• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1049-1058
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• 2012

Nonparametric methods are often used as an alternative to parametric methods to estimate density function and regression function. In this paper we consider improved methods to select the Bezier points in Bezier curve smoothing that is shown to have the same asymptotic properties as the kernel methods. We show that the proposed methods are better than the existing methods through numerical studies.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.408-413
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• 2005

A new methodology for discrete non-Gaussian probability density estimation is investigated in this paper based on a dynamic Bayesian network (DBN) and kernel functions. The estimator consists of a DBN in which the transition distribution is represented with kernel functions. The estimator parameters are determined through a recursive learning algorithm according to the maximum likelihood (ML) scheme. A discrete-type Poisson distribution is generated in a simulation experiment to evaluate the proposed method. In addition, an unknown probability density generated by nonlinear transformation of a Poisson random variable is simulated. Computer simulations numerically demonstrate that the method successfully estimates the unknown probability distribution function (PDF).

• Journal of Environmental Science International
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• v.22 no.8
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• pp.965-977
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• 2013

Reliable long-term streamflow forecasting is invaluable for water resource planning and management which allocates water supply according to the demand of water users. It is necessary to get probabilistic forecasts to establish risk-based reservoir operation policies. Probabilistic forecasts may be useful for the users who assess and manage risks according to decision-making responding forecasting results. Probabilistic forecasting of seasonal inflow to Andong dam is performed and assessed using selected predictors from sea surface temperature and 500 hPa geopotential height data. Categorical probability forecast by Piechota's method and logistic regression analysis, and probability forecast by conditional probability density function are used to forecast seasonal inflow. Kernel density function is used in categorical probability forecast by Piechota's method and probability forecast by conditional probability density function. The results of categorical probability forecasts are assessed by Brier skill score. The assessment reveals that the categorical probability forecasts are better than the reference forecasts. The results of forecasts using conditional probability density function are assessed by qualitative approach and transformed categorical probability forecasts. The assessment of the forecasts which are transformed to categorical probability forecasts shows that the results of the forecasts by conditional probability density function are much better than those of the forecasts by Piechota's method and logistic regression analysis except for winter season data.

• Journal of Information Processing Systems
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• v.8 no.4
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• pp.669-684
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• 2012

Discrete wavelet transforms are extensively preferred in biomedical signal processing for denoising, feature extraction, and compression. This paper presents a new denoising method based on the modeling of discrete wavelet coefficients of ECG in selected sub-bands with Kernel density estimation. The modeling provides a statistical distribution of information and noise. A Gaussian kernel with bounded support is used for modeling sub-band coefficients and thresholds and is estimated by placing a sliding window on a normalized cumulative density function. We evaluated this approach on offline noisy ECG records from the Cardiovascular Research Centre of the University of Glasgow and on records from the MIT-BIH Arrythmia database. Results show that our proposed technique has a more reliable physical basis and provides improvement in the Signal-to-Noise Ratio (SNR) and Percentage RMS Difference (PRD). The morphological information of ECG signals is found to be unaffected after employing denoising. This is quantified by calculating the mean square error between the feature vectors of original and denoised signal. MSE values are less than 0.05 for most of the cases.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.987-994
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• 2011

From the point view of credit evaluation whose population is divided into the default and non-default state, two methods are considered to estimate conditional distribution functions: one is to estimate under the assumption that the data is followed the mixture normal distribution and the other is to use the kernel density estimation. The parameters of normal mixture are estimated using the EM algorithm. For the kernel density estimation, five kinds of well known kernel functions and four kinds of the bandwidths are explored. In addition, the corresponding ROC functions are obtained based on the estimated distribution functions. The goodness-of-fit of the estimated distribution functions are discussed and the performance of the ROC functions are compared. In this work, it is found that the kernel distribution functions shows better fit, and the ROC function obtained under the assumption of normal mixture shows better performance.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.343-358
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• 2017

Let {$X_i$} be a sequence of stationary ${\alpha}-mixing$ random variables with probability density function f(x). The recursive kernel estimators of f(x) are defined by $$\hat{f}_n(x)={\frac{1}{n\sqrt{b_n}}{\sum_{j=1}^{n}}b_j{^{-\frac{1}{2}}K(\frac{x-X_j}{b_j})\;and\;{\tilde{f}}_n(x)={\frac{1}{n}}{\sum_{j=1}^{n}}{\frac{1}{b_j}}K(\frac{x-X_j}{b_j})$$, where 0 < $b_n{\rightarrow}0$ is bandwith and K is some kernel function. Under appropriate conditions, we establish the Berry-Esseen bounds for these estimators of f(x), which show the convergence rates of asymptotic normality of the estimators.

• Journal of the Korean Data and Information Science Society
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• v.6 no.1
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• pp.31-37
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• 1995

We consider density estimates of the usual type generated by a kernel function. By using the limit theorems for the maximum of normalized deviation of the estimate from its expected value, we propose to use data dependent bandwidth in the tests of goodness of fit based on these statistics. Also a small sample Monte Carlo simulation is conducted and proposed method is compared with Kolmogorov-Smirnov test.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.24 no.1
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• pp.1-9
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• 2012

Tidal residual is being an important factor by the influence of the climate change in terms of the coastal safety and defense. It is one of the most important factor for the determination of the reference sea level in order to check the safety and performance of the coastal structures in company with the typhoon intensity variation. The probability density function (pdf) of tidal residuals in the Korean coasts have a non-ignorable skewness and high kurtosis. It is highly restricted to the application of the normal pdf assumption as an approximated pdf of tidal residuals. In this study, the pdf of tidal residuals estimated using the Kernel function is suggested as a more reliable and accurate pdf of tidal residuals than the normal function. This suggested pdf shows a good agreement with the empirical cumulative distribution function and histogram. It also gives the more accurate estimation result on the extreme values in comparison with the results based on the normal pdf assumption.

• Journal of Communications and Networks
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• v.14 no.5
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• pp.540-545
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• 2012

In this paper, the lagged cross-correlation of two probability density functions constructed by kernel density estimation is proposed, and by maximizing the proposed function, adaptive filtering algorithms for supervised and unsupervised training are also introduced. From the results of simulation for blind equalization applications in multipath channels with impulsive and slowly varying direct current (DC) bias noise, it is observed that Gaussian kernel of the proposed algorithm cuts out the large errors due to impulsive noise, and the output affected by the DC bias noise can be effectively controlled by the lag ${\tau}$ intrinsically embedded in the proposed function.

• 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.