• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.574-574
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• 2000

Consider the problem of estimating regression function from a set of data which is contaminated by a long-tailed error distribution. The linear smoother is a kind of a local weighted average of response, so it is not robust against outliers. The kernel M-smoother and the lowess attain robustness against outliers by down-weighting outliers. However, the kernel M-smoother and the lowess requires the iteration for computing the robustness weights, and as Wang and Scott(1994) pointed out, the requirement of iteration is not a desirable property. In this article, we propose the robust nonparametic regression method which does not require the iteration. Robustness can be achieved not only by down-weighting outliers but also by transforming outliers. The rank transformation is a simple procedure where the data are replaced by their corresponding ranks. Iman and Conover(1979) showed the fact that the rank transformation is a robust and powerful procedure in the linear regression. In this paper, we show that we can also use the rank transformation to nonparametric regression to achieve the robustness.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.575-583
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• 2000

Consider the problem of estimating regression function from a set of data which is contaminated by a long-tailed error distribution. The linear smoother is a kind of a local weighted average of response, so it is not robust against outliers. The kernel M-smoother and the lowess attain robustness against outliers by down-weighting outliers. However, the kernel M-smoother and the lowess requires the iteration for computing the robustness weights, and as Wang and Scott(1994) pointed out, the requirement of iteration is not a desirable property. In this article, we propose the robust nonparametic regression method which does not require the iteration. Robustness can be achieved not only by down-weighting outliers but also by transforming outliers. The rank transformation is a simple procedure where the data are replaced by their corresponding ranks. Iman and Conover(1979) showed the fact that the rank transformation is a robust and powerful procedure in the linear regression. In this paper, we show that we can also use the rank transformation to nonparametric regression to achieve the robustness.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.463-473
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• 2015

We consider a nonparametric AR(1) model with nonparametric ARCH(1) errors. In order to estimate the unknown function of the ARCH part, we apply the stationary bootstrap procedure, which is characterized by geometrically distributed random length of bootstrap blocks and has the advantage of capturing the dependence structure of the original data. The proposed method is composed of four steps: the first step estimates the AR part by a typical kernel smoothing to calculate AR residuals, the second step estimates the ARCH part via the Nadaraya-Watson kernel from the AR residuals to compute ARCH residuals, the third step applies the stationary bootstrap procedure to the ARCH residuals, and the fourth step defines the stationary bootstrapped Nadaraya-Watson estimator for the ARCH function with the stationary bootstrapped residuals. We prove the asymptotic validity of the stationary bootstrap estimator for the unknown ARCH function by showing the same limiting distribution as the Nadaraya-Watson estimator in the second step.

• Journal of the Korean Data and Information Science Society
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• v.23 no.1
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• pp.79-87
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• 2012

In the case that the probability density function has a discontinuity point, Huh (2002) estimated the location and jump size of the discontinuity point based on the difference between the right and left kernel density estimators using the one-sided kernel function. In this paper, we consider the cross-validation, made by the right and left maximum likelihood cross-validations, for the bandwidth selection in order to estimate the location and jump size of the discontinuity point. This method is motivated by the one-sided cross-validation of Hart and Yi (1998). The finite sample performance is illustrated by simulated example.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.327-336
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• 2001

This work concerns estimating a regression function, which is not linear, using aggregate data. In much of the empirical research, data are aggregated for various reasons before statistical analysis. In a traditional parametric approach, a linear estimation of the non-linear function with aggregate data can result in unstable estimators of the parameters. More serious consequence is the bias in the estimation of the non-linear function. The approach we employ is the kernel regression smoothing. We describe the conditions when the aggregate data can be used to estimate the regression function efficiently. Numerical examples will illustrate our findings.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.205-216
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• 1996

The field of nonparametrics has shown its appeal in re-cent years with anarray of new tools for statistical analysis. As one of those tools nonparametric regression has become a prominent statis-tical research topic and also has been well established as a useful tool. In this article we investigate the biased cross-validation selector, BCV, which is proposed by Oh et al. (1995) for a less smoothing regression function. In the simulation study BCV selector is shown to perform well in parctice with respect to ASE ratio.

• Journal of the Korea Institute of Military Science and Technology
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• v.5 no.2
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• pp.207-216
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• 2002

In this paper, the study on the behavior of the deformation of brittle material, such as concrete, ceramic, was peformed by comparison of Lagrangian technique and Smoothed Particle Hydrodynamics using commercial nonlinear hydrodynamic numerical program, Autodyn_2D. The effect of SPH technique was proved by investigating the behavior of material deformation, velocity profile and pressure profile.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.425-433
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• 2005

Most of national-wide surveys are summarized by some statistical tables and graphs. In spite of high costs to get statistical results from surveys, we often find some statistical problems in the statistical reports. In this paper, we point out some statistical problems for the Korean Anthropometric Survey report. Also, we suggest some alternatives which may avoid the illustrated problems.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.10
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• pp.4887-4907
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• 2017

Accurate traffic flow forecasting is critical to the development and implementation of city intelligent transportation systems. Therefore, it is one of the most important components in the research of urban traffic scheduling. However, traffic flow forecasting involves a rather complex nonlinear data pattern, particularly during workday peak periods, and a lot of research has shown that traffic flow data reveals a seasonal trend. This paper proposes a new traffic flow forecasting model that combines seasonal relevance vector regression with the hybrid chaotic simulated annealing method (SRVRCSA). Additionally, a numerical example of traffic flow data from The Transportation Data Research Laboratory is used to elucidate the forecasting performance of the proposed SRVRCSA model. The forecasting results indicate that the proposed model yields more accurate forecasting results than the seasonal auto regressive integrated moving average (SARIMA), the double seasonal Holt-Winters exponential smoothing (DSHWES), and the relevance vector regression with hybrid Chaotic Simulated Annealing method (RVRCSA) models. The forecasting performance of RVRCSA with different kernel functions is also studied.

• Industrial Engineering and Management Systems
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• v.10 no.1
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• pp.84-94
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• 2011

In this paper, we propose a method to provide the distribution of option price under local volatility model when market-provided implied volatility data are given. The local volatility model is one of the most widely used smile-consistent models. In local volatility model, the volatility is a deterministic function of the random stock price. Before estimating local volatility surface (LVS), we need to estimate implied volatility surfaces (IVS) from market data. To do this we use local polynomial smoothing method. Then we apply the Dupire formula to estimate the resulting LVS. However, the result is dependent on the bandwidth of kernel function employed in local polynomial smoothing method and to solve this problem, the proposed method in this paper makes use of model averaging approach by means of bandwidth priors, and then produces a robust local volatility surface estimation with a confidence interval. After constructing LVS, we price barrier option with the LVS estimation through Monte Carlo simulation. To show the merits of our proposed method, we have conducted experiments on simulated and market data which are relevant to KOSPI200 call equity linked warrants (ELWs.) We could show by these experiments that the results of the proposed method are quite reasonable and acceptable when compared to the previous works.