• Water Engineering Research
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• v.2 no.1
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• pp.1-10
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• 2001

The frequency analyses for the precipitation data in Korea were performed. We used daily maximum series, monthly maximum series, and annual series. For nonparametric frequency analyses, variable kernel estimators were used. Nonparametric methods do not require assumptions about the underlying populations from which the data are obtained. Therefore, they are better suited for multimodal distributions with the advantage of not requiring a distributional assumption. In order to compare their performance with parametric distributions, we considered several probability density functions. They are Gamma, Gumbel, Log-normal, Log-Pearson type III, Exponential, Generalized logistic, Generalized Pareto, and Wakeby distributions. The variable kernel estimates are comparable and are in the middle of the range of the parametric estimates. The variable kernel estimates show a very small probability in extrapolation beyond the largest observed data in the sample. However, the log-variable kernel estimates remedied these defects with the log-transformed data.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.951-959
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• 2014

Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimator for the deconvolution problem. In the case of Gaussian kernels and measurement error, they argued that the weighted kernel density estimator is a competitive estimator over the classical deconvolution kernel estimator. In this paper we consider weighted kernel density estimators when sample observations are contaminated by double exponentially distributed errors. The performance of the weighted kernel density estimators is compared over the classical deconvolution kernel estimator and the kernel density estimator based on the support vector regression method by means of a simulation study. The weighted density estimator with the Gaussian kernel shows numerical instability in practical implementation of optimization function. However the weighted density estimates with the double exponential kernel has very similar patterns to the classical kernel density estimates in the simulations, but the shape is less satisfactory than the classical kernel density estimator with the Gaussian kernel.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1219-1231
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• 2008

The main object of this paper is to develop a leave-one-out(LOO) bound of all pairwise comparison error correcting output codes (APC-ECOC). To avoid using classifiers whose corresponding target values are 0 in APC-ECOC and requiring pilot estimates we developed a bound based on mean misclassification probability(MMP). It can be used to tune kernel hyperparameters. Our empirical experiment using kernel mean squared estimate(KMSE) as the binary classifier indicates that the bound leads to good estimates of kernel hyperparameters.

• Communications for Statistical Applications and Methods
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• v.2 no.1
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• pp.99-111
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• 1995

It is shown that the adaptive kernel methods can potentially produce superior density estimates to the fixed one. In using the adaptive estimates, problems pertain to the initial choice of the estimate can be solved by iteration. Also, simultaneous recommended for variety of distributions. Some data-based method for the choice of the parameters are suggested based on simulation study.

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.425-437
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• 2002

Let $\Omega$ be a smoothly bounded pseudoconvex domain in $C^{n}$ and let $z^{0}$ $\in$b$\Omega$ a point of finite type. We also assume that the Levi form of b$\Omega$ is comparable in a neighborhood of $z^{0}$ . Then we get precise estimates of the Bergman kernel function, $K_{\Omega}$(z, w), and its derivatives in a neighborhood of $z^{0}$ . .

• East Asian mathematical journal
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• v.33 no.1
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• pp.37-44
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• 2017

We will prove size estimates of the Bergman kernel for the generalized Fock space ${\mathcal{F}}^2_{\varphi}$, where ${\varphi}$ belongs to the class $\mathcal{W} $. The main tool for the proof is to use the estimate on the canonical solution to the ${\bar{\partial}}$-equation. We use Delin's weighted $L^2$-estimate ([3], [6]) for it.

• Journal of the Korean Data and Information Science Society
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• v.20 no.5
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• pp.949-954
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• 2009

The autoregressive process is applied in this paper to kernel regression in order to infer nonlinear models for predicting responses. We propose a kernel method for the autoregressive data which estimates the mean function by kernel machines. We also present the model selection method which employs the cross validation techniques for choosing the hyper-parameters which affect the performance of kernel regression. Artificial and real examples are provided to indicate the usefulness of the proposed method for the estimation of mean function in the presence of autocorrelation between data.

• Communications for Statistical Applications and Methods
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• v.15 no.6
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• pp.939-946
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• 2008

In this paper the support vector method is presented for the probability density function estimation when the sample observations are contaminated with random noise. The performance of the procedure is compared to kernel density estimates by the simulation study.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.359-368
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• 2002

Nonparametric kernel regression problem is considered for a stationary dependent sequence ｛(Xi, Yj) 1 j $\geq$ 1 ｝. In particular consistency and rates of convergence are discussed, which gives some useful insight for the effect of dependence for stationary $\alpha$-mixing sequences.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.191-202
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• 2022

In this paper, we obtain the quantitative weighted bounds of oscillatory singular integral with rough kernel. Moreover, the quantitative weighted bounds of maximally truncated oscillatory singular integral with rough kernel are also obtained.