• The Korean Journal of Applied Statistics
• /
• v.32 no.4
• /
• pp.607-618
• /
• 2019

A new and interesting task in statistics is to effectively analyze functional data that frequently comes from advances in modern science and technology in areas such as meteorology and biomedical sciences. Functional linear regression with scalar response is a popular functional data analysis technique and it is often a common problem to determine a functional association if a functional predictor variable affects the scalar response in the models. Recently, Kong et al. (Journal of Nonparametric Statistics, 28, 813-838, 2016) established classical testing methods for this based on functional principal component analysis (of the functional predictor), that is, the resulting eigenfunctions (as a basis). However, the eigenbasis functions are not generally suitable for regression purpose because they are only concerned with the variability of the functional predictor, not the functional association of interest in testing problems. Additionally, eigenfunctions are to be estimated from data so that estimation errors might be involved in the performance of testing procedures. To circumvent these issues, we propose a testing method based on fixed basis such as B-splines and show that it works well via simulations. It is also illustrated via simulated and real data examples that the proposed testing method provides more effective and intuitive results due to the localization properties of B-splines.

• The Korean Journal of Applied Statistics
• /
• v.24 no.2
• /
• pp.383-391
• /
• 2011

This paper presents a modified entropy-based test of fit for the inverse Gaussian distribution. The test is based on the entropy difference of the unknown data-generating distribution and the inverse Gaussian distribution. The entropy difference estimator used as the test statistic is obtained by employing Vasicek's sample entropy as an entropy estimator for the data-generating distribution and the uniformly minimum variance unbiased estimator as an entropy estimator for the inverse Gaussian distribution. The critical values of the test statistic empirically determined are provided in a tabular form. Monte Carlo simulations are performed to compare the proposed test with the previous entropy-based test in terms of power.

• Journal of Korean Elementary Science Education
• /
• v.42 no.1
• /
• pp.93-108
• /
• 2023

This study aims to analyze the types and roles of visualization materials presented in the third- and fourth-grade national and authorized science textbooks based on the 2015 revised curriculum. Using the type and role framework, 17 chapters were analyzed. The analysis revealed, first, that the national and authorized textbooks had different total amounts of visualization data and total amounts of simple illustrations. However, no difference in the amounts of simple illustrations and infographics used in the units was evident. The units that used the most infographics were Life, Earth and Universe, in that order, in both the national and the authorized textbooks. Second, simple illustrations were observed to have role differences according to the type of visualization data, but infographics had no such differences. Specifically, the motivational role in a simple illustration increased in all the authorized textbooks. Third, looking at the frequencies of the infographic subtypes, the Process, Structure, Comparative Analysis, and Timeline types accounted for 86% of the total, but the proportions of those subtypes varied in the national and authorized textbooks. Based on the results of this study, I suggest that to achieve differentiation in the types or roles of visualization materials, changes in the types, processes, and skills of inquiry must first occur, as must changes in the structure of chapters or lessons. Continuous research and discussion on the standards and methods for authorized textbooks are also needed.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2015.05a
• /
• pp.143-143
• /
• 2015

기존의 빈도해석에서는 자료의 정상성을 가정하며, 이에 따라 적정모형 선정 시에 $x^2$ 검정이나 PPCC(Probability Plot Correlation Coefficient)검정과 같은 적합도 검정방법을 사용한다. 하지만 자료에서 경향성이 나타나거나 평균, 분산, 매개변수 등이 시간에 따라 변하는 등의 비정상성 현상들이 관측됨에 따라 비정상성 빈도해석에 관한 연구들이 활발히 진행되고 있다. 비정상성 빈도해석에서는 시간항과 같은 공변량이 포함된 매개변수를 가지는 비정상성 모형을 적용하게 되는데, 시간에 따라 매개변수가 계속 변하므로 매개변수에 따라 검정통계량이 고정되어 있는 기존의 적합도 검정방법의 적용이 어렵다. 따라서 비정상성 빈도해석의 적정 모형 선정에 적용할 수 있는 방법으로 최우도 함수에 기반한 모형 평가 방법인 AIC와 BIC가 추천되고 있으며 자료길이가 충분하지 않은 경우에는 AIC 대신하여 AICc의 사용이 추천되고 있다. 본 연구에서는 극치사상을 나타내는데 적합한 분포형인 GEV분포형의 위치, 규모 매개변수를 시간항으로 나타낸 다양한 비정상성 GEV모형에 대하여 Monte-Carlo 모의실험을 통해 AICc와 BIC의 적용성을 검토하였으며, 비정상성이 관측되는 실측 자료에 적용해보았다.

• Proceedings of the Korean Statistical Society Conference
• /
• 2003.10a
• /
• pp.91-95
• /
• 2003

본 논문에서는 정보 전달 능력이 향상된 변형된 축차확률비검정을 소개한다. 새로운 검정은기존의 검정과 수학적인 면에서 공동된 점들을 갖고 있으나, 이상치의 영향을 덜 받고 더욱이 그 존재에 대하여 시각적으로 보여주며, 또한 자료의 변화에 보다 민감하게 반응하는 특성이 있다. 새롭게 제안된 로버스트 축차확률비검정 시스템을 Microsoft사의 Visual Basic 6.0 언어로 구현하여 본 연구에서 제안한 모델과 기존의 검정모델을 비교한 결과 제안된 검정 모델의 우수성과 실용가능성을 실증적으로 확인하였다.

• Journal of the Korean Data and Information Science Society
• /
• v.24 no.4
• /
• pp.815-824
• /
• 2013

Traditional Pearson chi-squared test is not appropriate for the data collected by the complex sample design. When one uses the traditional Pearson chi-squared test to the complex sample categorical data, it may give wrong test results, and the error may occur not only due to the biased variance estimators but also due to the biased point estimators of cell proportions. In this study, the design based consistent Wald test statistics was derived for k-population homogeneity test, and the traditional Pearson chi-squared test statistics was partitioned into three parts according to the causes of error; the error due to the bias of variance estimator, the error due to the bias of cell proportion estimator, and the unseparated error due to the both bias of variance estimator and bias of cell proportion estimator. An analysis was conducted for empirical results of the relative size of each error component to the Pearson chi-squared test statistics. The second year data from the fourth Korean national health and nutrition examination survey (KNHANES, IV-2) was used for the analysis. The empirical results show that the relative size of error from the bias of variance estimator was relatively larger than the size of error from the bias of cell proportion estimator, but its degrees were different variable by variable.

• The Korean Journal of Applied Statistics
• /
• v.11 no.1
• /
• pp.113-127
• /
• 1998

There have been a great deal of interests in comparing two survival distributins in clinical trials. This paper compares some well-known statistical methods for testing the equality of two survival distributions. Simulation studies also provide some insights into the properties of these test statistics across several types of survival distributions and degrees of censorship.

• The Korean Journal of Applied Statistics
• /
• v.21 no.2
• /
• pp.265-273
• /
• 2008

Kim (2001a) presented a modification of the Shapiro and Wilk (1972) test for exponentiality based on the ratio of two asymptotically efficient estimates of scale. In this paper we modify this test statistic when the sample is censored. We use the normalized spacings based on the sample data, which was used in Samanta and Schwarz (1988) to modify the Shapiro and Wilk (1972) statistic to the censored data. As a result the modified statistics have the same null distribution as the uncensored case with a corresponding reduction in sample size. Through a simulation study it is found that the proposed statistic has higher power than Samanta and Schwarz (1988) statistic especially for the alternatives with the coefficient of variation greater than or equal to 1.

• Journal of Korea Water Resources Association
• /
• v.42 no.10
• /
• pp.773-783
• /
• 2009

The effects of rainfall input uncertainty on predictions of stream flow are studied based extended GLUE (Generalized Likelihood Uncertainty Estimation) approach. The uncertainty in the rainfall data is implemented by systematic/non-systematic rainfall measurement analysis in Weida catchment, Germany. PDM (Probability Distribution Model) rainfall runoff model is selected for hydrological representation of the catchment. Using general correction procedure and DUE(Data Uncertainty Engine), feasible rainfall time series are generated. These series are applied to PDM in MC(Monte Carlo) and GLUE method; Posterior distributions of the model parameters are examined and behavioural model parameters are selected for simplified GLUE prediction of stream flow. All predictions are combined to develop ensemble prediction and 90 percentile of ensemble prediction, which are used to show the effects of uncertainty sources of input data and model parameters. The results show acceptable performances in all flow regime, except underestimation of the peak flows. These results are not definite proof of the effects of rainfall uncertainty on parameter estimation; however, extended GLUE approach in this study is a potential method which can include major uncertainty in the rainfall-runoff modelling.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2012.05a
• /
• pp.347-351
• /
• 2012

본 연구는 기후변화로 인한 국내 낙동강 유역의 기온, 강수, 상대습도의 변동 경향을 파악하고자, 낙동강 본류의 상, 중, 하류 지역을 연구대상 지역으로 선정하여 분석을 실시하였다. 이를 위하여 기상요소인 평균, 최저, 최고 기온과 상대습도 및 강우 자료를 기상청의 관측 자료를 활용하여 수집하였다. 분석을 실시함에 있어서 연평균, 최고, 최저 기온과 연평균, 최고, 최저 상대습도를 분석하였으며, 강우량 관측 자료를 통해 총 강우량, 강우집중률, 일 최대강우량을 고려하였다. 분석방법은 기후변화로 인한 기상자료의 변동 경향을 파악하기 위하여 비모수적 경향성 검정인 Mann-Kendall Test, Hotelling-Pabst Test, Sen's Test 3가지의 검정방법을 사용하였으며, 표준정규변량의 크기를 통하여 변동 경향의 유의성을 비교해보았다. 또한, 각 요소별 관측 자료의 상위 10개, 하위 10개의 자료를 통하여 최근(1995~2011)과 과거(1973~1994)의 기상요소들을 비교하여 변동 특성을 파악하였다. 연구지역 중 낙동강 중류 지점에 위치하는 구미의 경우, 요소별 자료 중 연평균기온의 상위 9개의 자료가 최근 17년 이내에 포함되어 있으며, 연 최저 및 최고 기온의 6개의 자료가 포함되어 있어 기후온난화가 진행되고 있음을 확인하였다. 연 최저 상대습도의 경우 3가지 경향성 검정 방법을 통하여 과거자료에 비해 하강하는 추세를 보이고 있다. 강우자료 분석 결과 관측이 시작된 이래 연강수량 중 상위 10개의 자료에서 7개가 최근에 발생한 것으로 분석되었고, 일 최대강우량은 9개가 포함되어 있다. 위의 요소별 분석 결과 낙동강 유역의 연강수량 및 강우강도는 대체적으로 증가하고, 기온 또한 증가하는 등 기후 변화로 인한 지구온난화현상이 국내에서도 나타나는 것을 확인 할 수 있었다.