountered in psychological research. As expected, no test had the highest power across all relationships. However, the distance correlation and the HHG-Pearson tests were found to have substantially greater power than all traditional tests for many relationships and only slightly less power in the worst case. A similar pattern was found in favor of the HHG-Pearson test compared to the distance correlation test. However, given that distance correlation performed better for linear relationships and is more widely accepted, we suggest considering its use in place or additional to traditional methods when there is no prior knowledge of the relationship type, as is often the case in psychological research.

A data depth based nonparametric test of independence between two random vectors

A new family of depth-based test statistics is proposed for testing the hypothesis of independence between two random vectors. In the procedure to derive the asymptotic distribution of the tests under the null hypothesis, we do not require any symmetric assumption of the distribution functions. Furthermore, a conditional distribution-free property of the tests is shown. The asymptotic relative efficiency of the tests is discussed under the class of elliptically symmetric distribution. Asymptotic relative efficiencies along with Monte Carlo results suggest that the performance of the proposed class is comparable to the existing ones, and under some circumstances, it has higher power. Finally, we apply the tests to two real data sets and also discuss the robustness of our tests.

More water, less light: how to improve silver fir seeding to convert Norway spruce monocultures into mixed stands in a drier region of Germany

Abstract Adaptive forest management gains importance as climate and disturbance regimes continue to change. Norway spruce monocultures are particularly vulnerable to those changes. Thus, there is a strong demand to convert pure spruce stands toward better adapted forest ecosystems. Silver fir has similar wood properties as Norway spruce, but is less vulnerable to droughts. Yet, little is known how to efficiently admix silver fir into Norway spruce monocultures. We analyzed seedling abundance in mature Norway spruce monocultures 1 year after soil scarification and silver fir seeding in a relatively dry region of southern Germany. Our objectives were to study the effect of soil scarification and seeding on regeneration density and to identify drivers of seedling abundance. We collected data on regeneration, forest structure, as well as soil and light conditions at 103 scarified and 25 untreated control plots. We used non-parametric independence tests to compare scarified and untreated plots. Subsequently, we used boosted regression trees to investigate the drivers of seedling abundance. Norway spruce strongly benefited from soil scarification (P < .001), with seedling numbers even exceeding those of silver fir. Both species thrived in soils with high plant available water capacity. In contrast, seedling numbers were overall negatively affected by light. Moreover, we found a higher density of silver fir regeneration at greater distance from neighboring trees and in soils devoid of carbonate. Our study indicates that water, not light, is the limiting factor for both Norway spruce and silver fir seedlings in the study region. Seeding silver fir will likely be most effective underneath an intact canopy on deep, fine-textured soils without carbonate, while maximizing the distance to Norway spruce trees. In conclusion, silver fir seeding can be optimized to become an effective adaptive measure to diversify Norway spruce monocultures, and thus to create more resistant and resilient forest ecosystems.

Nonparametric Tests of Independence for Circular Data Based on Trigonometric Moments

We introduce nonparametric tests of independence for bivariate circular data based on trigonometric moments. Our contributions lie in (i) proposing nonparametric tests that are locally and asymptotically optimal against bivariate cosine von Mises alternatives and (ii) extending these tests, via the empirical characteristic function, to obtain consistent tests against broader sets of alternatives, eventually being omnibus. We thus provide a collection of trigonometric-based tests of varying generality and known optimalities. The large-sample behaviours of the tests under the null and alternative hypotheses are obtained, while simulations show that the new tests are competitive against previous proposals. Two data applications in astronomy and forest science illustrate the usage of the tests.

Nonparametric tests of independence using copula-based Renyi and Tsallis divergence measures

Nonparametric tests of independence using copula-based Renyi and Tsallis divergence measures

A weighted independence test based on smooth estimation of Kendall distribution

In this study, we introduce a nonparametric test of independence which is based on a weighted Cramér-von Mises distance of the Bernstein estimate of the Kendall distribution function. We examine the power and the size of the new weighted test and, we compare it with the non-weighted nonparametric tests of independence through a Monte Carlo simulation study. The simulation results indicate that both of the choices of the weights and the polynomial degree has a significant effect on the test power. Finally, the procedure is applied to a dataset on chemical elements in water samples for the purpose of illustration.

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.

Multi-scale Fisher's independence test for multivariate dependence.

Identifying dependency in multivariate data is a common inference task that arises in numerous applications. However, existing nonparametric independence tests typically require computation that scales at least quadratically with the sample size, making it difficult to apply them in the presence of massive sample sizes. Moreover, resampling is usually necessary to evaluate the statistical significance of the resulting test statistics at finite sample sizes, further worsening the computational burden. We introduce a scalable, resampling-free approach to testing the independence between two random vectors by breaking down the task into simple univariate tests of independence on a collection of 2 × 2 contingency tables constructed through sequential coarse-to-fine discretization of the sample space, transforming the inference task into a multiple testing problem that can be completed with almost linear complexity with respect to the sample size. To address increasing dimensionality, we introduce a coarse-to-fine sequential adaptive procedure that exploits the spatial features of dependency structures. We derive a finite-sample theory that guarantees the inferential validity of our adaptive procedure at any given sample size. We show that our approach can achieve strong control of the level of the testing procedure at any sample size without resampling or asymptotic approximation and establish its large-sample consistency. We demonstrate through an extensive simulation study its substantial computational advantage in comparison to existing approaches while achieving robust statistical power under various dependency scenarios, and illustrate how its divide-and-conquer nature can be exploited to not just test independence, but to learn the nature of the underlying dependency. Finally, we demonstrate the use of our method through analysing a dataset from a flow cytometry experiment.

Testing bivariate independence based on α-divergence by improved probit transformation method for copula density estimation

Independence test based on empirical copula does not perform well in the presence of weak dependency or when dependency occurs only in the tails. The copula density, which is estimated by a local likelihood probit transformation method, is used to detect the independence. In this article, three nonparametric tests of independence based on α-divergence and copula density are introduced. These tests are capable of considering weak dependency. The asymptotic consistency of the copula-based α-divergence estimator is also derived. In addition, the empirical powers of the proposed tests are computed through extensive simulations. The results show that the new tests outperform in small sample sizes or weak dependencies. Finally, an application in uranium exploration is presented to illustrate the applicability of the proposed tests.

Signs of dysphagia and associated outcomes regarding mortality, length of hospital stay and readmissions in acute geriatric patients: Observational prospective study.

Dysphagia is a prevalent disorder in acute geriatric patients. This observational prospective study aimed at investigating adverse clinical outcomes linked to signs of dysphagia, including mortality, length of hospital stay (LOS), readmissions, among patients aged≥65 years at a Danish acute medical unit (AMU). Signs of dysphagia were assessed using bedside screening tools including the Eating Assessment Tool (EAT-10), a 30mL Water Swallowing Test (WST) and the Gugging Swallowing Screen tool (GUSS), as described in the preceding cross-sectional study. Data for the follow-up was twice retrieved from electronic medical charts 30 days and 90 days after the patients' primary admission to the hospital. Statistical analysis included non-parametric tests of independence and proportional hazards modelling. 444 patients were recruited, 334 of whom completed the dysphagia screening with 144 (43.1%) showing signs of dysphagia. Patients with signs of dysphagia, compared to those without, experienced higher mortality after 30 days (12.5% vs. 1.6%, p<0.001) and 90 days (21.5% vs. 5.8%, p<0.001), longer LOS (median [Q1; Q3]: 4 [2; 8] vs. 3 [1; 6] days, p=0.004), more total hospital days (THD) during both the 30-day and 90-day follow-up (for 90d: median [Q1; Q3]: 6 [2.25; 12] vs. 4 [2; 9] days, p=0.007), but no significant difference in frequency of readmissions. Multivariate proportional hazards modelling revealed signs of dysphagia, low performance status and high comorbidity to be independent risk factors for mortality. High comorbidity and low hemoglobin, but not signs of dysphagia, were revealed as independent risk factors for readmission. Dysphagia is a notable risk factor linked to increased mortality and length of hospital stay (LOS) for acute geriatric patients in general, not just those suffering from stroke, head and neck cancer or neurodegenerative diseases. Further research is needed to investigate the effectiveness and feasibility of systematic dysphagia screening within this population.

A non-parametric test for independence of time to failure and cause of failure for discrete competing risks data

Competing risks data with discrete lifetime come up in practice. However, only limited literature exists for such data. In this paper, we propose a non-parametric test based on U-statistics for testing independence of time to failure and cause of failure of competing risks data when the lifetime is a discrete random variable. Asymptotic distribution of the proposed test statistic is derived. An extensive Monte Carlo simulation study is conducted to assess the finite sample performance of the proposed test. The flexibility of the testing procedure is illustrated using real data sets on oral cancer patients and drug-exposed pregnancies.

A Kernel Log-Rank Test of Independence for Right-Censored Data

We introduce a general nonparametric independence test between right-censored survival times and covariates, which may be multivariate. Our test statistic has a dual interpretation, first in terms of the supremum of a potentially infinite collection of weight-indexed log-rank tests, with weight functions belonging to a reproducing kernel Hilbert space (RKHS) of functions; and second, as the norm of the difference of embeddings of certain finite measures into the RKHS, similar to the Hilbert–Schmidt Independence Criterion (HSIC) test-statistic. We study the asymptotic properties of the test, finding sufficient conditions to ensure our test correctly rejects the null hypothesis under any alternative. The test statistic can be computed straightforwardly, and the rejection threshold is obtained via an asymptotically consistent Wild Bootstrap procedure. Extensive investigations on both simulated and real data suggest that our testing procedure generally performs better than competing approaches in detecting complex nonlinear dependence.

Self-Regulated Learning On Program Entry in Doctor of Physical Therapy Students: A Pilot Study

Introduction. The transition to graduate study can be difficult for entry-level physical therapist (Doctor of Physical Therapy [DPT]) students to make. One factor that may support this transition is the development of self-regulated learning (SRL). SRL has been associated with academic success in graduate health professions programs. Despite previous academic achievement, some DPT students struggle with first semester coursework. It is unknown whether these students have adequate SRL skills. Therefore, this study examined students' perceived SRL skills on program entry. Methods. Participants enrolled in their first semester of a DPT program were recruited from a medium-sized historically minority serving institution in the Southeastern United States. Doctor of Physical Therapy students (N = 28) completed the Learning and Study Strategies Inventory (LASSI) instrument to discover perceived abilities in SRL. The LASSI is a valid and reliable instrument that assesses skills, strategies, and behaviors of SRL and has been used in other graduate health professions. Demographic data and LASSI scores were evaluated using descriptive statistics, and between-group comparisons were performed using nonparametric independent tests and analysis of variance. Significance was set at an alpha level of &lt;.05. Results. Entering students perceived a need for moderate or high levels of support in most areas of SRL as measured by the LASSI. Statistically significant demographic differences in scale scores found within the cohort included minority status, undergraduate institution, and gender. Discussion/Conclusion. This study provides insights into the areas of support DPT students need for SRL that may have implications for early academic support. Diverse students may have different supportive needs. Further research is needed to discover SRL development needs in DPT students.

Testing independence of functional variables by angle covariance

We propose a new nonparametric independence test for two functional random variables. The test is based on a new dependence metric, the so-called angle covariance, which fully characterizes the independence of the random variables and generalizes the projection covariance proposed for random vectors. The angle covariance has a number of desirable properties, including the equivalence of its zero value and the independence of the two functional variables, and it can be applied to any functional data without finite moment conditions. We construct a V-statistic estimator of the angle covariance, and show that it has a Gaussian chaos limiting distribution under the independence null hypothesis and a normal limiting distribution under the alternative hypothesis. The test based on the estimated angle covariance is consistent against all alternatives and easy to be implemented by the given random permutation method. Simulations show that the test based on the angle covariance outperforms other competing tests for functional data.

A kernel- and optimal transport- based test of independence between covariates and right-censored lifetimes.

We propose a nonparametric test of independence, termed optHSIC, between a covariate and a right-censored lifetime. Because the presence of censoring creates a challenge in applying the standard permutation-based testing approaches, we use optimal transport to transform the censored dataset into an uncensored one, while preserving the relevant dependencies. We then apply a permutation test using the kernel-based dependence measure as a statistic to the transformed dataset. The type 1 error is proven to be correct in the case where censoring is independent of the covariate. Experiments indicate that optHSIC has power against a much wider class of alternatives than Cox proportional hazards regression and that it has the correct type 1 control even in the challenging cases where censoring strongly depends on the covariate.

Knowledge, Attitude and Practice Regarding COVID-19 and its Impact on Dentistry: A Cross-sectional Survey among Nepalese Dentists

Background Coronavirus Disease, 2019 (COVID-19) is a highly infectious respiratory disease with high transmissibility. Dentists are at inherent risk because of aerosol generating procedures exposing dentists to the respiratory and oral secretions of the patients. Objective To assess the knowledge, awareness, and practice (KAP) of the Dentists to combat the pandemic which could help shape future guidelines and policies to be implemented in dental settings. Method This cross-sectional descriptive study included series of multiple-choice questions distributed online, assessing dentists' KAP towards COVID-19, its impact on dentistry and their psychological well-being. Statistical analysis was performed using SPSS (Statistical Package for Social Sciences) version 20 for mac Operating System (OS). Descriptive statistics was performed, and frequencies of responses were reported in proportion. Non-parametric tests of independence and Chi-square test were performed to see the association between the categorical variables. Result Around 84% of the respondents accurately answered mode of transmission, 68% inquired about the travel history while only 49% measured the body temperature. Also, only 42% were receiving salary. A statistically significant difference concerning impact and practice during the COVID-19 was observed between general practitioner and specialist working at different work places. Conclusion Majority of Dentists have good knowledge and awareness but there were certain pitfalls in attitude and practice level calling out for more efficient training programs, precise guidelines, and treatment protocols to put into practice. Also, the mental distress and the financial impact subjected upon dentist require to be further explored determining the association between their mental health during and post COVID-19 outbreak.

Multivariate tests of independence and their application in correlation analysis between financial markets

We consider the multivariate independence testing problem between pairs of random vectors for high-dimensional data and develop three high-dimensional nonparametric independence tests based on spatial sign and spatial rank, which have greater power than many existing popular tests, especially for heavy-tailed distributions. Under the elliptically symmetric distributions, which are much more general than the widely studied multivariate normal distributions, we establish asymptotic properties of the proposed tests and demonstrate their power superiority via frequently used numerical experiments. To explore the correlation between different financial markets, we first apply the proposed methods to test the dependence between the return rate data of the stocks from US S&P500 index and China CSI300 index, and then apply them to test the dependence between the return rate data of the stocks from the Shanghai Stock Exchange and the Shenzhen Stock Exchange in China.

Bayesian nonparametric test for independence between random vectors

A nonparametric approach for testing independence among groups of continuous random variables is proposed. Gaussian-centered multivariate finite Polya tree priors are used to model the underlying probability distributions. Integrating out the random probability measure, a tractable empirical Bayes factor is derived and used as the test statistic. The Bayes factor is consistent in the sense that it tends to infinity under the alternative, and zero under the null. A p-value is then obtained through a permutation test based on the observed Bayes factor. Through a series of simulation studies, the performance of the proposed approach is examined and compared to several existing approaches based on the power of the test as well as the observed Bayes factor. Lastly, the proposed method is applied to a set of real data in ecology.

Measuring and testing interdependence among random vectors based on Spearman’s $$\rho $$ and Kendall’s $$\tau $$

Inspired by the correlation matrix and based on the generalized Spearman’s $$\rho $$ and Kendall’s $$\tau $$ between random variables proposed in Lu et al. ( J Nonparametr Stat 30(4):860–883, 2018), $$\rho $$ -matrix and $$\tau $$ -matrix are suggested for multivariate data sets. The matrices are used to construct the $$\rho $$ -measure and the $$\tau $$ -measure among random vectors with statistical estimation and the asymptotic distributions under the null hypothesis of independence that produce the nonparametric tests of independence for multiple vectors. Simulation results demonstrate that the proposed tests are powerful under different grouping of the investigated random vector. An empirical application to detecting dependence of the closing price of a portfolio of stocks in NASDAQ also illustrates the applicability and effectiveness of our provided tests. Meanwhile, the corresponding measures are applied to characterize strength of interdependence of that portfolio of stocks during the recent two years.

Nonparametric tests of independence based on interpoint distances

We present novel tests for the hypothesis of independence when the number of variables is larger than the number of vector observations. We show that two multivariate normal vectors are independent if and only if their interpoint distance are independent. The proposed test statistics exploit different properties of the sample interpoint distances. A simulation study compares the new tests with three existing tests under various scenarios, including monotone and non-monotone dependence structures. Numerical results show that the new methods are effective for independence testing.