• Journal of the Korean Statistical Society
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• v.7 no.1
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• pp.17-26
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• 1978

For testing $\beta_i=\beta, i=1,...,k$, in the regression model $Y_{ij} = \alpha_i + \beta_ix_{ij} + e_{ij}, j=1,...,n_i$, a simple and robust test based on Kendall's tau is proposed. Its asymptotic distribution is proved to be chi-square under the null hypthesis and noncentral chi-square under an appropriate sequence of alternatives. For the optimal designs, the asymptotic relative efficiency of the proposed procedure with respect to the least squares procedure is the same as that of the Wilcoxon test with respect to the t-test.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.509-522
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• 2008

The main aim of this paper is to present some results related to asymptotic behavior of distribution functions of random variables of chi-square type $X^2_N={\Sigma}^N_{i=1}\;X^2_i$ with degrees of freedom N, where N is a positive integer-valued random variable independent on all standard normally distributed random variables $X_i$. Two ways for computing the distribution functions of chi-square type random variables with random degrees of freedom are considered. Moreover, some tables concerning considered distribution functions are demonstrated in Appendix.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.479-488
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• 1999

Moore and Stubblebine(1981) suggested a chi-square test for multivariate normality based on cell counts calculated from the sample Mahalanobis distances. They derived the limiting distribution of the test statistic only when equiprobable cells are employed. Using conditional limit theorems, we derive the limiting distribution of the statistic as well as the asymptotic normality of the cell counts. These distributions are valid even when equiprobable cells are not employed. We finally apply this method to a real data set.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.1007-1015
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• 2003

In this paper we introduced a new score generating function for the rank dispersion function in a general linear model. Based on the new score function, we derived the null asymptotic theory of the rank-based hypothesis testing in a linear model. In essence we showed that several rank test statistics, which are primarily focused on our new score generating function and new dispersion function, are mainly distribution free and asymptotically converges to a chi-square distribution.

• Journal of the Korean Statistical Society
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• v.30 no.1
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• pp.63-76
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• 2001

An adaptive estimation and testing method is proposed for comparing dispersions among several ordered groups. Based upon the large sampling theory for nonparametric quartile estimators, we derive the order restricted estimators and construct a simple test statistic. This test statistic has a mixture of several chi-square distributions as its asymptotic null distribution. The proposed test is illustratively applied to survival time data for the patients with carcinoma of the oropharynx.

• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.109-119
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• 1995

A two sample chi-square test is introduced for testing the equality of the distributions of two populations when observations are subject to random censorship. The statistic is appropriate in testing problems where a two-sided alternative is of interest. Under the null hypothesis, the asymptotic distribution of the statistic is a chi-square distribution. We obtain two types of chi-square statistics ; one as a nonnegative definite quadratic form in difference of observed cell probabilities based on the product-limit estimators, the other one as a summation form. Data pertaining to a cancer chemotheray experiment are examined with these statistics.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.349-365
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• 1994

We develop in this paper the likelihood ratio test (LRT) for testing $H_1 : F_1 \preceq F_2$ against $H_2 - H_1$ where $H_2$ imposes no restriction on $F_1$ and $F_2$ and '$\preceq$' means failure rate ordering. Both one and two-sample problems will be considered. In the one-sample case, one of the two distributions is known, while we assume in the other case both are unknown. We derive the asymptotic null distribution of the LRT statistic which will be of chi-bar-square type. The main issue here is to determine the least favorable distribution which is stochastically largest within the class of null distributions.

• Communications for Statistical Applications and Methods
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• v.8 no.3
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• pp.603-613
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• 2001

A test based on score statistic is derived for detecting homoscedasticity of errors in unbalanced random effects linear model. A small simulation study is performed to investigate the finite sample behaviour of the test statistic which is known to have an asymptotic chi-square distribution under the null hypothesis.

• 한국데이터정보과학회:학술대회논문집
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• 2002.06a
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• pp.51-73
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• 2002

Empirical likelihood ratio method is a new technique in nonparametric inference developed by A. Owen (1988, 2001). Sometimes empirical likelihood has difficulties to define itself. As such a case in point, we discuss the way to define a modified empirical likelihood for the location of symmetry using well-known points of symmetry as a side conditions. The side condition of symmetry is defined through a finite subset of the infinite set of constraints. The modified empirical likelihood under symmetry studied in this paper is to construct a constrained parameter space $\theta+$ of distributions imposing known symmetry as side information. We show that the usual asymptotic theory (Wilks theorem) still hold for the empirical likelihood ratio on the constrained parameter space and the asymptotic distribution of the empirical NPMLE of difference of two symmetric points is obtained.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1137-1146
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• 2010

In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.