• Journal for History of Mathematics
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• v.17 no.2
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• pp.15-20
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• 2004

We investigate the unbiasedness and consistency as the statistical properties of density estimators. We show histogram, kernel density estimation, and local adaptive smoothing as density smoothing in this paper. Also, the early and recent research on nonparametric density estimation is described and discussed.

• 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 the Korean Data and Information Science Society
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• v.11 no.2
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• pp.335-345
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• 2000

Most context use the classical norms on function spaces as the error criteria. Since these norms are all based on the vertical distances between the curves, these can be quite inappropriate from a visual notion of distance. Visual errors in Marron and Tsybakov(1995) correspond more closely to "what the eye sees". Simulation is performed to compare the performance of the regression smoothers in view of MISE and the visual error. It shows that the visual error can be used as a possible candidate of error criteria in the kernel regression estimation.

• Journal of Korea Water Resources Association
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• v.52 no.2
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• pp.141-148
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• 2019

When simulating the daily rainfall amount by existing Markov Chain model, it is general to simulate the rainfall occurrence and to estimate the rainfall amount randomly from the distribution which is similar to the daily rainfall distribution characteristic using Monte Carlo simulation. At this time, there is a limitation that the characteristics of rainfall intensity and distribution by time according to the rainfall duration are not reflected in the results. In this study, 1-day, 2-day, 3-day, 4-day rainfall event are classified, and the rainfall amount is estimated by rainfall duration. In other words, the distributions of the total amount of rainfall event by the duration are set using the Kernel Density Estimation (KDE), the daily rainfall in each day are estimated from the distribution of each duration. Total rainfall amount determined for each event are divided into each daily rainfall considering the type of daily distribution of the rainfall event which has most similar rainfall amount of the observed rainfall using the k-Nearest Neighbor algorithm (KNN). This study is to develop the limitation of the existing rainfall estimation method, and it is expected that this results can use for the future rainfall estimation and as the primary data in water resource design.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.911-915
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• 1997

The purpose of this paper is to consider the problem of selection of optimal smoothing parameter for kernel-type distribution function estimator, which asymptotically minimizes mean Hellinger distance.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.5
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• pp.494-503
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• 2002

A motion vector re-estimation algorithm for image downscaling in discrete consine transform domain is presented. Kernel functions are difined using SAD (Aum of Absolute Difference) and edge information of a macroblock. The proposed method uses these kernel functions to re-estimate a new motion vector of the downscaled image. The motion vectors from the incoming bitstream of transcoder are reused to reduce computation burden of the block-matching motion estimation, and we also reuse the given motion vectors. Several experiments in this paper show that the computation efficiency and the PSNR (Peak Signal to Noise Ratio) and better than the previous methods.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.385-397
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• 2016

The stress-strength models have been intensively investigated in the literature in regards of estimating the reliability ${\theta}$ = P(X > Y) using parametric and nonparametric approaches under different sampling schemes when X and Y are independent random variables. In this paper, we consider the problem of estimating ${\theta}$ when (X, Y) are dependent random variables with a bivariate underlying distribution. The empirical and kernel estimates of ${\theta}$ = P(X > Y), based on bivariate ranked set sampling (BVRSS) are considered, when (X, Y) are paired dependent continuous random variables. The estimators obtained are compared to their counterpart, bivariate simple random sampling (BVSRS), via the bias and mean square error (MSE). We demonstrate that the suggested estimators based on BVRSS are more efficient than those based on BVSRS. A simulation study is conducted to gain insight into the performance of the proposed estimators. A real data example is provided to illustrate the process.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1045-1054
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• 2012

Support vector machine is known to be the very useful statistical method in classification and nonlinear function estimation. In this paper we propose a monotone support vector regression (SVR) for the estimation of monotonically decreasing function. The proposed monotone SVR is applied to smooth the Kaplan-Meier estimate of survival function. Experimental results are then presented which indicate the performance of the proposed monotone SVR using survival functions obtained by exponential distribution.

• ALGAE
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• v.30 no.1
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• pp.49-58
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• 2015

In September 2007, reports of respiratory irritation and fish kills were received by the Florida Fish and Wildlife Conservation Commission (FWC) from the Jacksonville, Florida area. Water samples collected in this area indicated a bloom of Karenia brevis, the dinoflagellate that produces brevetoxin, which can cause neurotoxic shellfish poisoning. For the next four months, K. brevis was found along approximately 400 km of coastal and Intracoastal waterways from Jacksonville to Jupiter Inlet. This event represents the longest and most extensive red tide the east coast of Florida has experienced and the first time Karenia species other than K. brevis have been reported in this area. This extensive red tide influenced commercial and recreational shellfish harvesting activities along Florida's east coast. Fourteen shellfish harvesting areas (SHAs) were monitored weekly during this event and 10 SHAs were closed for an average of 53 days due to this red tide. The length of SHA closure was dependent on the shellfish species present. Interagency cooperation in monitoring this K. brevis bloom was successful in mitigating any human health impacts. Kernel density estimation was used to create geographic extent maps to help extrapolate discreet sample data points into $5km^2$ radius values for better visualization of the bloom.

• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.19-27
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• 1998

We considered the bandwidth selection method which has asymptotic optimal convergence rate $n^{-1/2}$ in kernel regression function estimation. For the proposed bandwidth selection, we considered Mean Averaged Squared Error as a performance criterion and its Taylor expansion to the fourth order. Then we estimate the bandwidth which minimizes the estimated approximate value of MASE. Finally we show the relative convergence rate between optimal bandwidth and proposed bandwidth.