• Communications for Statistical Applications and Methods
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• 제10권1호
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• pp.135-144
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• 2003

This work is concerned with comparison of the recently developed disparity measures for the partial association model in three dimensional categorical data. Data are generated by using simulation on each term in the log-linear model equation based on the partial association model, which is a proposed method in this paper. This alternative Monte Carlo methods are explored to study the behavior of disparity measures such as the power divergence statistic I(λ), the Pearson chi-square statistic X$^2$, the likelihood ratio statistic G$^2$, the blended weight chi-square statistic BWCS(λ), the blended weight Hellinger distance statistic BWHD(λ), and the negative exponential disparity statistic NED(λ) for moderate sample sizes. We find that the power divergence statistic I(2/3) and the blended weight Hellinger distance family BWHD(1/9) are the best tests with respect to size and power.

• Journal of the Korean Data and Information Science Society
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• 제24권6호
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• pp.1465-1475
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• 2013

The chi-square type test statistic is the most commonly used test in terms of measuring testing goodness-of-fit for multinomial logistic regression model, which has its grouped data (binomial data) and ungrouped (binary) data classified by a covariate pattern. Chi-square type statistic is not a satisfactory gauge, however, because the ungrouped Pearson chi-square statistic does not adhere well to the chi-square statistic and the ungrouped Pearson chi-square statistic is also not a satisfactory form of measurement in itself. Currently, goodness-of-fit in the ordinal setting is often assessed using the Pearson chi-square statistic and deviance tests. These tests involve creating a contingency table in which rows consist of all possible cross-classifications of the model covariates, and columns consist of the levels of the ordinal response. I examined goodness-of-fit tests for a proportional odds logistic regression model-the most commonly used regression model for an ordinal response variable. Using a simulation study, I investigated the distribution and power properties of this test and compared these with those of three other goodness-of-fit tests. The new test had lower power than the existing tests; however, it was able to detect a greater number of the different types of lack of fit considered in this study. I illustrated the ability of the tests to detect lack of fit using a study of aftercare decisions for psychiatrically hospitalized adolescents.

• Communications for Statistical Applications and Methods
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• 제7권2호
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• pp.403-414
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• 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.

• Geosystem Engineering
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• 제21권5호
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• pp.262-272
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• 2018

The U-statistic method is one of the most important structural methods to separate the anomaly from background. It considers the location of samples and carries out the statistical analysis of the data without judging from a geochemical point of view and tries to separate subpopulations and determine anomalous areas. In the present study, 3D U-statistic method has been applied for the first time through the three-dimensional (3D) modeling of an ore deposit. In order to achieve this purpose, 3D U-statistic is applied on the data (Fe grade) resulted from the drilling network in Baghak mine, central part of the Sangan iron mines (in Khorassan Razavi Province, Iran). Afterward, results from applying 3D U-statistic method are used for 3D modeling of the iron mineralization. Results show that the anomalous values are well separated from background so that the determined samples as anomalous are not dispersed and according to their positioning, denser areas of anomalous samples could be considered as anomaly areas. And also, final results (3D model of iron mineralization) show that output model using this method is compatible with designed model for mining operation. Moreover, seen that U-statistic method in addition for separating anomaly from background, could be very efficient for the 3D modeling of different ore type.

• Journal of the Korean Data and Information Science Society
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• 제17권2호
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• pp.543-557
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• 2006

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.

• Communications for Statistical Applications and Methods
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• 제16권4호
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• pp.697-705
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• 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.

• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.951-963
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• 2003

In this paper, we propose goodness of fit test statistics based on the estimated Kullback-Leibler information functions using the data from three step stress accelerated life test. This acceleration model is assumed to be a tampered random variable model. The power of the proposed test under various alternatives is compared with Kolmogorov-Smirnov statistic, Cramer-von Mises statistic and Anderson-Darling statistic.

• Communications for Statistical Applications and Methods
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• 제21권4호
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• pp.297-307
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• 2014

We derive a test statistic for the general linear test in the ridge regression model. The exact distribution for the test statistic is too difficult to derive; therefore, we suggest an approximate reference distribution. We use numerical studies to verify that the suggested distribution for the test statistic is appropriate. A asymptotic result for the test statistic also is considered.

• Journal of the Korean Data and Information Science Society
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• 제12권1호
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• pp.103-125
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• 2001

The Box-Cox transformation is a well known family of power transformation that brings a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. This paper proposes a new method for estimating the Box-Cox transformation using maximization of the Sample Entropy statistic which forces the data to get closer to normal as much as possible. A comparative study of the proposed procedure with the maximum likelihood procedure, the procedure via artificial regression estimation, and the recently introduced maximization of the Shapiro-Francia W' statistic procedure is given. In addition, we generate a table for the optimal spacings parameter in computing the Sample Entropy statistic.

• 한국산림과학회지
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• 제79권3호
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• pp.260-268
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• 1990

수확(收穫) 예측(豫測) model이 multicollinearity 문제점(問題點) 가질때 보다 정확한 추정식(推定式)을 얻기 위하여 두 종류의 ridge estimator와 최소(最小) 자승법(自乘法)(OLS)의 추정치를 비교(比較)하였다. 본 연구(硏究)에서 사용(使用)된 ridge estmator는 Mallows's (1973)Cp-like statistic과 Allens's (1974) PRESS-like statistic 이었다. 위의 세가지 estimator 예측(豫測) 능력(能力) 평가(評賣)는 Matney 등(等)(1988)에 의하여 개발(開發)된 수확(收穫) model을 이용(利用)하여 비교(比較)하였다. 사용되어진 자료(資料)는 미국(美國) 남부(南部) 테에다 소나무 시험림(試驗林)의 총(總)522개(個) plot을 이용(利用)하였다. 두 개(個)의 ridge estimator가 최소(最小) 자승법(自乘法)에 의한 추정치 보다 수확(收穫) 예측(豫測) 능력(能力)이 우수(優秀)하였으며, 특히 Mallows's statistic에 의한 ridge estimator가 가장 우수(優秀)하였다. 따라서 ridge estimator는 수확(收穫) 예측(豫測) model의 독립(獨立) 변수(變數) 간(間)에 multicollinearity 문제점(問題點)이 있을 때 최소(最小) 자승법(自乘法)에 의 한 추정치를 대치(代置)할 수 있는 estimator로서 추천(推薦)할 수 있었다.