• Journal of the Korean Statistical Society
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• v.33 no.4
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• pp.435-447
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• 2004

In additive nonparametric regression, Linton and Nielsen (1995) showed that the marginal integration when applied to the local linear smoother produces a rate-optimal estimator of each univariate component function for the case where the dimension of the predictor is two. In this paper we give new formulas for the bias and variance of the marginal integration regression estimators which are valid for boundary areas as well as fixed interior points, and show the local linear marginal integration estimator is in fact rate-optimal when the dimension of the predictor is less than or equal to four. We extend the results to the case of the local polynomial smoother, too.

• Journal of Advanced Marine Engineering and Technology
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• v.15 no.4
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• pp.46-53
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• 1991

In the present study, Navier-Stokes equation is numerically solved by use of a Finite analytic method to obtain the 2-dimensional flow field in the square cavity. The basic idea of F.A.M. is the incorporation of local analytic solutions in the numerical solution of linear or non-linear partial differential equations. In the F.A.M., the total problem is subdivided into a number of all elements. The local analytic solution is obtained for the small element in which the governing equation, if non-linear, to be linearized. The local analytic solutions are then expressed in algebraic form and are overlapped to cover the entire region of the problem. The assembly of these local analytic solutions, which still preserve the overall nonlinearity of the governing equations, results in a system of linear algebraic equations. The system of algebraic equations is then solved to provide the numerical solutions of the total problem. The computed flow field shows the same characteristics to physical concept of flow phenomena.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.519-524
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• 2003

We suggest a method of identifying outliers, using local influence, in regression when linear constraints are imposed on the regression coefficients. An example is given for illustration.

• 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 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.

• Journal of Institute of Control, Robotics and Systems
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• v.2 no.2
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• pp.88-95
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• 1996

It is inevitable for local systems to have deviations which represent interactions and modeling errors originated from the decomposition process of a large scale system. This paper presents a decentralized control scheme for interconnected systems using local linear models and a neuro-coordinator. In the proposed method, the local system is composed of a linear model and unknown deviations caused by linearizing the subsystems around operating points or by estimating parameters of the subsystems. Because the local system has unmeasurable deviations we define a local reference model which consists of a local linear model and a neural network to estimate the deviations indirectly. The reference model is reformed into a linear model which has no deviations through a transformation of input variables and we obtain an optimum feedback control law which minimizes a local performance index. Finally, we derive a decentralized feedback control law which consists of local linear states and neural network outputs. In the decentralized control, the neuro-coordinator generates a corrective control signal to cancel the effect of deviations through backpropagation learning with the errors obtained from the differences of the local system outputs and reference model outputs. Also, the stability of local system is proved by the degree of learning of the neural network under an assumption on a neural network learning index. It is shown by computer simulations that the proposed control scheme can be applied successfully to the control of a biased two-link planar robot manipulator.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1341-1364
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• 2023

This article introduces a method for estimating the conditional hazard function of a real-valued response variable based on a functional variable. The method uses local linear estimation of the conditional density and cumulative distribution function and is applied to a functional stationary ergodic process where the explanatory variable is in a semi-metric space and the response is a scalar value. We also examine the uniform almost complete convergence of this estimation technique.

• Journal of the Korea Society of Computer and Information
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• v.23 no.12
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• pp.1-9
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• 2018

The multiple-choice multidimensional knapsack problem (MMKP) is a variant of the well known 0-1 knapsack problem, which is known as an NP-hard problem. This paper proposes a method for solving the MMKP using the integer programming-based local search (IPbLS). IPbLS is a kind of a local search and uses integer programming to generate a neighbor solution. The most important thing in IPbLS is the way to select items participating in the next integer programming step. In this paper, three ways to select items are introduced and compared on 37 well-known benchmark data instances. Experimental results shows that the method using linear programming is the best for the MMKP. It also shows that the proposed method can find the equal or better solutions than the best known solutions in 23 data instances, and the new better solutions in 13 instances.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1999.05a
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• pp.141-146
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• 1999

A new method, so called MMA(Method of Moving Asymptotes) was applied to the optimization problems of non-linear functions and non-linear structures. In each step of the iterative process, tile MMA generates a strictly convex approximation subproblems and solves them by using the dual problems. The generation of these subproblems is controlled by so called 'moving asymptotes', which may both make no oscillation and speed up tile convergence rate of optimization process. By contrast in generalized dual function, the generated function by MMA is always explicit type. Both the objective and behaviour constraints which were approximated are optimized by dual function. As the results of some examples, it was found that this method is very effective to obtain the global solution for problems with many local solutions. Also it was found that MMA is a very effective approximate method using the original function and its 1st derivatives.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.408-410
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• 2003

In this paper, an improved gradient direction assisted linking algorithm is proposed. This algorithm begins with initial seeds satisfying some local criteria. Then it will search along the direction provided by the initial point. A window will be generated in the gradient direction of the current point. Instead of the conventional method which only considers the value of the local salient structure, an improved mathematical model is proposed to describe the desired linear features. This model not only considers the value of the salient structure but also the direction of it. Furthermore, the linking problem under this model can be efficiently solved by dynamic programming method. This algorithm is tested for linear features detection in IKONOS images. The result demonstrates this algorithm is quite promising.