• Journal of the Korean Data and Information Science Society
• /
• v.20 no.3
• /
• pp.587-592
• /
• 2009

The most frequent use of the chi-square distribution is in the area of goodness-of-t of a distribution. The likelihood ratio test is a commonly used test statistic as the maximum likelihood estimate in statistical inferences. The recently revised versions of the likelihood ratio test statistics are used in estimating the parameter in the chi-square distribution. The estimates are compared with the commonly used method of moments and the maximum likelihood estimate.

• Journal of the Korean Data and Information Science Society
• /
• v.17 no.2
• /
• pp.543-557
• /
• 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
• /
• v.13 no.2
• /
• pp.429-440
• /
• 2006

In statistical computing, it is often for researchers to need the distribution of a weighted sum of noncentral chi-square variables. In this case, it is very limited to know its exact distribution. There are many works to contribute to this topic, e.g. Imhof (1961) and Solomon-Stephens (1977). Imhof's method gives good approximation to the true distribution, but it is not easy to apply even though we consider the development of computer technology Solomon-Stephens's three moment chi-square approximation is relatively easy and accurate to apply. However, they skipped many details, and their simulation is limited to a weighed sum of central chi-square random variables. This paper gives details on Solomon-Stephens's method. We also extend their simulation to the weighted sum of non-central chi-square distribution. We evaluated approximated powers for homogeneous test and compared them with the true powers. Solomon-Stephens's method shows very good approximation for the case.

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

• Communications for Statistical Applications and Methods
• /
• v.7 no.2
• /
• pp.385-392
• /
• 2000

Many tests for multivariate normality are based on the spherical coordinates of the scaled residuals of multivariate observations. Moore and Stubblebine's (1981) Pearson chi-square test is based on the radii of the scaled residuals, or equivalently the sample Mahalanobis distances of the observations from the sample mean vector. The chi-square statistic does not have a limiting chi-square distribution since the unknown parameters are estimated from ungrouped data. We will derive a simple closed form of the Rao-Robson chi-square test statistic and provide a self-contained proof that it has a limiting chi-square distribution. We then provide an illustrative example of application to a real data with a simulation study to show the accuracy in finite sample of the limiting distribution.

• Communications for Statistical Applications and Methods
• /
• v.2 no.2
• /
• pp.330-335
• /
• 1995

The rebustness of one sample Chi-square test for multivariate normal mean vector is investigated when the multivariate normal population is mixed with another multivariate normal population with differing in the mean vector. Explicit expressions for the level of significance and power of the test are derived. Some numerical results indicate that the Chi-square test procedure is quite robust against slight mixtures of multivariate normal populations differing in location parameters.

• Communications for Statistical Applications and Methods
• /
• v.1 no.1
• /
• pp.81-86
• /
• 1994

A Chi-square approximation to the distribution of product of independent Beta variates denoted by U is developed. The distribution is commonly used as a test criterion for the general linear hypothesis about the multivariate linear models. The approximation is obtained by fitting a logarithmic function of U to a Chi-square variate in terms of the first three moments. It is compared with the well known approximations due to Box(1949), Rao(1948), and Mudholkar and Trivedi(1980). It is found that the Chi-square approximation compares favorably with the other three approximations.

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

• 한국데이터정보과학회:학술대회논문집
• /
• 2004.04a
• /
• pp.25-38
• /
• 2004

Association rule mining searches for interesting relationships among items in a given database. Association rules are frequently used by retail stores to assist in marketing, advertising, floor placement, and inventory control. There are three primary quality measures for association rule, support and confidence and lift. In this paper we present the relation between the measure of association based on chi square statistic and the criteria of association rule for nominal database and propose the objective criteria for association.

• The Korean Journal of Applied Statistics
• /
• v.35 no.4
• /
• pp.469-484
• /
• 2022

Since a large text corpus contains hundred-thousand unique words, text data is one of the typical large-dimensional data. Therefore, various feature selection methods have been proposed for dimension reduction. Feature selection methods can improve the prediction accuracy. In addition, with reduced data size, computational efficiency also can be achieved. The chi-square statistic and the information gain are two of the most popular measures for identifying interesting terms from text data. In this paper, we investigate the theoretical properties of the chi-square statistic and the information gain. We show that the two filtering metrics share theoretical properties such as non-negativity and convexity. However, they are different from each other in the sense that the information gain is prone to select more negative features than the chi-square statistic in imbalanced text data.