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

• Communications for Statistical Applications and Methods
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• v.19 no.6
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• pp.781-791
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• 2012

A $2{\times}2$ Cross-over design is widely used in clinical trials for comparison studies of two kinds of drugs or medical treatments. This design has many statistical methods such as Hills-Armitage's (1979) method or Koch's (1972) method. In this paper, we propose a nonparametric test for $2{\times}2$ Cross-over design based on a two-sample test suggested by Baumgartner et al. (1998). In addition, a Monte Carlo simulation study is adapted to compare the power of the proposed methods with those of previous methods.

• Journal of the Korean Statistical Society
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• v.18 no.1
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• pp.46-61
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• 1989

This paper is concerned with the development of a nonparametric procedure for the statistical inference about the nonlinear regression parameters. A confidence region and a hypothesis testing procedure based on a class of signed linear rank statistics are proposed and the asymptotic distributions of the test statistic both under the null hypothesis and under a sequence of local alternatives are investigated. Some desirable asymptotic properties including the asymptotic relative efficiency are discussed for various score functions.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.177-183
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• 1997

A data-adaptive order selection procedure is proposed for local polynomial nonparametric regression. For each given polynomial order, bias and variance are estimated and the adaptive polynomial order that has the smallest estimated mean squared error is selected locally at each location point. To estimate mean squared error, empirical bias estimate of Ruppert (1995) and local polynomial variance estimate of Ruppert, Wand, Wand, Holst and Hossjer (1995) are used. Since the proposed method does not require fitting polynomial model of order higher than the model order, it is simpler than the order selection method proposed by Fan and Gijbels (1995b).

• Communications for Statistical Applications and Methods
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• v.14 no.3
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• pp.551-560
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• 2007

Kruskal and Wallis (1952) proposed typical nonparametric method in one-way layout problem. A special feature of this procedure is use of rank in mixed samples. In this paper, the new procedure based on placement as extension of the two sample placement tests described in Orban and Wolfe (1982) was proposed. Some critical values in small sample cases and comparative results of a Monte Carlo power study are presented.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.30 no.1
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• pp.87-94
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• 2017

Reliability analysis(RA) and Reliability-based design optimization(RBDO) require statistical modeling of input random variables, which is parametrically or nonparametrically determined based on experimental data. For the parametric method, goodness-of-fit (GOF) test and model selection method are widely used, and a sequential statistical modeling method combining the merits of the two methods has been recently proposed. Kernel density estimation(KDE) is often used as a nonparametric method, and it well describes a distribution function when the number of data is small or a density function has multimodal distribution. Although accurate statistical models are needed to obtain accurate RA and RBDO results, accurate statistical modeling is difficult when the number of data is small. In this study, the accuracy of two statistical modeling methods, SSM and KDE, were compared according to the number of data. Through numerical examples, the RA results using the input models modeled by two methods were compared, and appropriate modeling method was proposed according to the number of data.

• Journal of Periodontal and Implant Science
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• v.44 no.6
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• pp.288-292
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• 2014

Purpose: The purposes of this study were to assess the trend of use of statistical methods including parametric and nonparametric methods and to evaluate the use of complex statistical methodology in recent periodontal studies. Methods: This study analyzed 123 articles published in the Journal of Periodontal & Implant Science (JPIS) between 2010 and 2014. Frequencies and percentages were calculated according to the number of statistical methods used, the type of statistical method applied, and the type of statistical software used. Results: Most of the published articles considered (64.4%) used statistical methods. Since 2011, the percentage of JPIS articles using statistics has increased. On the basis of multiple counting, we found that the percentage of studies in JPIS using parametric methods was 61.1%. Further, complex statistical methods were applied in only 6 of the published studies (5.0%), and nonparametric statistical methods were applied in 77 of the published studies (38.9% of a total of 198 studies considered). Conclusions: We found an increasing trend towards the application of statistical methods and nonparametric methods in recent periodontal studies and thus, concluded that increased use of complex statistical methodology might be preferred by the researchers in the fields of study covered by JPIS.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.193-211
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• 2012

This paper deals with robust nonparametric regression analysis when the regressors are functional random fields. More precisely, we consider $Z_i=(X_i,Y_i)$, $i{\in}\mathbb{N}^N$ be a $\mathcal{F}{\times}\mathbb{R}$-valued measurable strictly stationary spatial process, where $\mathcal{F}$ is a semi-metric space and we study the spatial interaction of $X_i$ and $Y_i$ via the robust estimation for the regression function. We propose a family of robust nonparametric estimators for regression function based on the kernel method. The main result of this work is the establishment of the asymptotic normality of these estimators, under some general mixing and small ball probability conditions.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.463-473
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• 2015

We consider a nonparametric AR(1) model with nonparametric ARCH(1) errors. In order to estimate the unknown function of the ARCH part, we apply the stationary bootstrap procedure, which is characterized by geometrically distributed random length of bootstrap blocks and has the advantage of capturing the dependence structure of the original data. The proposed method is composed of four steps: the first step estimates the AR part by a typical kernel smoothing to calculate AR residuals, the second step estimates the ARCH part via the Nadaraya-Watson kernel from the AR residuals to compute ARCH residuals, the third step applies the stationary bootstrap procedure to the ARCH residuals, and the fourth step defines the stationary bootstrapped Nadaraya-Watson estimator for the ARCH function with the stationary bootstrapped residuals. We prove the asymptotic validity of the stationary bootstrap estimator for the unknown ARCH function by showing the same limiting distribution as the Nadaraya-Watson estimator in the second step.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.899-908
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• 2008

If the regression function has jump points, nonparametric estimation method based on local smoothing is not statistically consistent. Therefore, when we estimate regression function, it is quite important to know whether it is reasonable to assume that regression function is continuous. If the regression function appears to have jump points, then we should estimate first the location of jump points. In this paper, we propose a procedure which can do both the testing hypothesis of discontinuity of regression function and the estimation of the number and the location of jump points simultaneously. The performance of the proposed method is evaluated through a simulation study. We also apply the procedure to real data sets as examples.