• Journal of the Korean Statistical Society
• /
• v.9 no.2
• /
• pp.181-193
• /
• 1980

A class of nonparametric estimators of the ratio of scale parameters is proposed. The estimators are based on the distribution-free rank-like test suggested by Fligner and Killeen (1976). An explicit form of the estimator is the median of the ratios of absolute deviations from the combined sample median. A small-sample Monte Carlo study shows that the proposed estimator is more efficient than the Bhattacharyya (1977) estimator. The proposed estimator is is reasonably insensitive to small failures in the assumption of equal medians. A modified estimator is also considered when the meidans are unequal.

• Communications for Statistical Applications and Methods
• /
• v.22 no.3
• /
• pp.223-232
• /
• 2015

The area under the ROC curve (AUC), the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) are defined and interpreted with probability that measures the discriminant power of classification models. AUC, VUS and HUM are expressed with the summation and integration notations for discrete and continuous random variables, respectively. AUC for discrete two random samples is represented as the nonparametric Mann-Whitney statistic. In this work, we define conditional Mann-Whitney statistics to compare more than two discrete random samples as well as propose that VUS and HUM are represented as functions of the conditional Mann-Whitney statistics. Three and four discrete random samples with some tie values are generated. Values of VUS and HUM are obtained using the proposed statistic. The values of VUS and HUM are identical with those obtained by definition; therefore, both VUS and HUM could be represented with conditional Mann-Whitney statistics proposed in this paper.

• Communications for Statistical Applications and Methods
• /
• v.9 no.1
• /
• pp.13-19
• /
• 2002

In nonparametric entropy estimation, both mass and mean-preserving maximum entropy distribution (Theil, 1980) and the underlying distribution of the sample entropy (Vasicek, 1976), the most widely used entropy estimator, consist of nb mass-preserving densities based on disjoint Intervals of the simple averages of two adjacent order statistics. In this paper, we notice that those nonparametric density functions do not actually keep the mass-preserving constraint, and propose a modified sample entropy by considering the generalized 0-statistics (Kaigh and Driscoll, 1987) in averaging two adjacent order statistics. We consider the proposed estimator in a goodness of fit test for normality and compare its performance with that of the sample entropy.

• The Korean Journal of Applied Statistics
• /
• v.31 no.5
• /
• pp.599-610
• /
• 2018

The method of Mack and Skillings (Technometrics, 23, 171-177, 1981) is a nonparametric multiple comparison method in a randomized block design with replications. This method is likely to result in loss of information because each block is ranked using the average of observations instead of repeated observations. In this paper, we proposed a new nonparametric multiple comparison method in the randomized block model with replications using an alignment method proposed by Hodges and Lehmann (The Annals of Mathematical Statistics, 33, 482-497, 1962) that extend the joint placement method proposed by Chung and Kim (Communications for Statistical Applications and Methods, 14, 551-560, 2007). In addition, Monte Carlo simulation compared the family wise error rate and power with the parametric method and the nonparametric method.

• Proceedings of the Korean Statistical Society Conference
• /
• 2002.05a
• /
• pp.1-5
• /
• 2002

We consider the problem of optimal bandwidth choice for nonparametric classification, based on kernel density estimators, where the problem of interest is distinguishing between two univariate distributions. When the densities intersect at a single point, optimal bandwidth choice depends on curvatures of the densities at that point. The problem of empirical bandwidth selection and classifying data in the tails of a distribution are also addressed.

• Journal of the Korean Data and Information Science Society
• /
• v.19 no.2
• /
• pp.421-429
• /
• 2008

We consider a general semiparametric additive risk model that consists of three components. They are parametric, purely and smoothly nonparametric components. In parametric component, time dependent term is known up to proportional constant. In purely nonparametric component, time dependent term is an unknown function, and time dependent term in smoothly nonparametric component is an unknown but smoothly function. As an estimation method of this model, we use the weighted least square estimation by Huffer and McKeague (1991). We provide an illustrative example as well as a simulation study that compares the performance of our method with the ordinary least square method.

• Journal of the Korean Data and Information Science Society
• /
• v.9 no.2
• /
• pp.357-363
• /
• 1998

In this paper we propose a nonparametric lack of fit test based on the bootstrap method for testing the null parametric linear model by using linear smoothers. Most of existing nonparametric test statistics are based on the residuals. Our test is based on the centered bootstrap residuals. Power performance of proposed bootstrap lack of fit test is investigated via Monte carlo simulation.

• Journal of the Korean Statistical Society
• /
• v.30 no.2
• /
• pp.265-280
• /
• 2001

Estimation of the edge of a distribution has many important applications. It is related to classification, cluster analysis, neural network, and statistical image recovering. The problem also arises in measuring production efficiency in economic systems. Three most promising nonparametric estimators in the existing literature are introduced. Their statistical properties are provided, some of which are new. Themes of future study are also discussed.

• Journal of the Korean Statistical Society
• /
• v.26 no.1
• /
• pp.89-100
• /
• 1997

In this paper we are concerned with comparing ordered treatment effects with a control in a randomized block design with multiple observations per cell. Two nonparametric procedures for detecting which treatment are better than the control are proposed and compared. An example is given and the results of a Monte Carlo power study are discussed.

• Communications for Statistical Applications and Methods
• /
• v.4 no.2
• /
• pp.453-463
• /
• 1997

Nonparametric kernel regression has recently gained widespread acceptance as an attractive method for the nonparametric estimation of the mean function from noisy regression data. Also, the practical implementation of kernel method is enhanced by the availability of reliable rule for automatic selection of the bandwidth. In this article, we propose a method for automatic selection of the bandwidth that minimizes the asymptotic mean square error. Then, the estimated bandwidth by the proposed method is compared with the theoretical optimal bandwidth and a bandwidth by plug-in method. Simulation study is performed and shows satisfactory behavior of the proposed method.