• The Korean Journal of Applied Statistics
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• v.26 no.4
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• pp.687-696
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• 2013

The detection and the examination of outliers are important parts of data analysis because some outliers in the data may have a detrimental effect on statistical analysis. Outlier detection methods have been discussed by many authors. In this article, we propose to apply Hadi and Simonoff's (1993) method to penalized spline a regression model to detect multiple outliers. Simulated data sets and real data sets are used to illustrate and compare the proposed procedure to a penalized spline regression and a robust penalized spline regression.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.537-551
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• 2021

We conducted a study on a regression spline estimator with a few pre-specified auxiliary variables. For the implementation of the proposed estimators, we adapted a coordinate descent algorithm. This was implemented by considering a structure of the sum of the residuals squared objective function determined by the B-spline and the auxiliary coefficients. We also considered an efficient stepwise knot selection algorithm based on the Bayesian information criterion. This was to adaptively select smoothly functioning estimator data. Numerical studies using both simulated and real data sets were conducted to illustrate the proposed method's performance. An R software package psav is available.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.277-285
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• 1998

The smoothing parameter $\lambda$ in smoothing spline regression is usually selected by minimizing cross-validation (CV) or generalized cross-validation (GCV). But, simple CV or GCV is poor candidate for estimating prediction error. We defined MGCV (Multifold Generalized Cross-validation) as a criterion for selecting smoothing parameter in smoothing spline regression. This is a version of cross-validation using $leave-\kappa-out$ method. Some numerical results comparing MGCV and GCV are done.

• Journal of the Korean Data and Information Science Society
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• v.6 no.1
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• pp.63-71
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• 1995

We have consider the study of local influence for smoothing parameter estimates in spline regression model with heteroscedasticity. Practically, generalized cross-validation does not work well in the presence of heteroscedasticity. Thus we have proposed the local influence measure for generalized cross-validation estimates when errors are heteroscedastic. And we have examined effects of diagnostic by above measures through Hyperinflation data.

• Geomechanics and Engineering
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• v.3 no.4
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• pp.285-290
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• 2011

This article employs Multivariate Adaptive Regression Spline (MARS) for determination of friction capacity of driven piles in clay. MARS is non-parametric adaptive regression procedure. Pile length, pile diameter, effective vertical stress, and undrained shear strength are considered as input of MARS and the output of MARS is friction capacity. The developed MARS gives an equation for determination of $f_s$ of driven piles in clay. The results of the developed MARS have been compared with the Artificial Neural Network. This study shows that the developed MARS is a robust model for prediction of $f_s$ of driven piles in clay.

• The Korean Journal of Applied Statistics
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• v.13 no.2
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• pp.371-381
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• 2000

In this paper, we describes smoothing spline in nonparametric regression and some asymptotic results for estimates of the regression cofficients in the parametric part were biased on semi parametric regression estimator.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.695-705
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• 2003

In this article, we propose a regression and correlation analysis via dynamic graphs and implement them in Java Web Start. For the polynomial relations between dependent and independent variables, dynamic graphics are implemented for both polynomial regression and spline estimates for an instant model selection. The results include basic statistics. They are available both as a web-based service and an application.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1247-1253
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• 2008

In this paper, we propose a interval censored regression spline model with a variance function (non-constant variance that depends on a predictor). Simulation studies show our estimates from MCECM algorithm are consistent, but biased when the sample size is small because of boundary effects. Also, we examined how the distribution of $x_i$ affects the converging speed of these consistent estimates.

• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.105-112
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• 1990

Let (X, Y) be a pair random variables and let f denote the regression function of the response Y on the measurement variable X. Let K(f) denote a derivative of f. The least squares method is used to obtain a tensor spline estimator $\hat{f}$ of f based on a random sample of size n from the distribution of (X, Y). Under some mild conditions, it is shown that $K(\hat{f})$ achieves the optimal rate of convergence for the estimation of K(f) in $L_2$ and $L_{\infty}$ norms.

• The Korean Journal of Applied Statistics
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• v.4 no.2
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• pp.171-178
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• 1991

For the polynomial spline regression with fixed knots, some properties of the D-optimal design are discussed. Also the D-optimal design for some cases are found analytically by using a normalized B-spline basis for $S(P_m : k : \Delta)$. Based on the Kiefer-Wolfowitz equivalence theorem, the D-optimal design for some cases are found by numerical methods.