USP: an independence test that improves on Pearson’s chi-squared and the G -test

We present the U -statistic permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearson’s χ 2 -test of independence, or the G -test, are typically used for this task, but we argue that these tests have serious deficiencies, both in terms of their inability to control the size of the test, and their power properties. By contrast, the USP test is guaranteed to control the size of the test at the nominal level for all sample sizes, has no issues with small (or zero) cell counts, and is able to detect distributions that violate independence in only a minimal way. The test statistic is derived from a U -statistic estimator of a natural population measure of dependence, and we prove that this is the unique minimum variance unbiased estimator of this population quantity. The practical utility of the USP test is demonstrated on both simulated data, where its power can be dramatically greater than those of Pearson’s test, the G -test and Fisher’s exact test, and on real data. The USP test is implemented in the R package USP .

Caregiving Between Spouse and Adult Child Caregivers of Older Adults with Cognitive Impairment

Prior studies of caregiving characteristics by type of caregivers are inconsistent, particularly those who are spouses and adult children. This study examined caregiving characteristics between spouses and adult children of cognitively impaired older adults. We analyzed phone-screening data from an ongoing trial of a dyadic sleep intervention program for persons with dementia and their caregivers. Data included spouse caregivers (n=52) and adult child caregivers (n=24). Nearly all participants (95%) lived with their care recipients (91% with dementia). Types of caregiving activities were measured by activities of daily living [ADLs] and instrumental ADLs [IADLs] with their levels of intensity (0 [total independent] to 3 [total dependent]). Care recipients’ sleep was measured by the Neuropsychiatric Inventory-Nighttime Behavioral Subscale (8 items). Analyses included Pearson correlations and t-tests. Adult child caregivers helped their care recipients at significantly higher levels as indicated by their measure of dependence in dressing (1.46±1.22 vs. 0.87±1.16, p=0.044), continence (1.22±1.38 vs. 0.54±1.04, p=0.021), laundry (2.87±0.46 vs. 2.13±1.24, p=0.007), and transportation (3.00±0.00 vs. 2.63±0.79, respectively; p=0.031) than spouse caregivers. Adult child caregivers also reported their care recipients having more difficulty falling asleep (56% vs. 19%, respectively; p=0.004) and having more numbers of sleep problems than spouse caregivers (3.54±2.08 vs. 2.48±1.51, respectively; p=0.014). The findings suggest that adult child caregivers may involve higher levels of caregiving responsibilities during daytime and nighttime, compared to spouse caregivers. Further research needs to explore complimentary ways to involve spouse and adult child caregivers in the care of this vulnerable population.

On the Use of Entropy as a Measure of Dependence of Two Events

We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate probability distribution produced by these events and depending on one parameter (the probability of intersection of A and B) varying within a closed interval I. The entropy function attains its global maximum when the events A and B are independent. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a minimum at the left endpoint of I exactly when one of the events and the complement of the other are connected with the relation of inclusion (maximal negative dependence). It has a minimum at the right endpoint of I exactly when one of these events is included in the other (maximal positive dependence). Moreover, the deviation of the entropy from its maximum is equal to average information that carries one of the binary trials defined by A and B with respect to the other. As a consequence, the degree of dependence of A and B can be expressed in terms of information theory and is invariant with respect to the choice of unit of information. Using this formalism, we describe completely the screening tests and their reliability, measure efficacy of a vaccination, the impact of some events from the financial markets to other events, etc. A link is available for downloading an Excel program which calculates the degree of dependence of two events in a sample space with equally likely outcomes.

On the Use of Entropy as a Measure of Dependence of Two Events

We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate probability distribution produced by these events and depending on one parameter (the probability of intersection of A and B) varying within a closed interval I. The entropy function attains its global maximum when the events A and B are independent. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a minimum at the left endpoint of I exactly when one of the events and the complement of the other are connected with the relation of inclusion (maximal negative dependence). It has a minimum at the right endpoint of I exactly when one of these events is included in the other (maximal positive dependence). Moreover, the deviation of the entropy from its maximum is equal to average information that carries one of the binary trials defined by A and B with respect to the other. As a consequence, the degree of dependence of A and B can be expressed in terms of information theory and is invariant with respect to the choice of unit of information. Using this formalism, we describe completely the screening tests and their reliability, measure efficacy of a vaccination, the impact of some events from the financial markets to other events, etc.

On the Use of Entropy as a Measure of Dependence of Two Events

We define degree of dependence of two events A and B in a probability space by using Boltzmann-Shannon entropy function of an appropriate probability distribution produced by these events and depending on one parameter (the probability of intersection of A and B) varying within a closed interval I. The entropy function attains its global maximum when the events A and B are independent. The important particular case of discrete uniform probability space motivates this definition in the following way. The entropy function has a minimum at the left endpoint of I exactly when one of the events and the complement of the other are connected with the relation of inclusion (maximal negative dependence). It has a minimum at the right endpoint of I exactly when one of these events is included in the other (maximal positive dependence). Moreover, the deviation of the entropy from its maximum is equal to average information that carries one of the binary trials defined by A and B with respect to the other. As a consequence, the degree of dependence of A and B can be expressed in terms of information theory and is invariant with respect to the choice of unit of information. Using this formalism, we describe completely the screening tests and their reliability, measure efficacy of a vaccination, the impact of some events from the financial markets to other events, etc.

psi-Hilfer Fractional Approximations of Csiszar's f-Divergence

Here are given tight probabilistic inequalities that provide nearly best estimates for the Csiszar's f-divergence. These use the right and left psi -Hilfer fractional derivatives of the directing function f. Csiszar's f- divergence or the so called Csiszar's discrimination is used as a measure of dependence between two random variables which is a very essential aspect of stochastics, we apply our results there. The Csiszar's discrimination is the most important and general measure for the comparison between two probability measures. We give also other applications.

Confidence set for connected stocks of stock market

The problem of analysis of pairwise connections between stocks of financial market by observations on stock returns is considered. Such problem arise in stock market network analysis. It is assumed that joint distribution of stock returns belongs to the wide class of elliptical distributions. Classical Pearson correlation, Fechner correlation and Kendall correlation are used as measure of dependence. The construction problems of sets of stocks with strong connections between its returns are investigated. The construction problems of sets of stocks with strong connections between its returns are investigated. To construct such sets the multiple hypotheses testing procedures on values of correlations are used. The properties of these statistical procedures are investigated by simulations. The simulation results show that procedures based on individual Fechner and Kendall tests lead to such sets of stocks with given confidence probability unlike procedure based on Pearson individual tests which do not control the confidence probability. At the same time it is emphasized that for Student distribution the constructed set is nearly the same to the confidence set. The procedure of consistency testing with elliptical model is proposed and exemplified. The peculiarities of the model are discussed.

Mutual information analysis of the factors influencing port throughput

Purpose Port throughput analysis is a challenging task, as it consists of intertwined interactions between a variety of cargos and numerous influencing factors. This study aims to propose a quantitative method to facilitate port throughput analysis by identification of important cargos and key macroeconomic variables. Design/methodology/approach Mutual information is applied to measure the linear and nonlinear correlation among variables. The method gives a unique measure of dependence between two variables by quantifying the amount of information held in one variable through another variable. Findings This study uses the mutual information to the Port of Isafjordur in Iceland to underpin the port throughput analysis. The results show that marine products are the main export cargo, whereas most imports are fuel oil, industrial materials and marine product. The aggregation of these cargos, handled in the port, meaningfully determines the non-containerized port throughput. The relation between non-containerized export and the national gross domestic product (GDP) is relatively high. However, non-containerized import is mostly related to the world GDP. The non-containerized throughput shows a strong relation to the national GDP. Furthermore, the results reveal that the volume of national export trade is the key influencing macroeconomic variable to the containerized throughput. Originality/value Application of the mutual information in port throughput analysis effectively reduces epistemic uncertainty in the identification of important cargos and key influencing macroeconomic variables. Thus, it increases the reliability of the port throughput forecast.

On a characterization of exponential, Pearson and Pareto distributions via covariance and pseudo-covariance

Properties of linear regression of order statistics and their functions are usually utilized for the characterization of distributions. In this paper, based on such statistics, the concept of Pearson covariance and the pseudo-covariance measure of dependence is used to characterize the exponential, Pearson and Pareto distributions.

Nicotine Dependence and Loss of Autonomy among Greek Adolescent Smokers: A Countrywide Cross-Sectional Study

Nicotine dependence is one of the main reasons for the continuation of smoking among adolescents. Loss of autonomy (LOA) is a measure of dependence. This study is the first to investigate LOA and its determinants among Greek adolescents. In 2013, 13-to-15-year-old middle-school students were selected by multi-stage clustered sampling. LOA was evaluated with the Hooked-on-Nicotine Checklist (HONC). Multiple univariate analysis was used to assess the association between adolescent demographics, smoking habits, and loss of autonomy. Three-hundred thirty-nine current smokers responded to the questionnaire (response rate: 82.3%). Of these respondents, 51.2% were male and 88.8% reported at least one LOA symptom. The mean HONC score was 4.13/10 (95% CI: 3.82–4.45). Higher scores were negatively associated with lower smoking frequency (cumulative odds ratio (cOR): 0.240, 95% CI: 0.144–0.400) and positively associated with lower age at first cigarette (cOR: 2.29, 95% CI: 1.38–3.82). Female gender was significantly associated with the prevalence but not the degree of LOA. Overall, the prevalence and the degree of nicotine dependence among adolescent smokers in Greece is similar to other countries. Frequent smoking and initiation of smoking at a younger age are linked to nicotine dependence, although it was not possible to make causal inferences. The relationship between nicotine dependence and gender remains unclear.