• Communications for Statistical Applications and Methods
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• v.21 no.1
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• pp.105-114
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• 2014

In this paper we suggest an efficient method to estimate the distribution function using the Bezier curve, and compare it with existing methods by simulation studies. In addition, we suggest a robust version of cross-validation criterion to estimate the number of Bezier points, and showed that the proposed method is better than the existing methods based on simulation studies.

• 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.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.891-901
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• 1997

The objective of this research is to investigate the problem of goodness of fit testing based on nonparametric density estimation with a data-driven smoothing parameter. The small and large smaple properties of the proposed test statistic $Z_{mn}$ are investigated with the minimizer $\widehat{m}$ of the estimated mean integrated squared error by the Diggle and Hall (1986) method.

• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.149-158
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• 1994

Nonparametric regression technique using kernel estimator is an attractive alternative that has received some attention, recently. The kernel estimate depends on two quantities which have to be provided by the user : the kernel function and the bandwidth. However, the more difficult problem is how to find an appropriate bandwidth which controls the amount of smoothing (see Silverman, 1986). Thus, in practical situation, it is certainly desirable to determine an appropriate bandwidth in some automatic fashion. Thus, the problem is to find a data-driven or adaptive (i.e., depending only on the data and then directly computable in practice) bandwidth that performs reasonably well relative to the best theoretical bandwidth. In this paper, we introduce a relation between bias and variance of mean square error. Thus, we present a simple and effective algorithm for selecting local bandwidths in kernel regression.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.713-727
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• 2005

Among different regression approaches, nonparametric procedures perform well under different conditions. In practice it is very hard to identify which is the best procedure for the data at hand, thus model combination is of practical importance. In this paper, we focus on one dimensional regression with fixed design. Polynomial regression, local regression, and smoothing spline are considered. The data are split into two parts, one part is used for estimation and the other part is used for prediction. Prediction performances are used to assign weights to different regression procedures. Simulation results show that the combined estimator performs better or similarly compared with the estimator chosen by cross validation. The combined estimator generates a similar risk to the best candidate procedure for the data.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.113-123
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• 1996

Data-dependent (adaptive) choice of asymptotically efficient score functions for rank estimators and M-estimators of regression parameters in a linear regression model with left-truncated and right-censored data are developed herein. The locally adaptive smoothing techniques of Muller and Wang (1990) and Uzunogullari and Wang (1992) provide good estimates of the hazard function h and its derivative h' from left-truncated and right-censored data. However, since we need to estimate h'/h for the asymptotically optimal choice of score functions, the naive estimator, which is just a ratio of estimated h' and h, turns out to have a few drawbacks. An altermative method to overcome these shortcomings and also to speed up the algorithms is developed. In particular, we use a subroutine of the PPR (Projection Pursuit Regression) method coded by Friedman and Stuetzle (1981) to find the nonparametric derivative of log(h) for the problem of estimating h'/h.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1245-1253
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• 2010

There are two main approaches for estimating the discontinuous regression function nonparametrically. One is the direct approach, the other is the indirect approach. The major goal of the two approaches are different. The direct approach focuses on the overall good estimation of the regression function itself, whereas the indirect approach focuses on the good estimation of jump locations. Apparently, the two approaches are quite different in nature. Gijbels et al. (2007) argue that the comparison of two approaches does not make much sense and that it is even difficult to choose an appropriate criterion for comparisons. However, it is obvious that the indirect approach also has the regression curve estimate as the subsidiary result. Therefore it is necessary to verify the appropriateness of the indirect approach as the estimator of the discontinuous regression function itself. Park (2009a) compared the performance of two approaches through a simulation study. In this paper, we consider a more general case and draw some useful conclusions.

• Industrial Engineering and Management Systems
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• v.8 no.2
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• pp.93-100
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• 2009

In this paper, we review widely used methods to extract local volatility surfaces (LVSs) from implied volatility surfaces (IVSs) and suggest a model averaging method for constructing implied and local volatility surfaces weighted by trading volumes. It makes use of model averaging method by means of bandwidth priors, and then produces a robust LVS estimation. The method is shown to provide the information about the confidence interval of estimators as well as a rather less variable weighted mean value for the IVS and LVS. To show the merits of our proposed method, we conduct simulations on equity-linked warrants (ELWs) with reasonable and acceptable results.

• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.937-944
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• 2021

The problem of selecting variables is addressed in partial linear regression. Model selection for partial linear models is not easy since it involves nonparametric estimation such as smoothing parameter selection and estimation for linear explanatory variables. In this work, several approaches for variable selection are proposed using a fast forward selection algorithm, least angle regression (LARS). The proposed procedures use t-test, all possible regressions comparisons or stepwise selection process with variables selected by LARS. An example based on real data and a simulation study on the performance of the suggested procedures are presented.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.48.4-49
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• 2020

We reconstruct the expansion history of the universe using type Ia supernovae (SN Ia) in a manner independent of any cosmological model assumptions. To do so, we implement a nonparametric iterative smoothing method on the Joint Light-curve Analysis (JLA) data while exploring the SN Ia light-curve hyperparameter space by Markov Chain Monte Carlo (MCMC) sampling. We test to see how the posteriors of these hyperparameters depend on cosmology, whether using different dark energy models or reconstructions shift these posteriors. Our constraints on the SN Ia light-curve hyperparameters from our model-independent analysis are very consistent with the constraints from using different parameterizations of the equation of state of dark energy, namely the flat ΛCDM cosmology, the Chevallier-Polarski-Linder model, and the Phenomenologically Emergent Dark Energy (PEDE) model. This implies that the distance moduli constructed from the JLA data are mostly independent of the cosmological models. We also studied that the possibility the light-curve parameters evolve with redshift and our results show consistency with no evolution. The reconstructed expansion history of the universe and dark energy properties also seem to be in good agreement with the expectations of the standard ΛCDM model. However, our results also indicate that the data still allow for considerable flexibility in the expansion history of the universe. This work is published in ApJ.