• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.379-387
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• 2006

Local polynomial regression is widely used because of good properties such as such as the adaptation to various types of designs, the absence of boundary effects and minimax efficiency Choi and Hall (1998) proposed an estimator of regression function using a convex combination idea. They showed that a convex combination of three local linear estimators produces an estimator which has the same order of bias as a local cubic smoother. In this paper we suggest another estimator of regression function based on a convex combination of five local constant estimates. It turned out that this estimator has the same order of bias as a local cubic smoother.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38A no.2
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• pp.183-190
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• 2013

In this paper, we propose a spatially adaptive noise detection and removal algorithm for a single degraded image. Under the assumption that an observed image is Gaussian-distributed, the noise information is estimated by local statistics of degraded image, and the degree of the additive noise is detected by the local statistics of the estimated noise. In addition, we describe a noise removal method taking a modified Gaussian filter which is adaptively determined by filter parameters and window size. The experimental results demonstrate the capability of the proposed algorithm.

• Journal of the Korean Statistical Society
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• v.11 no.2
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• pp.88-93
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• 1982

A local limit theorem for large deviations for the i.i.d. random variables was given by Richter (1957), who used the saddle point method of complex variables to prove it. In this paper we give an alternative form of local limit theorem for large deviations for the i.i.d. random variables which is essentially equivalent to that of Richter. We prove the theorem by more direct and heuristic method under a rather simple condition on the moment generating function (m.g.f.). The theorem is proved without assuming that $E(X_i)=0$.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.251-260
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• 2002

The aim of this paper is to consider of detecting the location, the jump size and the number of change-points in regression functions by using the local linear fit which is one of nonparametric regression techniques. It is obtained the asymptotic properties of the change points and the jump sizes. and the correspondin grates of convergence for change-point estimators.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.607-617
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• 2003

This paper offers a practical comparison of efficiency between local likelihood approach and conventional kernel approach in density estimation. The local likelihood estimation procedure maximizes a kernel smoothed log-likelihood function with respect to a polynomial approximation of the log likelihood function. We use two types of data driven bandwidths for each method and compare the mean integrated squares for several densities. Numerical results reveal that local log-linear approach with simple plug-in bandwidth shows better performance comparing to the standard kernel approach in heavy tailed distribution. For normal mixture density cases, standard kernel estimator with the bandwidth in Sheather and Jones(1991) dominates the others in moderately large sample size.

• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.587-598
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• 2006

The number of variables exceeds the number of samples in microarray data. We propose a nonparametric local linear logistic classification procedure using orthogonal components for classifying high-dimensional microarray data. The proposed method is based on the local likelihood and can be applied to multi-class classification. We applied the local linear logistic classification method using PCA, PLS, and factor analysis components as new features to Leukemia data and colon data, and compare the performance of the proposed method with the conventional statistical classification procedures. The proposed method outperforms the conventional ones for each component, and PLS has shown best performance when it is embedded in the proposed method among the three orthogonal components.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.12C
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• pp.1194-1200
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• 2006

In this paper, we propose an adaptive MAP (Maximum A Posteriori) high-resolution image reconstruction algorithm using local statistics. In order to preserve the edge information of an original high-resolution image, a visibility function defined by local statistics of the low-resolution image is incorporated into MAP estimation process, so that the local smoothness is adaptively controlled. The weighted non-quadratic convex functional is defined to obtain the optimal solution that is as close as possible to the original high-resolution image. An iterative algorithm is utilized for obtaining the solution, and the smoothing parameter is updated at each iteration step from the partially reconstructed high-resolution image is required. Experimental results demonstrate the capability of the proposed algorithm.

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1009-1018
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• 2012

Persistence homology (a type of methodology in computational algebraic topology) can be used to capture the topological characteristics of functional data. To visualize the characteristics, a persistence diagram is adopted by plotting baseline and the pairs that consist of local minimum and local maximum. We use the bottleneck distance to measure the topological distance between two different functions; in addition, this distance can be applied to multidimensional scaling(MDS) that visualizes the imaginary position based on the distance between functions. In this study, we use handwriting data (which has functional forms) to get persistence diagram and check differences between the observations by using bottleneck distance and the MDS.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.44 no.3
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• pp.80-87
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• 2007

In this paper, we investigate an enhancement method for Western epigraphic images, which is based on local statistics. Image data is partitioned into two regions, background and information. Statistical and functional analyses are proceeded for image modeling. The Western epigraphic images, for the most part, have shown the Gaussian distribution. It is clarified that each region can be differentiated statistically. The local normalization process algorithm is designed on this model. The parameter is extracted and it‘s properties are verified with the size of moving window. The spatial gray-level distribution is modified and regions are differentiated by adjusting parameter and the size of moving window. Local statistics are utilized for realization of the enhancement, so that difference between regions can be enhanced and noise or speckles of region can be smoothed. Experimental results are presented to show the superiority of the proposed algorithm over the conventional methods.

• The Korean Journal of Applied Statistics
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• v.23 no.3
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• pp.595-607
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• 2010

This paper addresses the problem of reducing the speckle noise in SAR images by wavelet transformation, using a non-local means(NLM) filter originated for Gaussian noise removal. Log-transformed SAR image makes multiplicative speckle noise additive. Thus, non-local means filtering and wavelet thresholding are used to reduce the additive noise, followed by an exponential transformation. NLM filter is an image denoising method that replaces each pixel by a weighted average of all the similarly pixels in the image. But the NLM filter takes an acceptable amount of time to perform the process for all possible pairs of pixels. This paper, also proposes an alternative strategy that uses the t-test more efficiently to eliminate pixel pairs that are dissimilar. Extensive simulations showed that the proposed filter outperforms many existing filters terms of quantitative measures such as PSNR and DSSIM as well as qualitative judgments of image quality and the computational time required to restore images.