• The Korean Journal of Applied Statistics
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• v.30 no.2
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• pp.259-269
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• 2017

Due to the nonnegativity of variance, most of nonparametric estimations of discontinuous variance function have used the Nadaraya-Watson estimation with residuals. By the modification of Chen et al. (2009) and Yu and Jones (2004), Huh (2014, 2016a) proposed the estimators of the log-variance function instead of the variance function using the local linear estimator which has no boundary effect. Huh (2016b) estimated the variance function using the adjusted squared residuals by the estimated jump size in the discontinuous variance function. In this paper, we propose an estimator of the discontinuous log-variance function using the local linear estimator with the adjusted log-squared residuals by the estimated jump size of log-variance function like Huh (2016b). The numerical work demonstrates the performance of the proposed method with simulated and real examples.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.27-40
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• 2001

The purpose of this study is to test a multiple change point in the regression model with the passage of time, using the estimated residual variance figure suggested by Gasser, Sroka and Jennen - Steinmez (GSJS). As a result of the simulation, it is showed that there is a jump change of the estimated residual variance figure at that time of change point. The way to analyse a intuitive multiple change point through graphics is more effective and accurate than any other existing ways.

• Journal of the Korean Data and Information Science Society
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• v.27 no.1
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• pp.111-120
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• 2016

In usual, the discontinuous variance function was estimated nonparametrically using a kernel type estimator with data sets split by an estimated location of the change point. Kang et al. (2000) proposed the Gasser-$M{\ddot{u}}ller$ type kernel estimator of the discontinuous regression function using the adjusted observations of response variable by the estimated jump size of the change point in $M{\ddot{u}}ller$ (1992). The adjusted observations might be a random sample coming from a continuous regression function. In this paper, we estimate the variance function using the Nadaraya-Watson kernel type estimator using the adjusted squared residuals by the estimated location of the change point in the discontinuous variance function like Kang et al. (2000) did. The rate of convergence of integrated squared error of the proposed variance estimator is derived and numerical work demonstrates the improved performance of the method over the exist one with simulated examples.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.87-95
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• 2014

In the regression model, Kang and Huh (2006) studied the estimation of the discontinuous variance function using the Nadaraya-Watson estimator with the squared residuals. The local linear estimator of the log-variance function, which may have the whole real number, was proposed by Huh (2013) based on the kernel weighted local-likelihood of the ${\chi}^2$-distribution. Chen et al. (2009) estimated the continuous variance function using the local linear fit with the log-squared residuals. In this paper, the estimator of the discontinuous log-variance function itself or its derivative using Chen et al. (2009)'s estimator. Numerical works investigate the performances of the estimators with simulated examples.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.591-601
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• 2005

In this paper we consider detection of a discontinuity point in the variance function. When the mean function is discontinuous at a point, the variance function is usually discontinuous at the point. In this case, we had better estimate the location of the discontinuity point with the mean function rather than the variance function. On the other hand, the variance function only has a discontinuity point. The target function in order to estimate the location can be used the second moment function since the variance function and the second moment function have the same location and jump size of the discontinuity point. We propose a nonparametric detection method of the discontinuity point with the second moment function. We give the asymptotic results of these estimators. Computer simulation demonstrates the improved performance of the method over the existing ones.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.11-23
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• 1996

본 연구에서는 선형회귀분석에서 Hadi와 Simonoff의 다중이상점 식별방법을 수정하여 새로운 알고리즘을 제시하였다. Hadi와 Simonoff의 알고리즘 첫 단계에서 이상점일 가능성이 없는 점들의 집합을 추출할 때 가장효과와 편승효과에 영향을 받을 수 있음으로, 이 첫 단계를 수정하였다. 우리는 잔차가 일정한 분산을 갖는 정규분포에 다르다는 가정하에서 잔차의 신뢰구간을 생각하고, 이 구간안에서 잔차의 MAD가 최소인 새로운 모형을 탐색하고, 이를 이상점일 가능성이 없는 점들의 집합을 추출하는데 일용하는 새로운 알로리즘을 제시하였다. 제시된 방법은 실제자료에서 다른 방법에 비해 효율적으로 이상점을 식별할 수 있었다.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.12 no.19
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• pp.31-37
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• 1989

The recursive residuals are obtained by the iterative processes as descrbed in section 2. They may require more efforts and time to compute and may face difficultie in ordering of data. But we can investigate each case to be deleted and gather more informations on each case. The recursive residuals are much more effective with conjecture of cusum technique. We suggest to use the predicted residual for the construction of recursive residuals in nonlinear regression models. The assessment of influence and leverage by the connection with recursive residuals will be necessary.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.407-414
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• 2000

Carroll and Ruppert(1988) analyzed the esterase assay data with regression model based on quasi-likelihood. Jung and Lee(1997) introduced a goodness-of-fit test for testing the adequacy of the quasi-likelihood and claimed that there is no gross inadequacy with the model because their test was not rejected. However, Lee and Xelder(199S)'s residual plots revealed that the model did not sufficiently reflect the increase of the variance with that of the mean. In this paper, we re-analyze the esterase assay data with the joint modelling of mean and dispersion in Lee and l\elder(1998) and evaluate the validity of the fitted model by applying the residual plots. And it is illustrated that Lee and Nelder(199S)'s restricted likelihood is more efficient in goodness-of-fit test for the dispersion model.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1770-1773
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• 2008

수위-유량 관계 곡선식에 포함되어져 있는 매개변수를 추정하기 위해 많이 사용되는 로그선형 회귀분석은 잔차의 비등분산성(heterocesdascity)을 고려하지 못하므로 본 연구에서는 의사우도추정법(Pseudo-likelihood Estimation, P-LE)에 의해 분산함수를 추정하고 이와 함께 회귀계수를 추정할 수 있는 방법을 제시하였다. 이 과정에서 제시된 회귀잔차를 최소화하기 위하여 SA(simulated annealing)이라는 전역 최적화 알고리즘을 적용하였다. 또한 수위-유량 관계 곡선식은 단면 등의 영향으로 인해 구간에 따라 각각 다르게 구축되어져야 하므로 이를 보다 객관적으로 판단하고 분리 위치를 정확히 추정하기 위하여 Heaviside 함수를 의사우도함수에 포함시켜 결과를 추정하도록 하였으며, 2개의 구간을 가지는 유량자료를 이용하여 제시된 방법의 합리성을 통계적으로 실험하였다. 이와 같이 통계적 실험을 통해 제시된 방법들이 기존 방법과 비교하여 가질 수 있는 장점을 파악하였으며, 제시된 방법들을 금강유역 5개 지점에서 대해 수행하여 효율성을 검증하였다.

• Survey Research
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• v.5 no.2
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• pp.49-70
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• 2004

This paper is a broad review about general regression estimators, which are very useful when auxiliary variables are available in survey sampling. We investigate the process of development of general regression estimators from birth to suggestion of variance estimation method and examine some properties of general regression estimators by comparing with calibration and QR estimators. We also present some forms of general regression estimators available under complex sampling designs such as stratified sampling and cluster sampling. Finally, we comment some advantages as well as disadvantages of general regression estimators and theoretical and practical development in the future.