• International Journal of Reliability and Applications
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• v.1 no.2
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• pp.133-143
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• 2000

Data from weighted distributions appear, among other situations, when some of the data are missing or are damaged, a case that is important in reliability and life testing. The kernel method for hazard rate estimation is discussed for these data where the basic large sample properties are given. As a by product, the basic properties of the kernel estimate of the distribution function for data from weighted distribution are presented.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.5
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• pp.561-566
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• 2021

The optimum kernel size for error-distribution estimation with given error samples cannot be used in the weight adjustment of minimum Euclidean distance between error distributions (MED) algorithms. In this paper, a new adaptive kernel estimation method for convergence enhancement of MED algorithms is proposed. The proposed method uses the average rate of change in error power with respect to a small interval of the kernel width for weight adjustment of the MED learning algorithm. The proposed kernel adjustment method is applied to experiments in communication channel compensation, and performance improvement is demonstrated. Unlike the conventional method yielding a very small kernel calculated through optimum estimation of error distribution, the proposed method converges to an appropriate kernel size for weight adjustment of the MED algorithm. The experimental results confirm that the proposed kernel estimation method for MED can be considered a method that can solve the sensitivity problem from choosing an appropriate kernel size for the MED algorithm.

• 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.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.835-844
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• 2007

This paper considers the problem of estimating the error distribution function in nonparametric regression models. Sufficient conditions are given under which the kernel estimator of the error distribution function based on nonparametric residuals satisfies the law of iterated logarithm.

• Journal of the Korean Data and Information Science Society
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• v.3 no.1
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• pp.17-24
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• 1992

The problem of estimating symmetric probability density with high kurtosis is considered. Such densities are often estimated poorly by a global bandwidth kernel estimation since good estimation of the peak of the distribution leads to unsatisfactory estimation of the tails and vice versa. In this paper, we propose a transformation technique before using a global bandwidth kernel estimator. Performance of density estimator based on proposed transformation is investigated through simulation study. It is observed that our method offers a substantial improvement for the densities with high kurtosis. However, its performance is a little worse than that of ordinary kernel estimator in the situation where the kurtosis is not high.

• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.825-832
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• 2012

We propose a novel way of forecasting the market shares of several brands simultaneously in a multiplicative competitive interaction model, which uses kernel regression technique incorporated with kernel machine technique applied in support vector machines and other machine learning techniques. Traditionally, the estimations of the market share attraction model are performed via a maximum likelihood estimation procedure under the assumption that the data are drawn from a normal distribution. The proposed method is shown to be a good candidate for forecasting method of the market share attraction model when normal distribution is not assumed. We apply the proposed method to forecast the market shares of 4 Korean car brands simultaneously and represent better performances than maximum likelihood estimation procedure.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.503-512
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• 2006

In this paper, the Inverse Weibull distribution parameters have been estimated using a new estimation technique based on the non-parametric kernel density function that introduced as an alternative and reliable technique for estimation in life testing models. This technique will require bootstrapping from a set of sample observations for constructing the density functions of pivotal quantities and thus the confidence intervals for the distribution parameters. The performances of this technique have been studied comparing to the conditional inference on the basis of the mean lengths and the covering percentage of the confidence intervals, via Monte Carlo simulations. The simulation results indicated the robustness of the proposed method that yield reasonably accurate inferences even with fewer bootstrap replications and it is easy to be used than the conditional approach. Finally, a numerical example is given to illustrate the densities and the inferential methods developed in this paper.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.607-617
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• 2003

This paper offers a practical comparison of efficiency between local likelihood approach and conventional kernel approach in density estimation. The local likelihood estimation procedure maximizes a kernel smoothed log-likelihood function with respect to a polynomial approximation of the log likelihood function. We use two types of data driven bandwidths for each method and compare the mean integrated squares for several densities. Numerical results reveal that local log-linear approach with simple plug-in bandwidth shows better performance comparing to the standard kernel approach in heavy tailed distribution. For normal mixture density cases, standard kernel estimator with the bandwidth in Sheather and Jones(1991) dominates the others in moderately large sample size.

• 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).

• The Mathematical Education
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• v.31 no.2
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• pp.133-140
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• 1992

The problem of estimating a smooth distribution function F at a point $\tau$ based on randomly right censored data is treated under certain smoothness conditions on F . The asymptotic performance of a certain class of kernel estimators is compared to that of the Kap lan-Meier estimator of F($\tau$). It is shown that the .elative deficiency of the Kaplan-Meier estimate. of F($\tau$) with respect to the appropriately chosen kernel type estimate. tends to infinity as the sample size n increases to infinity. Strong uniform consistency and the weak convergence of the normalized process are also proved.