Null Hypothesis Of Independence Research Articles

RANK-BASED INDICES FOR TESTING INDEPENDENCE BETWEEN TWO HIGH-DIMENSIONAL VECTORS.

To test independence between two high-dimensional random vectors, we propose three tests based on the rank-based indices derived from Hoeffding's , Blum-Kiefer-Rosenblatt's and Bergsma-Dassios-Yanagimoto's . Under the null hypothesis of independence, we show that the distributions of the proposed test statistics converge to normal ones if the dimensions diverge arbitrarily with the sample size. We further derive an explicit rate of convergence. Thanks to the monotone transformation-invariant property, these distribution-free tests can be readily used to generally distributed random vectors including heavily tailed ones. We further study the local power of the proposed tests and compare their relative efficiencies with two classic distance covariance/correlation based tests in high dimensional settings. We establish explicit relationships between and Pearson's correlation for bivariate normal random variables. The relationships serve as a basis for power comparison. Our theoretical results show that under a Gaussian equicorrelation alternative, (i) the proposed tests are superior to the two classic distance covariance/correlation based tests if the components of random vectors have very different scales; (ii) the asymptotic efficiency of the proposed tests based on and are sorted in a descending order.

Tests of independence and randomness for arbitrary data using copula-based covariances

In this article, we study tests of independence for data with arbitrary distributions in the non-serial case, i.e., for independent and identically distributed random vectors, as well as in the serial case, i.e., for time series. These tests are derived from copula-based covariances and their multivariate extensions using Möbius transforms. We find the asymptotic distributions of these statistics under the null hypothesis of independence or randomness, as well as under contiguous alternatives. This enables us to find out locally most powerful test statistics for some alternatives, whatever the margins. Numerical experiments are performed for Wald’s type combinations of these statistics to assess the finite sample performance.

Probabilistic approaches for investigating species co-occurrence from presence-absence maps.

In this research, we propose probabilistic approaches to identify pairwise patterns of species co-occurrence by using presence-absence maps only. In particular, the two-by-two contingency table constructed from a presence-absence map of two species would be sufficient to compute the test statistics and perform the statistical tests proposed in this article. Some previous studies have investigated species co-occurrence through incidence data of different survey sites. We focus on using presence-absence maps for a specific study plot instead. The proposed methods are assessed by a thorough simulation study. A Chi-squared test is used to determine whether the distributions of two species are independent. If the null hypothesis of independence is rejected, the Chi-squared method can not distinguish positive or negative association between two species. We propose six different approaches based on either the binomial or Poisson distribution to obtain p-values for testing the positive (or negative) association between two species. When we test to investigate a positive (or negative) association, if the p-value is below the predetermined level of significance, then we have enough evidence to support that the two species are positively (or negatively) associated. A simulation study is conducted to demonstrate the type-I errors and the testing powers of our approaches. The probabilistic approach proposed by Veech (2013) is served as a benchmark for comparison. The results show that the type-I error of the Chi-squared test is close to the significance level when the presence rate is between 40% and 80%. For extremely low or high presence rate data, one of our approaches outperforms Veech (2013)'s in terms of the testing power and type-I error rate. The proposed methods are applied to a tree data of Barro Colorado Island in Panama and a tree data of Lansing Woods in USA. Both positive and negative associations are found among some species in these two real data.

Point estimation in sign-restricted SVARs based on independence criteria with an application to rational bubbles

The median and median target estimates in sign-restricted SVARs are driven by a highly informative prior for the set-identified structural parameters. This paper proposes an approach for point elicitation by minimizing the evidence against the null hypothesis of independence with respect to the orthogonalized residuals implied by the identified set. Finite sample properties of the estimator are studied in a Monte Carlo experiment. As an empirical illustration, we analyze monetary policy effects within the rational bubble model of equity valuation (Galí, 2014). The detected monetary policy shocks lead to distinct response profiles of the fundamental and bubble components of asset prices.

A distance-based test of independence between two multivariate time series

We contribute to recent research on distance correlation by extending its capability to test for independence between two time series. The proposed test is a Portmanteau-type test based on double-centered distance cross-covariances. We show that the test statistic constructed in this way is asymptotically normal and pivotal under the null hypothesis of independence, and it is consistent under fixed alternative hypotheses of dependence. We also propose a fast wild bootstrap procedure that can significantly improve the performance of the asymptotic test in finite samples. An extensive Monte Carlo simulation study designed to compare the proposed test with other existing procedures shows that both the proposed test and its bootstrap version can achieve a good size and power performance for several data generating processes (DGPs), and they can significantly outperform other tests under model misspecification. An empirical application to illustrate the applicability of the proposed method is also given.

Correlations between alignment gaps and nucleotide substitution or amino acid replacement

To assess the conventional treatment in evolutionary inference of alignment gaps as missing data, we propose a simple nonparametric test of the null hypothesis that the locations of alignment gaps are independent of the nucleotide substitution or amino acid replacement process. When we apply the test to 1,390 protein alignments that are informed by protein tertiary structure and use a 5% significance level, the null hypothesis of independence between amino acid replacement and gap location is rejected for ∼65% of datasets. Via simulations that include substitution and insertion-deletion, we show that the test performs well with true alignments. When we simulate according to the null hypothesis and then apply the test to optimal alignments that are inferred by each of four widely used software packages, the null hypothesis is rejected too frequently. Via further simulations and analyses, we show that the overly frequent rejections of the null hypothesis are not solely due to weaknesses of widely used software for finding optimal alignments. Instead, our evidence suggests that optimal alignments are unrepresentative of true alignments and that biased evolutionary inferences may result from relying upon individual optimal alignments.

A new non-parametric test for testing positive quadrant dependence

We develop a simple non-parametric test for testing independence of two random variables against the alternative that they are positive quadrant dependent. The asymptotic distribution of the proposed test statistic is distribution free under the null hypothesis of independence. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the proposed test. We illustrate the proposed method with a real data set.

Analysis of Categorical Data with the R Package confreq

The person-centered approach in categorical data analysis is introduced as a complementary approach to the variable-centered approach. The former uses persons, animals, or objects on the basis of their combination of characteristics which can be displayed in multiway contingency tables. Configural Frequency Analysis (CFA) and log-linear modeling (LLM) are the two most prominent (and related) statistical methods. Both compare observed frequencies (foi…k) with expected frequencies (fei…k). While LLM uses primarily a model-fitting approach, CFA analyzes residuals of non-fitting models. Residuals with significantly more observed than expected frequencies (foi…k>fei…k) are called types, while residuals with significantly less observed than expected frequencies (foi…k<fei…k) are called antitypes. The R package confreq is presented and its use is demonstrated with several data examples. Results of contingency table analyses can be displayed in tables but also in graphics representing the size and type of residual. The expected frequencies represent the null hypothesis and different null hypotheses result in different expected frequencies. Different kinds of CFAs are presented: the first-order CFA based on the null hypothesis of independence, CFA with covariates, and the two-sample CFA. The calculation of the expected frequencies can be controlled through the design matrix which can be easily handled in confreq.

ASYMPTOTIC DISTRIBUTIONS OF HIGH-DIMENSIONAL DISTANCE CORRELATION INFERENCE.

Distance correlation has become an increasingly popular tool for detecting the nonlinear dependence between a pair of potentially high-dimensional random vectors. Most existing works have explored its asymptotic distributions under the null hypothesis of independence between the two random vectors when only the sample size or the dimensionality diverges. Yet its asymptotic null distribution for the more realistic setting when both sample size and dimensionality diverge in the full range remains largely underdeveloped. In this paper, we fill such a gap and develop central limit theorems and associated rates of convergence for a rescaled test statistic based on the bias-corrected distance correlation in high dimensions under some mild regularity conditions and the null hypothesis. Our new theoretical results reveal an interesting phenomenon of blessing of dimensionality for high-dimensional distance correlation inference in the sense that the accuracy of normal approximation can increase with dimensionality. Moreover, we provide a general theory on the power analysis under the alternative hypothesis of dependence, and further justify the capability of the rescaled distance correlation in capturing the pure nonlinear dependency under moderately high dimensionality for a certain type of alternative hypothesis. The theoretical results and finite-sample performance of the rescaled statistic are illustrated with several simulation examples and a blockchain application.

A multiple-response chi-square framework for the analysis of Free-Comment and Check-All-That-Apply data

Free-Comment (FC) and Check-All-That-Apply (CATA) provide a contingency table containing citation counts of descriptors by products. The analyses performed on this table are most often related to the chi-square statistic. However, such practices are not well suited because they consider experimental units as being the citations (one descriptor for one product by one subject) while the evaluations (vector of citations for one product by one subject) should be considered instead. This results in incorrect expected frequencies under the null hypothesis of independence between products and descriptors and thus in an incorrect chi-square statistic. Thus, analyses related to this incorrect chi-square statistic, which include Correspondence Analysis, can lead to wrong interpretations. This paper presents a modified chi-square square framework dedicated to the analysis of multiple-response data in which experimental units are the evaluations and which is, therefore, better suited to FC and CATA data. This new framework includes a multiple-response dimensionality test of dependence, a multiple-response Correspondence Analysis, and a multiple-response hypergeometric test to investigate which descriptors are significantly associated with which product. The benefits of the multiple-response chi-square framework over the usual chi-square framework are exhibited on real CATA data. An R package called “MultiResponseR” is available upon request to the authors and on GitHub to perform the multiple-response chi-square analyses.

An association test for functional data based on Kendall’s Tau

We consider the problem of testing for association between a functional variable belonging to a Hilbert space and a scalar variable. Particularly, we propose a distribution-free test statistic based on Kendall’s Tau, which is a popular method for determining the association between two random variables. The distribution of the test statistic under the null hypothesis of independence is established using the theory of U-statistics taking values in a Hilbert space. We also consider the case where the functional data is sparsely observed, a situation that arises in many applications. Simulations show that the proposed method outperforms the alternatives under multiple settings, demonstrating the effectiveness and robustness of our approach. We provide data applications that further showcase the utility of our method.

Effect of Direct Oral Anticoagulant, Patient, and Surgery Characteristics on Clinical Outcomes in the Perioperative Anticoagulation Use for Surgery Evaluation Study.

Introduction The Perioperative Anticoagulation Use for Surgery Evaluation (PAUSE) Study assessed a standardized perioperative management strategy in patients with atrial fibrillation who were taking a direct oral anticoagulant (DOAC) and required an elective surgery or procedure. The aim of this substudy is to analyze the safety of this management strategy across different patient subgroups, according to four presurgical variables: (1) DOAC type and dose, (2) surgery/procedure bleed risk, (3) patient renal function, and (4) age. Methods Clinical outcomes analyzed included major bleeding (MB), arterial thromboembolism, any bleeding, and any thromboembolism. We used descriptive statistics to summarize clinical outcomes, where the frequency, proportion, and 95% confidence interval were reported. Fisher's exact tests were used for testing the null hypothesis of independence between the clinical outcome and patient characteristic, where the test p -values were reported. Results There were 3,007 patients with atrial fibrillation requiring perioperative DOAC management. There was no significant difference in bleeding or thromboembolic outcomes according to DOAC type/dose regimen, renal function, or patient age. The rate of MB was significantly higher with high bleed risk procedures than low bleed risk procedures in apixaban-treated patients (2.9 vs. 0.59%; p < 0.01), but not in dabigatran-treated patients (0.88 vs. 0.91%; p = 1.0) or rivaroxaban-treated patients (2.9 vs. 1.3%; p = 0.06). The risk for thromboembolism did not differ according to surgery/procedure-related bleed risk. Conclusion Our results suggest that in DOAC-treated patients who received standardized perioperative management, surgical bleed risk is an important determinant of bleeding but not thromboembolic outcomes, although this finding was not consistent across all DOACs. There were no differences in bleeding and thromboembolism according to DOAC type and dose, renal function, or age.

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.

Awareness on Hazard Analysis and Critical Control Points (HACCP) Principles in TVET and University Hospitality Schools in Kenya

The purpose of this study was to assess the level of awareness on Hazard Analysis and Critical Control Points (HACCP) principles in TIVET and University hospital schools in Kenya. A total of 671 respondents participated in the study (Comprising 249 from universities, 250 from Institutes of Technology, 64 from Polytechnics and 128 from Technical Institutions). Primary data sources included using structured questionnaires, taking photographs, oral interviews, observation check list and focus group discussions. Secondary sources, on the other hand, involved retrieving information from desk research where journals, books and other relevant literature were obtained. Both descriptive and inferential statistics were used to analyze the quantitative data while content analysis was used to analyze the qualitative data. The analyzed data were presented in terms of graphs and tables. The study found that 83% of the respondents interviewed were aware of the HACCP principles while 17% were not aware. The study revealed that (45%) respondents from Universities were aware of food safety and hygienic practices compared to respondents from TVET colleges at (38%). In testing the independence of institution category on awareness, the test yielded a p-value = 0.001, which was less than 0.05. Since the p-value was less than the level of significance, the null hypothesis of independence was rejected. This decision implied that there was a significant relationship between institution category and code of practice on awareness. The study concluded that even though the majority of the respondents indicated that they were aware of HACCP principles and food safety, they did not practice what they knew. It was recommended that there is need to create more awareness on HACCP principles and for food safety by holding workshops, seminars and sensitization programme to the stakeholders of hospitality industry

Oczekiwania pielęgniarek dotyczące formy zwracania się do nich pacjentów

&lt;p&gt;Umiejętności z zakresu komunikacji międzyludzkiej w relacji pacjent – pielęgniarka wydają się być kluczowe w całym procesie opieki. Współcześnie coraz częściej daje się zauważyć niechęć pielęgniarek do formy zwrotu „siostro”. Celem pracy było poznanie opinii pielęgniarek na temat różnych form zwracania się pacjentów do nich i oceny, która z form jest najwłaściwsza i dlaczego. Badania były prowadzone w listopadzie i grudniu 2017 roku w miejscach pracy pielęgniarek (szpitale i przychodnie). Objęto nimi 115 osób. Metodę badań stanowił sondaż diagnostyczny. W badaniach za zmienne niezależne przyjęto następujące czynniki: staż pracy w zawodzie, rodzaj ukończonej szkoły, zajmowane stanowisko i tryb pracy. Zastosowano technikę ankietową, a narzędziem badawczym był kwestionariusz ankiety własnego autorstwa. Do opracowania statystycznego badań posłużono się testem niezależności Chi kwadrat. Do pomiaru wielkości siły związku w przypadku odrzucenia hipotezy zerowej o niezależności wykorzystano test fi i V Craméra. Na podstawie przeprowadzonych badań stwierdzono, że pielęgniarki nie akceptują formy zwrotu „siostro”. Nie akceptują również form zdrobniałych, nadmiernie ugrzecznionych. W badaniach wykazano zależność między stażem, stanowiskiem, trybem pracy a wyborem najlepszej formy zwrotu do pielęgniarki i akceptacją zwrotu „siostro”.&lt;/p&gt;

Preferencias del consumidor de carne de cerdo en la región centro de México

La carne de cerdo es una de las tres principales carnes rojas consumidas en la dieta de los mexicanos, provee proteínas, minerales (hierro y zinc) y vitaminas. El objetivo de esta investigación fue conocer los hábitos y tendencias del consumo de esta carne, en los estados de Tlaxcala, Morelos, Hidalgo, Guerrero, Puebla y México, al ser la principal región de comercialización y consumo en el país, de acuerdo con el nivel de ingresos y los servicios integrados a esta carne. La información se obtuvo al aplicar una encuesta semiestructurada a 702 personas en expendios de alimentos, mediante el uso de tablas de contingencia que permiten segmentar las variables cuantitativas y categóricas de carácter económico-social, posteriormente, se probó la hipótesis nula de independencia al correlacionar parejas de estas variables, mediante pruebas ji-cuadrada. Los resultados muestran que, al correlacionar consumo e ingreso con el tipo de corte y lugar de compra, las personas de menor ingreso prefieren la carne pre-cortada, sin empacar y la compran en carnicerías y mercados por no estar congelada ni refrigerada. Se encontró que los consumidores de esta región destinan hasta 1,500 pesos para la compra de esta carne y la consumen hasta 10 veces mensualmente.

Specification testing in nonparametric AR‐ARCH models

AbstractIn this paper, an autoregressive time series model with conditional heteroscedasticity is considered, where both conditional mean and conditional variance function are modeled nonparametrically. Tests for the model assumption of independence of innovations from past time series values are suggested. Tests based on weighted L2‐distances of empirical characteristic functions are considered as well as a Cramér–von Mises‐type test. The asymptotic distributions under the null hypothesis of independence are derived, and the consistency against fixed alternatives is shown. A smooth autoregressive residual bootstrap procedure is suggested, and its performance is shown in a simulation study.

Fisher's exact approach for post hoc analysis of a chi-squared test.

This research is motivated by one of our survey studies to assess the potential influence of introducing zebra mussels to the Lake Mead National Recreation Area, Nevada. One research question in this study is to investigate the association between the boating activity type and the awareness of zebra mussels. A chi-squared test is often used for testing independence between two factors with nominal levels. When the null hypothesis of independence between two factors is rejected, we are often left wondering where does the significance come from. Cell residuals, including standardized residuals and adjusted residuals, are traditionally used in testing for cell significance, which is often known as a post hoc test after a statistically significant chi-squared test. In practice, the limiting distributions of these residuals are utilized for statistical inference. However, they may lead to different conclusions based on the calculated p-values, and their p-values could be over- o6r under-estimated due to the unsatisfactory performance of asymptotic approaches with regards to type I error control. In this article, we propose new exact p-values by using Fisher’s approach based on three commonly used test statistics to order the sample space. We theoretically prove that the proposed new exact p-values based on these test statistics are the same. Based on our extensive simulation studies, we show that the existing asymptotic approach based on adjusted residual is often more likely to reject the null hypothesis as compared to the exact approach due to the inflated family-wise error rates as observed. We would recommend the proposed exact p-value for use in practice as a valuable post hoc analysis technique for chi-squared analysis.

Utilizing advances in correlation analysis for community structure detection

Build the connection between correlation analysis and community detection.A framework of utilizing correlation analysis to advance community detection.A novel graphic analysis for selecting methods.Solve the resolution problem through the proposed framework. In the era of big data, some data records are interrelated with each other in many areas, such as marketing, management, health care, and education. These interrelated data can be more naturally represented as networks with nodes and edges. Inside this type of networks, there is usually a hidden community structure where each community represents a relatively independent functional module. Such hidden community structures are useful for many applications, such as word-of-mouth marketing, promoting decentralized social interactions inside organizations, and searching biological pathways related to various diseases. Therefore, how to detect hidden community structures becomes an important task with wide applications. Currently, modularity-based methods are widely-used among many existing community structure detection methods. They detect communities with more internal edges than expected under the null hypothesis of independence. Since research in correlation analysis also searches for patterns which occur more than expected under the null hypothesis of independence, this paper proposed a framework of changing the original modularity function according to different existing correlation functions in the correlation analysis research area. Such a framework can utilize not only the current but also the future potential research progresses in correlation analysis to advance community detection. In addition, a novel graphical analysis on different modified-modularity functions is conducted to analyze their different preferences, which are also validated by our evaluation on both real life and simulated networks. Our work to connect modularity-based methods with correlation analysis has several significant impacts on the community detection research and its applications to expert and intelligent systems. First, the research progress in correlation analysis can be utilized to define a more effective objective function in community detection for better detection results since different real-life applications might need communities with different resolutions. Second, any existing research progress for the modularity function, such as the Louvain method for speeding up the search and different extensions for overlapping community detection, can be applied in a similar way to the new objective function derived from existing correlation functions, because the new objective function is unified within one framework with the modularity function. Third, our framework opens a large unexplored area for the researchers interested in community detection. For example, what is the best heuristic search method for each different objective function? What are the characteristics of each objective function when applied to overlapping community detection? Among different extensions to overlapping community detection, which extension is better for each objective function?

Consistent Testing for Pairwise Dependence in Time Series

ABSTRACTWe consider the problem of testing pairwise dependence for stationary time series. For this, we suggest the use of a Box–Ljung-type test statistic that is formed after calculating the distance covariance function among pairs of observations. The distance covariance function is a suitable measure for detecting dependencies between observations as it is based on the distance between the characteristic function of the joint distribution of the random variables and the product of the marginals. We show that, under the null hypothesis of independence and under mild regularity conditions, the test statistic converges to a normal random variable. The results are complemented by several examples. This article has supplementary material online.