• Communications for Statistical Applications and Methods
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• 제19권4호
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• pp.607-617
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• 2012

The goodness-of-fit test for multivariate normal distribution is important because most multivariate statistical methods are based on the assumption of multivariate normality. We propose goodness-of-fit test statistics for multivariate normality based on the modified squared distance. The empirical percentage points of the null distribution of the proposed statistics are presented via numerical simulations. We compare performance of several test statistics through a Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
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• 제4권
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• pp.137-146
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• 1993

The Proposed goodness-of-fit test Statistic $\hat{\lambda}_{\alpha}$ derived from the test Statistc in Kim (1992) is itself a smoothing parameter which is selected to minimize an estimated MISE for a truncated series estimator, $d_{\hat{\lambda}{n}}$, of the comparison density function. Therefore, this test statistic leads immediately to a point estimate of the density function in the event that $H_{0}$ is ejected. The limiting distribution of $\hat{\lambda}_{\alpha}$ was obtained under the null hypothesis. It is also shown that this test is consistent against fixed alternatives.

• Communications for Statistical Applications and Methods
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• 제15권5호
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• pp.709-717
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• 2008

The difference of two one-sided kernel estimators is usually used to detect the location of the discontinuity points of regression function. The large absolute value of the statistic imply discontinuity of regression function, so we may use the difference of two one-sided kernel estimators as the test statistic for testing null hypothesis of a smooth regression function. The problem is, however, we only know the asymptotic distribution of the test statistic under $H_0$ and we hardly expect the good performance of test if we rely solely on the asymptotic distribution for determining the critical points. In this paper, we show that if we adjust the bias of test statistic properly, the asymptotic rules hold for even small sample size situation.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.235-240
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• 2000

In this paper a test of fit for exponentiality and we propose the estimator of Kullback-Leibler Information functions using the data from accelerated life tests. This acceleration model is assumed to be a tampered random variable model. The procedure is applicable when the exponential parameter based on the data from accelerated life tests is or is not specified under null hypothesis. Using Simulations, the power of the proposed test based on use condition of accelerated life test under alternatives is compared with that of other standard tests in the small sample.

• Journal of the Korean Statistical Society
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• 제28권4호
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• pp.469-478
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• 1999

We propose a Kolmogorov-Smirnov-type test for independence of paired failure times in the presence of independent censoring times. This independent censoring mechanism is often assumed in case-control studies. To do this end, we first introduce a process defined as the difference between the bivariate survival function estimator proposed by Wang and Wells (1997) and the product of the product-limit estimators (Kaplan and Meier (1958)) for the marginal survival functions. Then, we derive its asymptotic properties under the null hypothesis of independence. Finally, we assess the performance of the proposed test by simulations, and illustrate the proposed methodology with a dataset for remission times of 21 pairs of leukemia patients taken from Oakes(1982).

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.337-346
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• 2001

In this paper we consider the problem of identifying and testing the outliers in linear regression. first we consider the problem for testing the null hypothesis of no outliers. The test based on the ratio of two scale estimates is proposed. We show the asymptotic distribution of the test statistic by Monte Carlo simulation and investigate its properties. Next we consider the problem of identifying the outliers. A forward sequential procedure based on the suggested test is proposed and shown to perform fairly well. The forward sequential procedure is unaffected by masking and swamping effects because the test statistic is based on robust estimate.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 추계 학술발표회 논문집
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• pp.233-238
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• 2003

Goodness of fit test statistics based on the information discrepancy have been shown to perform very well (Vasicek 1976, Dudewicz and van der Meulen 1981, Chandra et al 1982, Gohkale 1983, Arizona and Ohta 1989, Ebrahimi et al 1992, etc). Although the test is well defined for the non-censored case, censored case has not been discussed in the literature. Therefore we consider a goodness of fit test based on the partial Kullback-Leibler(KL) information with the type II censored data. We derive the partial KL information of the null distribution function and a nonparametric distribution function, and establish a goodness of fit test statistic. We consider the exponential and normal distributions and made Monte Calro simulations to compare the test statistics with some existing tests.

• 응용통계연구
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• 제7권1호
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• pp.35-46
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• 1994

이변량 변화시점 모형에서 위치모수에 대한 비모수적 방법인 순위-모양 검정법을 제시하였다. 이를 경험적인 검정력을 통하여 모수적인 검정과 비교한 결과, 귀무가설분포가 이변량 정규분포일 때를 제외하고는 순위-모양 검정이 월등히 우수함을 알 수 있었다. 또한 변화시점에 대한 점추정량들을 경험적인 평균제곱오차를 이용하여 비교 분석하였다.

• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.673-685
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• 2003

In this paper we consider the problem of identifying and testing outliers in linear regression. First we consider the problem for testing the null hypothesis of no outliers. A test based on the ratio of two residual scale estimates is proposed. We show the asymptotic distribution of the test statistics by Monte Carlo simulation and investigate its properties. Next we consider the problem of identifying the outliers. A forward sequential procedure using the suggested test is proposed and shown to perform fairly well. Unlike other forward procedures, the present one is unaffected by masking and swamping effects because the test statistic is based on robust scale estimate.

• Communications for Statistical Applications and Methods
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• 제16권2호
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• pp.389-396
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• 2009

Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.