• 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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2018.05a
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• pp.422-423
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• 2018

In this paper, we implement Frenelet transform for decomposition of the fringe pattern and analyze its characteristics. The implemented wavelet-like basis functions are well suited for reconstruction and processing of optically generated Fresnel holograms. After analyzing the characteristics of the B-spline function, we will discuss the wavelet-like multi-resolution analysis method. Through this process, we implemented a transform tool that can decompose fringe patterns effectively. We have implemented a B-spline function with various decomposition properties and showed the results of decomposing the fringe pattern.

• Journal of Korean Association for Spatial Structures
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• v.12 no.1
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• pp.109-119
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• 2012

For membrane structure, there are three main steps in design and construction, which are form finding, statistical load analysis, and cutting patterning. Unlike the first two stages, the step of cutting pattern involves the translation of a double-curved surface in 3D space into a 2D plane with minimal error. For economic reasons, the seam lines of generated cutting patterns rely greatly on the geodesic line. Generally, as searching regions of the seam line are plane elements in the step of shape analysis, the seam line is not a smooth curve, but an irregularly divided straight line. So, it is how we make an irregularly divided straight line a smooth curve that defines the quality of the pattern. Accordingly, in this paper, we analyzed interpolation schemes using spline, and apply these methods to cutting pattern generation on the curved surface. To generate the pattern, three types of spline functions were used, i.e., cubic spline function, B-spline, and least-square spline approximation, and simple model and the catenary-shaped membrane was adopted to examine the result of generation. The result of comparing the approximation curves by the number of elements and the number of extracted nodes of simple model revealed that the seam line for less number of extracted nodes with large number of elements were more efficient, and the least-square spline approximation provided smoother seam line than other methods.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.10a
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• pp.544-547
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• 2008

Navigation in 3D virtual environment(VE) is very difficult because the virtual environment is lack information than real 3D world. So navigation is import research subject in 3D VE. In this paper, we study tour path setting method using spline curve. The spline curve is augmented polynomial function. So the curve is differentiable. In particular, since the curves which are order of 2 and 3 are second order differentiable those are sufficiently smooth for using the computer graphics and CAD system.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.199-203
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• 2008

수위관측지점의 수위-유량관계는 하천단면 형태와 경사에 따라 1개의 유량곡선이 형성될 수도 있으나, 저수위, 평수위, 고수위 등 여러 개 구간의 곡선이 각각 다른 형태로 구성될 수 있다. 또한 이러한 곡선의 연결접점에서 연결이 연속적이어야 하고 부드러워야 한다고 알려져 있다. 각 수위구간에서 유도된 수위-유량관계곡선이 수위구간을 나눈 경계수위에서 곡선식이 일치하지는 경우가 종종 나타난다. 본 연구에서는 경계수위와 곡선접점이 일치하는지 여부를 판단하고 오차의 크기를 확인하기 위하여 할선법을 적용하여 Excel의 VBA로 프로그램을 작성하여 사용하였다. 한편, 수위유량곡선의 연결부에서 부드럽게 연결되는 것이 바람직 하지만, 지금까지 실무에서는 경계수위에서 기울기가 급변하는 형태의 수위-유량관계곡선을 사용하고 있다. 왜냐하면 최소자승회귀분석을 통하여 유도되는 과정에서 경계수위지점의 1차 도함수를 일치시키는 것은 현실적으로 불가능하기 때문이다. 본 연구에서는 이러한 문제를 해결하기 위하여, 회귀분석으로 지수함수의 형태로 유도된 수위-유량관계곡선으로부터 수위와 유량의 대표 값을 계산하고 이들 대표 값들을 3차 스플라인 보간법을 이용하여 1차 도함수를 접점에서 일치시키는 부드러운 연결과 함께 수위-유량관계곡선과도 잘 일치하는 새로운 대안을 제시하였다. 2006년도 한국수문조사연보(유량편)의 자료를 검토하여 문제점들을 도출하고, 본 연구에서 제안한 방법들을 적용하여 보았다.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.2
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• pp.50-55
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• 2002

The standard approach of image resampling is to fit the original image with continuous model and resample the function at a desired rate. We used the B-spline function as the continuous model because it oscillates less than the others. The main purpose of this paper is the derivation of a nonuniform optimal resampling algorithm. To derive it, needing approximation can be computed in three steps: 1) determining the I-spline coefficients by matrix inverse process, 2) obtaining the transformed-spline coefficients by the optimal resampling algorithm derived from the orthogonal projection theorem, 3) converting of the result back into the signal domain by indirect B-spline transformation. With these methods, we can use B-spline in the non-uniform resampling, which is proved to be a good kernel in uniform resampling, and can also verify the applicability from our experiments.

• 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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.205-208
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• 2008

In numerical analysis numerical values of thermodynamic properties such as temperature, pressure, specific volume, enthalpy and entropy are required. But most of the thermodynamic properties of the steam table are determined by experiment. Therefore they are supposed to have measurement errors. In order to make noised thermodynamic properties corresponding to errors, random numbers are generated, adjusted to appropriate magnitudes and added to original thermodynamic properties. the neural networks and quadratic spline interpolation method are introduced for function approximation of these modified thermodynamic properties in the saturated water based on pressure. It was proved that the neural networks give smaller percentage error compared with quadratic spline interpolation. From this fact it was confirmed that the neural networks trace the original values of thermodynamic properties better than the quadratic interpolation method.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1047-1058
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• 2008

Prediction of total sales in information security industry is considered. Exponential smoothing and spline smoothing is applied to the time series of annual sales data. Due to the different survey items of every year, we recollect the original survey data by some basic criterion and predict the sales to 2014. We show the total sales in infonnation security industry are increasing gradually by year.

• Journal of the Korean Data and Information Science Society
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• v.20 no.1
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• pp.89-96
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• 2009

We examined the characteristics of temperature variation in Seoul between 1961 to 2008 using the spectral heteroscedastic model. The mean function in the propsed model explains the season effect using periodic functions and the overall increase using the quadratic regression spline. The variance function also had periodic functions to explain the seasonality of variance. We found that there has been annual mean temperature increase by about $1.5^{\circ}C$ for the last 48 years. The increase of annual mean temperature was mainly caused by the increase in winter, which made the amplitude decreased.