• The Korean Journal of Applied Statistics
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• v.20 no.3
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• pp.561-571
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• 2007

Local linear regression estimator is the most widely used nonparametric regression estimator which has a number of advantages over the traditional kernel estimators. It is well known that local linear estimator can produce erratic result in sparse regions in the realization of the design and the interpolation method of Hall and Turlach (1997) is the very efficient way to resolve this problem. However, it has been never pointed out that Hall and Turlach's interpolation method is very sensitive to outliers. In this paper, we propose the robust version of the interpolation method for adapting to sparse design. The finite sample properties of the method is compared with Hall and Turlach's method by the simulation study.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.195-202
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• 2017

We can sometimes find instability against numerical solutions in nonlinear regression. All iterative procedures in nonlinear regression require initial parameter values to be selected. Poor starting values may result in convergence to an unwanted stationary point of the error sum of squares surface. Starting values can sometimes cause the chaos effect in the nonlinear regression model. We can find the chaos phenomena with the convergence plot of starting values in the parameter space.

• The Korean Journal of Applied Statistics
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• v.30 no.5
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• pp.733-745
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• 2017

Local composite quantile regression is a useful non-parametric regression method widely used for its high efficiency. Data smoothing methods using kernel are typically used in the estimation process with performances that rely largely on the smoothing parameter rather than the kernel. However, $L_2$-norm is generally used as criterion to estimate the performance of the regression function. In addition, many studies have been conducted on the selection of smoothing parameters that minimize mean square error (MSE) or mean integrated square error (MISE). In this paper, we explored the optimality of selecting smoothing parameters that determine the performance of non-parametric regression models using local linear composite quantile regression. As evaluation criteria for the choice of smoothing parameter, we used mean absolute error (MAE) and mean integrated absolute error (MIAE), which have not been researched extensively due to mathematical difficulties. We proved the uniqueness of the optimal smoothing parameter based on MAE and MIAE. Furthermore, we compared the optimal smoothing parameter based on the proposed criteria (MAE and MIAE) with existing criteria (MSE and MISE). In this process, the properties of the proposed method were investigated through simulation studies in various situations.

• 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.

• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.923-936
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• 2021

A large number of non-responses are occurring in the sample survey, and various methods have been developed to deal with them appropriately. In particular, the bias caused by non-ignorable non-response greatly reduces the accuracy of estimation and makes non-response processing difficult. Recently, Chung and Shin (2017, 2020) proposed an estimator that improves the accuracy of estimation using parametric super-population model and response rate model. In this study, we suggested a bias corrected non-response mean estimator using a nonparametric function generalizing the form of a parametric super-population model. We confirmed the superiority of the proposed estimator through simulation studies.

• Journal of the Korean Data and Information Science Society
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• v.21 no.1
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• pp.51-59
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• 2010

In the case that the regression function has a discontinuity point in generalized linear model, Huh (2009) estimated the location and jump size using the log-likelihood weighted the one-sided kernel function. In this paper, we consider estimation of the unknown number of the discontinuity points in the regression function. The proposed algorithm is based on testing of the existence of a discontinuity point coming from the asymptotic distribution of the estimated jump size described in Huh (2009). The finite sample performance is illustrated by simulated example.

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