• Journal of the Korean Data and Information Science Society
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• v.28 no.5
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• pp.1179-1189
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• 2017

In this study, we propose an alternative method for discriminant analysis using a multivariate empirical distribution function to express multivariate data as a simple one-dimensional statistic. This method turns to be the estimation process of the optimal threshold based on classification accuracy measures and an empirical distribution function of data composed of classes. This can also be visually represented on a two-dimensional plane and discussed with some measures in ROC curves, surfaces, and manifolds. In order to explore the usefulness of this method for discriminant analysis in the study, we conducted comparisons between the proposed method and the existing methods through simulations and illustrative examples. It is found that the proposed method may have better performances for some cases.

• Communications for Statistical Applications and Methods
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• v.26 no.6
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• pp.623-633
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• 2019

This paper proposes two distance measures between two cumulative hazard functions that can be obtained by comparing their difference and ratio, respectively. Then we estimate the measures and present goodness of t test statistics. Since the proposed test statistics are expressed in terms of the cumulative hazard functions, we can easily give more weights on earlier (or later) departures in cumulative hazards if we like to place an emphasis on earlier (or later) departures. We also show that these test statistics present comparable performances with other well-known test statistics based on the empirical distribution function for an exponential null distribution. The proposed test statistic is an omnibus test which is applicable to other lots of distributions than an exponential distribution.

• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.889-904
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• 2021

This study is a follow-up study of Kang and Kim (2020). In this study, we derive the sample influence functions of the t-statistic which were not directly derived in previous researches. Throughout these results, we both mathematically examine the relationship between the empirical influence function and the sample influence function, and consider a method to approximate the sample influence function by the empirical influence function. Also, the validity of the relationship between an approximated sample influence function and the empirical influence function is verified by a simulation of a random sample of size 300 from normal distribution. As a result of the simulation, the relationship between the sample influence function which is derived from the t-statistic and the empirical influence function, and the method of approximating the sample influence function through the empirical influence function were verified. This research has significance in proposing both a method which reduces errors in approximation of the empirical influence function and an effective and practical method that evolves from previous research which approximates the sample influence function directly through the empirical influence function by constant revision.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.195-203
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• 2007

In this paper we propose support vector quantile regression (SVQR) for randomly right censored data. The proposed procedure basically utilizes iterative method based on the empirical distribution functions of the censored times and the sample quantiles of the observed variables, and applies support vector regression for the estimation of the quantile function. Experimental results we then presented to indicate the performance of the proposed procedure.

• 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.28 no.1
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• pp.87-98
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• 2017

The multivaiate empirical distribution function (MEDF) is defined in this work. The MEDF's expectation and variance are derived and we have shown the MEDF converges to its real distribution function. Based on random samples from bivariate standard normal distribution with various correlation coefficients, we also obtain MEDFs and propose two kinds of graphical methods to visualize MEDFs on two dimensional plane. One is represented with at most n stairs with similar arguments as the step function, and the other is described with at most n curves which look like bivariate quantile vector. Even though these two descriptive methods could be expressed with three dimensional space, two dimensional representation is obtained with ease and it is enough to explain characteristics of bivariate distribution functions. Hence, it is possible to visualize trivariate empirical distribution functions with three dimensional quantile vectors. With bivariate and four variate illustrative examples, the proposed MEDFs descriptive plots are obtained and explored.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.213-224
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• 2014

In this paper, we study the problem of transforming to normality. We propose to estimate the transformation parameter by minimizing a weighted squared distance between the empirical characteristic function of transformed data and the characteristic function of the normal distribution. Our approach also allows for other symmetric target characteristic functions. Asymptotics are established for a random sample selected from an unknown distribution. The proofs show that the weight function $t^{-2}$ needs to be modified to have thinner tails. We also propose the method to compute the influence function for M-equation taking the form of U-statistics. The influence function calculations and a small Monte Carlo simulation show that our estimates are less sensitive to a few outliers than the maximum likelihood estimates.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.185-191
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• 2013

Kiefer (1961) studied asymptotic behavior of empirical distribution using the law of the iterated logarithm. Robertson and Wright (1974a) discussed whether this type of result would hold for a maximum likelihood estimator of a stochastically ordered distribution function; however, we show that this cannot be achieved. We provide only a partial answer to this problem. The result is applicable to both estimation and testing problems under the restriction of stochastic ordering.

• East Asian mathematical journal
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• v.39 no.5
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• pp.537-547
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• 2023

In this paper, we introduce the optimal approximation by a Gaussian function for a probability density function. We show that the approximation can be obtained by solving a non-linear system of parameters of Gaussian function. Then, to understand the non-normality of the empirical distributions observed in financial markets, we consider the nearly Gaussian function that consists of an optimally approximated Gaussian function and a small periodically oscillating density function. We show that, depending on the parameters of the oscillation, the nearly Gaussian functions can have fairly thick heavy tails.

• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.563-571
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• 2001

In this paper, we study selecting a transformation so that the transformed variable is nearly symmetrically distributed. The large sample properties of an M-estimator of transformation parameter that is obtained by minimizing the integrated square of the imaginary part of the empirical characteristic function are investigated when a random sample is selected from some unspecified distribution. According to influence function calculations and Monte Carlo simulations, these estimates are less sensitive, than the normal model maximum likelihood estimates, to a few outliers.