• Journal of the Korean Data and Information Science Society
• /
• v.16 no.1
• /
• pp.137-144
• /
• 2005

In $I{\times}J$ incomplete contingency tables, the test of independence proposed by Chen and Fienberg(1974) uses $I{\times}J-1$ instead of (I-1)(J-1) degrees of freedom without providing much of an increase in the value of the test statistic. For these reasons, Chen and Fienberg tests are expected to have less power. New Wald test statistic related to the part of Chen and Fienberg test statistic is proposed using delta method. These two tests are compared through Monte Carlo studies.

• The Pure and Applied Mathematics
• /
• v.20 no.2
• /
• pp.109-116
• /
• 2013

In this paper, we propose a Jonckheere type test statistic for testing the parallelism of k regression lines against ordered alternatives. The order restriction problems could arise in various settings such as location, scale, and regression problems. But most of theory about the statistical inferences under order restrictions has been developed to deal with location parameters. The proposed test is an application of Jonckheere's procedure to regression problem. Asymptotic normality and asymptotic distribution-free properties of the test statistic are obtained under some regularity conditions.

• Communications for Statistical Applications and Methods
• /
• v.7 no.2
• /
• pp.563-573
• /
• 2000

In this thesis, we propose the test statistic for ordered alternatives on c-sample ranked set samples(RSS). The proposed test statistic JRSS is Jonckheere type statistic using the median of the i-th samples in each cycle. We obtained the asymptotic property of the proposed test statistic and the asymptotic relative efficiencies of the proposed test statistic with respect to J SRS which Jonckheere type statistic on simple random samples(SRS). From the simulation works, J RSS is superior to J SRS. We compared the empirical powers of J RSS with respect to U RSS on ranked set sample and U SRS on simple random sample using all samples, which are proposed by Kim, Kim and Lee(1999). The powers of J RSS are nearly the same values when entire sample size is large. J RSS is superior to U RSS. J RSS is simpler than U RSSon calculating process.

• Communications for Statistical Applications and Methods
• /
• v.8 no.2
• /
• pp.395-406
• /
• 2001

In this paper, we propose the test statistic for the umbrella alternatives on c-samples ranked set samples(RSS), where the peak of the umbrella is known. We obtain the asymptotic property of the proposed test statistic and the asymptotic relative efficiencies of the proposed test statistic with respect to U-statistic based on simple random samples(SRS). From the simulation work, we compare the empirical powers of the proposed test statistic with U-statistic based on SRS.

• Communications for Statistical Applications and Methods
• /
• v.8 no.2
• /
• pp.473-481
• /
• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent. Kim(2001) proposed a modified Shapiro-Wilk's test statistic based on the ratio of tow asymptotically efficient estimates of scale. In this paper, we study the asymptotic behavior of the statistic using the approximation of the quantile process by a sequence of Brownian bridges and represent the limit null distribution as an integral of a Brownian bridge.

• Communications for Statistical Applications and Methods
• /
• v.30 no.4
• /
• pp.423-435
• /
• 2023

The Jarque and Bera (1980) statistic is one of the well known statistics to test univariate normality. It is based on the sample skewness and kurtosis which are the sample standardized third and fourth moments. Desgagné and de Micheaux (2018) proposed an alternative form of the Jarque-Bera statistic based on the sample second power skewness and kurtosis. In this paper, we generalize the statistic to a multivariate version by considering some data driven directions. They are directions given by the normalized standardized scaled residuals. The statistic is a modified multivariate version of Kim (2021), where the statistic is generalized using an empirical standardization of the scaled residuals of data. A simulation study reveals that the proposed statistic shows better power when the dimension of data is big.

• Communications for Statistical Applications and Methods
• /
• v.28 no.5
• /
• pp.463-475
• /
• 2021

Desgagné and de Micheaux (2018) proposed an alternative univariate normality test to the Jarque-Bera test. The proposed statistic is based on the sample second power skewness and kurtosis while the Jarque-Bera statistic uses sample Pearson's skewness and kurtosis that are the third and fourth standardized sample moments, respectively. In this paper, we generalize their statistic to a multivariate version based on orthogonalization or an empirical standardization of data. The proposed multivariate statistic follows chi-squared distribution approximately. A simulation study shows that the proposed statistic has good control of type I error even for a very small sample size when critical values from the approximate distribution are used. It has comparable power to the multivariate version of the Jarque-Bera test with exactly the same idea of the orthogonalization. It also shows much better power for some mixed normal alternatives.

• Communications for Statistical Applications and Methods
• /
• v.7 no.2
• /
• pp.403-414
• /
• 2000

A diagnostic tool for testing homogeneity for random effects is proposed in unbalanced linear mixed model based on score statistic. The finite sample behavior of the test statistic is examined using Monte Carlo experiments examine the chi-square approximation of the test statistic under the null hypothesis.

• Communications for Statistical Applications and Methods
• /
• v.8 no.1
• /
• pp.1-14
• /
• 2001

This paper discusses choosing the weight function of the Hardle and Mammen statistic in nonparametric goodness-of-fit test for regression curve. For this purpose, we modify the Hardle and Mammen statistic and derive its asymptotic distribution. Some results on the test statistic from the wild bootstrapped sample are also obtained. Through Monte Carlo experiment, we check the validity of these results. Finally, we study the powers of the test and compare with those of the Hardle and Mammen test through the simulation.

• Communications for Statistical Applications and Methods
• /
• v.16 no.4
• /
• pp.697-705
• /
• 2009

The Pearson chi-squared statistic or the deviance statistic is widely used in assessing the goodness-of-fit of the generalized linear models. But these statistics are not proper in the situation of continuous explanatory variables which results in the sparseness of cell frequencies. We propose a goodness-of-fit test statistic for the cumulative logit models with ordinal responses. We consider the grouping of a dataset based on the ordinal scores obtained by fitting the assumed model. We propose the Pearson chi-squared type test statistic, which is obtained from the cross-classified table formed by the subgroups of ordinal scores and the response categories. Because the limiting distribution of the chi-squared type statistic is intractable we suggest the parametric bootstrap testing procedure to approximate the distribution of the proposed test statistic.