• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.285-299
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• 2020

In many cases, we are interested in identifying independence between variables. For continuous random variables, correlation coefficients are often used to describe the relationship between variables; however, correlation does not imply independence. For finite discrete random variables, we can use the Pearson chi-square test to find independency. For the mixed type of continuous and discrete random variables, we do not have a general type of independent test. In this study, we develop a independence test of a continuous random variable and a discrete random variable without assuming a specific distribution using kernel density estimation. We provide some statistical criteria to test independence under some special settings and apply the proposed independence test to Pima Indian diabetes data. Through simulations, we calculate false positive rates and true positive rates to compare the proposed test and Kolmogorov-Smirnov test.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.411-416
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• 1998

A simple nonparametric test of complete or total independence is suggested for continuous multivariate distributions. This procedure first discretizes the original variables based on their order statistics, and then tests the hypothesis of complete independence for the resulting contingency table. Under the hypothesis of independence, the chi-squared test statistic has an asymptotic chi-squared distribution. We present a simulation study to illustrate the accuracy in finite samples of the limiting distribution of the test statistic. We compare our method to another nonparametric test of complete independence via a simulation study. Finally, we apply our method to the residuals from a real data set.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.115-122
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• 2006

A test is suggested for detecting deviations from both multivariate normality and independence. This test can be used for assessing the normality and independence of univariate time series residuals. We derive the limiting distribution of the test statistic and a simulation study is conducted to study the accuracy of the limiting distribution in finite samples. Finally, we apply our method to a real data of time series.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.191-197
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• 2003

This paper considers the independence test for two stationary infinite order autoregressive processes. For a test, we follow the empirical process method devised by Hoeffding (1948) and Blum, Kiefer and Rosenblatt (1961), and construct the Cram${\acute{e}}$r-von Mises type test statistics based on the least squares residuals. It is shown that the proposed test statistics behave asymptotically the same as those based on true errors.

• Communications for Statistical Applications and Methods
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• v.23 no.3
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• pp.215-230
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• 2016

The powers of some tests for independence hypothesis against positive (negative) quadrant dependence in generalized Farlie-Gumbel-Morgenstern distribution are compared graphically by simulation. Some of these tests are usual linear rank tests of independence. Two other possible rank tests of independence are locally most powerful rank test and a powerful nonparametric test based on the $Cram{\acute{e}}r-von$ Mises statistic. We also evaluate the empirical power of the class of distribution-free tests proposed by Kochar and Gupta (1987) based on the asymptotic distribution of a U-statistic and the test statistic proposed by $G{\ddot{u}}ven$ and Kotz (2008) in generalized Farlie-Gumbel-Morgenstern distribution. Tests of independence are also compared for sample sizes n = 20, 30, 50, empirically. Finally, we apply two examples to illustrate the results.

• Journal of the Korean Data and Information Science Society
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• v.25 no.5
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• pp.1039-1055
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• 2014

The distribution of a test statistic under a null hypothesis depends on the unknown distribution of the data and thus is unknown as well. Conditional tests replace the unknown null distribution by the conditional null distribution, that is, the distribution of the test statistic given the observed data. This approach is known as permutation tests and was developed by Fisher (Fisher, 1935). Theoretical framework for permutation tests was given by Strasser and Weber(1999). The coin package developed by Hothon et al. (2006, 2008) implements a unified approach for conditional inference via the generic independence test. Because convenient functions for the most prominent problems are available, users will not have to use the extremely flexible procedure. In this article we briefly review the underlying theory from Strasser and Weber (1999) and explain how to transform the data to perform the generic function independence test. Finally it was illustrated with a few real data sets.

• Journal of the Korean Statistical Society
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• v.32 no.2
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• pp.163-174
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• 2003

We propose a test for independence of bivariate censored data under univariate censorship. To do this, we first introduce a process defined by the difference between bivariate survival function estimator proposed by Lin and Ying (1993) and the product of the product-limit estimators (Kaplan and Meier, 1958) for the marginal survival functions, and derive its asymptotic properties under the null hypothesis of independence. We propose a Cramer-von Mises-type test procedure based on the process . We conduct simulation studies to investigate the finite-sample performance of the proposed test and illustrate the proposed test with a real example.

• Journal of the Korean Statistical Society
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• v.27 no.2
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• pp.197-203
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• 1998

To test the hypothesis of complete or total independence for a multi-way contingency table, the Pearson chi-squared test statistic is usually employed under Poisson or multinomial models. It is well known that, under the hypothesis, this statistic follows an asymptotic chi-squared distribution. We consider the case where all marginal sums of the contingency table are fixed. Using conditional limit theorems, we show that the chi-squared test statistic has the same limiting distribution for this case.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.377-383
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• 2003

In this paper, we consider two components system in which the lifetimes follow the bivariate Pareto model with random censored data. We assume that the censoring time is independent of the lifetimes of the two components. We develop large sample tests for testing independence between two components. Also we present simulated study which is the test based on asymptotic normal distribution in testing independence.

• Communications for Statistical Applications and Methods
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• v.29 no.5
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• pp.547-559
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• 2022

For a chi-squared test, which is a statistical method used to test the independence of a contingency table of two factors, the expected frequency of each cell must be greater than 5. The percentage of cells with an expected frequency below 5 must be less than 20% of all cells. However, there are many cases in which the regional expected frequency is below 5 in general small area studies. Even in large-scale surveys, it is difficult to forecast the expected frequency to be greater than 5 when there is small area estimation with subgroup analysis. Another statistical method to test independence is to use the Bayes factor, but since there is a high ratio of data dependency due to the nature of the Bayesian approach, the low expected frequency tends to decrease the precision of the test results. To overcome these limitations, we will borrow information from areas with similar characteristics and pool the data statistically to propose a pooled Bayes test of independence in target areas. Jo et al. (2021) suggested hierarchical Bayesian pooling models for small area estimation of categorical data, and we will introduce the pooled Bayes factors calculated by expanding their restricted pooling model. We applied the pooled Bayes factors using bone mineral density and body mass index data from the Third National Health and Nutrition Examination Survey conducted in the United States and compared them with chi-squared tests often used in tests of independence.