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A Simple Chi-squared Test of Multivariate Normality Based on the Spherical Data
Park, Cheolyong The Korean Statistical Society 2001 Communications for statistical applications and me Vol.8 No.1
We provide a simple chi-squared test of multivariate normality based on rectangular cells on the spherical data. This test is simple since it is a direct extension of the univariate chi-squared test to multivariate case and the expected cell counts are easily computed. We derive the limiting distribution of the chi-squared statistic via the conditional limit theorems. We study the accuracy in finite samples of the limiting distribution and then compare the poser of our test with those of other popular tests in an application to a real data.
A Note on the Chi-Square Test for Multivariate Normality Based on the Sample Mahalanobis Distances
Park, Cheolyong The Korean Statistical Society 1999 Journal of the Korean Statistical Society Vol.28 No.4
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.
The Chi-squared Test of Independence for a Multi-way Contingency Table wish All Margins Fixed
Park, Cheolyong The Korean Statistical Society 1998 Journal of the Korean Statistical Society Vol.27 No.2
To test the hypothesis of complete or total independence for a multi-way contingency table, the Pearson chi-squared test statistic is usually employed under Poisson or multinomial models. It is well known that, under the hypothesis, this statistic follows an asymptotic chi-squared distribution. We consider the case where all marginal sums of the contingency table are fixed. Using conditional limit theorems, we show that the chi-squared test statistic has the same limiting distribution for this case.
Dickey-Fuller Test for an Extended MA Model
Cheolyong Park,Jeongcheol Ha,Tae Yoon Kim,Sun-Young Hwang,Heesoo Lee 계명대학교 자연과학연구소 2019 Quantitative Bio-Science Vol.38 No.1
The AR(1) model Xt=ρXt-1+ϵt with iid error ϵt has been used extensively for the inference of the stochastic process Xt where its key parameter ρ plays an essential role. In particular, the Dickey-Fuller test (DF test) has been extensively used for testing random walk model (or ρ=1) in the literatures. However, it is well known that the DF test is subject to serious size distortion when errors are correlated. This study proposes the use of an extended MA(∞) model Xt=∑<SUP>∞</SUP>(i=0) bi ϵt-i for a more precise inference of Xt by the DF test. We develop and investigate a new persistency parameter b∞=limj→∞ bj from the extended MA(∞) model. It is shown that the DF test serves well for testing the MA(∞) model with the new persistency parameter b∞. Our approach critically addresses the size distortion issues in the literatures.
A Rao-Robson Chi-Square Test for Multivariate Normality Based on the Mahalanobis Distances
Park, Cheolyong The Korean Statistical Society 2000 Communications for statistical applications and me Vol.7 No.2
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.
Time Series Model Identification in the Frame of Random Walk Model
Cheolyong Park,Seul Gee Kim,JinCheol Park,Jeongcheol Ha,Tae Yoon Kim 계명대학교 자연과학연구소 2018 Quantitative Bio-Science Vol.37 No.1
In principle, any stochastic process can be expressed in the frame of the random walk model (RWM) because it equals to the sum of its regular increments (or errors), with its initial value equal to 0. Using this intrinsic versatility of the RWM, we herein demonstrate that the RWM can serve as a useful frame for identifying the underlying time series models. This is done by reparametrization of the RWM based on the “linear dependency of error”. Our approach is applied to various time series models (e.g., stationary processes, trend stationary process (TSP), mixture model, asymmetric difference, fractional Brownian motion and symmetric α-stable self-similar stationary increment process). As an empirical application of our approach, we discuss the well-known RWM vs. TSP controversy over macroeconomic time series.
A Simple Estimator of Error Correlation in Non-parametric Regression Models
PARK, BYEONG U.,LEE, YOUNG KYUNG,KIM, TAE YOON,PARK, CHEOLYONG Almqvist & Wiksell Periodical Co 2006 Scandinavian journal of statistics, theory and app Vol.33 No.3
<P>Abstract. </P><P>It is well known that major strength of non-parametric regression function estimation breaks down when correlated errors exist in the data. Positively (negatively) correlated errors tend to produce undersmoothing (oversmoothing). Several remedies have been proposed in the context of bandwidth selection problem, but they are hard to implement without prior knowledge of error correlations. In this paper we propose a simple estimator of error correlation which is ready to implement and reports a reasonably good performance.</P>
스포츠 경쟁력 지수로서 페이지랭크 기반 방법론 사용에 대한 소고
박철용(Cheolyong Park) 한국데이터정보과학회 2021 한국데이터정보과학회지 Vol.32 No.6
최근에 스포츠 경쟁력을 객관적으로 판단하는 방법으로 페이지랭크 (PageRank) 방법이 사용되기 시작하였다. 원래 페이지랭크가 웹사이트의 연결 네트워크 정보를 이용하여 특정 웹사이트의 중요도를 평가하는 것에 착안하여, 특정 운동 경기의 승패 관계를 연결 네트워크로 파악하여 페이지랭크를 해당 운동 경기의 경쟁력 지수로 사용하고자 하는 시도이다. 페이지랭크는 경쟁력이 높은 상대에게 얻은 승리를 경쟁력이 낮은 상대에게 얻은 승리보다 더 높이 평가하는 구조이기 때문에 단순 승패만 따지는 방법보다 경쟁력을 판단하기 더 합리적인 방법으로 여겨진 것이다. 페이지랭크는 연결여부만 고려하기 때문에 가중페이지랭크 (weighted PageRank)로 발전하였고, 학술지 평가에서는 SJR (Scimago Journal Rank)와 아이겐팩터 (Eigenfactor)로 발전하게 되었다. 이 논문에서는 이 방법에서 사용된 공식을 중심으로 각 항목들이 스포츠 경쟁력 관점에서 어떤 의미를 가지는지 살펴본다. 마지막으로 2018년 중학교와 고등학교의 배드민턴 단체 경기 자료에 이 방법들을 적용하고 그 결과를 비교한다. Recently PageRank has started being used as an objective method of measuring a sports competency. This is based on the observation that PageRank measures a website’s importance in a network of websites’ connection and thus can be applied to sports by considering win-loss results of the sports as a network. PageRank can be considered a more reasonable method than simple win-loss counts because PageRank gives more weights to a win over higher rankers than to lower rankers. Since PageRank just considers whether two websites are connected or not, it is evolved into weighted PageRank, and further into SJR (Scimago Journal Rank) and Eigenfactor as journal citation indices. In this article, we will review the formulas of these methods to understand the meaning of each term from the perspective of a sports competency index. Finally we will apply these methods to badminton team match data of middle and high schools in 2018 and then compare the results.