• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.271-282
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• 1996

this paper deal with the estimation of the power spectral density function of time series. A kernel estimator which is based on local average is defined and the rates of convergence of the pointwise, $$L_2$-norm; and; $L{\infty}$-norm associated with the estimator are investigated by restricting as to kernels with suitable assumptions. Under appropriate regularity conditions, it is shown that the optimal rate of convergence for 0$N^{-r}$ both in the pointwiseand $$L_2$-norm, while; $N^{r-1}(logN)^{-r}$is the optimal rate in the $L{\infty}-norm$. Some examples are given to illustrate the application of main results.

• Journal of the Korean Statistical Society
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• v.16 no.2
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• pp.80-91
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• 1987

Minimum $L_i$ norm estimation is a robust procedure ins the sense that it leads to an estimator which has greater statistical eficiency than the least squares estimator in the presence of outliers. And the $L_1$ norm estimator has some desirable statistical properties. In this paper a new computational procedure for $L_1$ norm estimation is proposed which combines the idea of reweighted least squares method and the linear programming approach. A modification of the projective transformation method is employed to solve the linear programming problem instead of the simplex method. It is proved that the proposed algorithm terminates in a finite number of iterations.

• The Korean Journal of Applied Statistics
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• v.28 no.1
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• pp.9-21
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• 2015

The support vector machine has been successfully applied to various classification areas due to its flexibility and a high level of classification accuracy. However, when analyzing imbalanced data with uneven class sizes, the classification accuracy of SVM may drop significantly in predicting minority class because the SVM classifiers are undesirably biased toward the majority class. The weighted $L_2$-norm SVM was developed for the analysis of imbalanced data; however, it cannot identify irrelevant input variables due to the characteristics of the ridge penalty. Therefore, we propose the weighted $L_1$-norm SVM, which uses lasso penalty to select important input variables and weights to differentiate the misclassification of data points between classes. We demonstrate the satisfactory performance of the proposed method through simulation studies and a real data analysis.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.231-241
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• 2013

On the framework of the 2-adic group $\mathcal{Z}_2$, we study a Sobolev-like inequality where we estimate the $L^2$ norm by a geometric mean of the BV norm and the $\dot{B}_{\infty}^{-1,{\infty}}$ norm. We first show, using the special topological properties of the $p$-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space ˙$\dot{B}_1^{1,{\infty}}$. This identification lead us to the construction of a counterexample to the improved Sobolev inequality.

• Asian-Australasian Journal of Animal Sciences
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• v.33 no.8
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• pp.1301-1309
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• 2020

Objective: To evaluate the use of nurse sows and post-weaning nutrition strategies for low wean weight (WW) pigs on lifetime growth and efficiency. Methods: Animals (n = 270) were assigned to one of five treatments at 28 d. Low WW pigs (<6 kg) were either weaned and offered a special dietary regime recommended for low WW pigs (WEAN) or placed on a nurse sow (NURSE) and weaned at 49 d. Normal WW pigs (9 kg) (NORM) were also weaned at 28 d. After weaning, NORM and NURSE pigs were offered either a 'high' (4 kg/pig of starter 1 diet followed by 8 kg/pig of starter 2 diet) or 'low' (8 kg/pig of starter 2 diet) starter diet allowance in a 2×2 factorial arrangement. A typical grower diet was then offered, followed by a typical finisher diet until 147 d of age. Results: NORM pigs where heavier throughout their life compared to NURSE pigs (91.4 kg vs 76.2 kg at 147 d; p<0.001). WEAN pigs were heavier at 70 d compared to NURSE pigs (23.9 kg vs 21.0 kg; p<0.001), but there was no significant difference at 147 d between NURSE and WEAN treatments. NURSE pigs had reduced feed intake throughout the finishing period (1.6 kg/d; p<0.001) compared to WEAN (2.0 kg/d) and NORM (1.9 kg/d) pigs. Feed conversion ratio (FCR) of NURSE (2.20) was lower than NORM and WEAN during the finishing period (2.40 and 2.79, respectively). Conclusion: Extended (up to 49 d) nursing for low WW pigs resulted in improved FCR during the finishing period, but no overall improvement in growth rate compared to low WW pigs weaned at 28 d and offered a specialised starter regime. Normal WW pigs where significantly heavier than low WW pigs throughout the study.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.4
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• pp.20-28
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• 2008

We propose a radial image processing method in a discrete polar coordinate system based on L1-norm. For this purpose, we first verified that the polar coordinate based on L2-norm can not exist in discrete system and then develop a method converting the Cartesian coordinate to the discrete polar coordinate. We apply the proposed method to smooth mass images of breast tissue and to detect the boundaries of extremely deformable objects. Compared to the Gaussian smoothing method performed in the Cartesian coordinate system, the proposed method stabilized the image signal while maintaining the overall radial shape of mass images. The proposed boundary detection method can detect shapes with high precision while conventional edge detectors can not accurately detect the shape of deformable objects. We also exploit the method to perform pupil detection and have had good experimental results.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.373-385
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• 2006

To solve a class of nonlinear parameter estimation problems, a method combining the regularized structured nonlinear total least norm (RSNTLN) method and parameter separation scheme is suggested. The method guarantees the convergence of parameters and has an advantages in reducing the residual norm over the use of RSNTLN only. Numerical experiments for two models appeared in signal processing show that the suggested method is more effective in obtaining solution and parameter with minimum residual norm.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.151-164
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• 2005

The regularized structured total least norm (RSTLN) method finds an approximate solution x and error matrix E to the overdetermined linear system (H + E)x $\approx$ b, preserving structure of H. A new separation scheme by parts of variables for the regularized structured total least norm on blind deconvolution problem is suggested. A method combining the regularized structured total least norm method with a separation by parts of variables can be obtain a better approximated solution and a smaller residual. Computational results for the practical problem with Block Toeplitz with Toeplitz Block structure show the new method ensures more efficiency on image restoration.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.1-17
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• 2005

In this paper we present a pair of operators (t-norm, t-conorm) dual with a strong negation with n-threshold $a_1,\;{\ldots}, a_n\;{\in}(0,1),\;a_1\;<\;a_2\;<\;{\ldots}\;<\;a_n$. In this way we obtain an extension of operators with threshold, that are obtained for n = 1. The new pair is obtained from given one.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.