• 대한수학회지
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• 제52권3호
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• pp.447-467
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• 2015

In this paper, we consider a multi-risk model based on the policy entrance process with n independent policies. For each policy, the entrance process of the customer is a non-homogeneous Poisson process, and the claim process is a renewal process. The loss process of the single-risk model is a random sum of stochastic processes, and the actual individual claim sizes are described as extended upper negatively dependent (EUND) structure with heavy tails. We derive precise large deviations for the loss process of the multi-risk model after giving the precise large deviations of the single-risk model. Our results extend and improve the existing results in significant ways.

• 응용통계연구
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• 제26권5호
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• pp.759-766
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• 2013

본 논문에서는 두꺼운 꼬리를 갖는 확률분포들의 여러 부류에 대해서 살펴본다. 주어진 하나의 확률분포가 이들 중 어떤 부류에 속하는 지를 알려면 해당 분포의 꼬리 확률에 대한 (점근) 표현식을 알아야만 한다. 그러나 대다수의 절대 연속 확률분포들은 분포함수가 아닌 확률밀도함수로 명시되기 때문에 통상적으로 이들의 꼬리 확률에 대한 표현식을 얻는 작업은 그리 쉬운 일이 아니다. 본 논문에서는 이러한 경우 확률밀도함수만을 이용하여 꼬리 확률에 대한 점근 표현식을 쉽게 얻을 수 있는 하나의 방법을 제안한다. 또한 제안한 방법을 설명하기 위하여 몇가지 예를 첨부한다.

• 응용통계연구
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• 제23권4호
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• pp.651-668
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• 2010

금융 포트폴리오의 두 위험측도인 VaR와 ES에 대한 여러 추정방법을 1일 후와 10일 후의 경우로 나누어 각각 비교하였다. 2008년 미국발 세계 금융위기 기간을 포함한 KOSPI 자료와 해외 5개국의 종합주가지수 자료를 이용하여 실증적으로 비교하였다. 손실 분포의 두터운 꼬리와 조건부 이분산성을 동시에 고려하는 방법을 중심으로 여러 방법을 추가적으로 고려하였고, 국내 자료에 어떤 방법이 적절하며 종합적인 성능은 어떤가를 살펴보았다.

• Communications for Statistical Applications and Methods
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• 제10권2호
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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.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.5-12
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• 2000

Meta-analysis refers to quantitative methods for combining results from independent studies in order to draw overall conclusions. We consider hierarchical models including selection models under a skewed heavy tailed error distribution and it is shown to be useful in such Bayesian meta-analysis. A general class of skewed elliptical distribution is reviewed and developed. These rich class of models combine the information of independent studies, allowing investigation of variability both between and within studies, and weight function. Here we investigate sensitivity of results to unobserved studies by considering a hierarchical selection model and use Markov chain Monte Carlo methods to develop inference for the parameters of interest.

• Communications for Statistical Applications and Methods
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• 제19권1호
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• pp.177-182
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• 2012

A structural break in the level as well as in the innovation variance has often been exhibited in economic time series. In this paper we propose robust unit root tests based on a sign-type test statistic when a time series has a shift in its level and the corresponding volatility. The proposed tests are robust to a wide class of partially stationary processes with heavy-tailed errors, and have an exact binomial null distribution. Our tests are not affected by the size or location of the break. We set the structural break under the null and the alternative hypotheses to relieve a possible vagueness in interpreting test results in empirical work. The null hypothesis implies a unit root process with level shifts and the alternative connotes a stationary process with level shifts. The Monte Carlo simulation shows that our tests have stable size than the OLSE based tests.

• 대한수학회논문집
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• 제20권1호
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• pp.145-159
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• 2005

In this paper we consider the problem of testing statistical hypotheses for unknown parameters in nonlinear regression models and propose three asymptotically equivalent tests based on regression quantiles estimators, which are Wald test, Lagrange Multiplier test and Likelihood Ratio test. We also derive the asymptotic distributions of the three test statistics both under the null hypotheses and under a sequence of local alternatives and verify that the asymptotic relative efficiency of the proposed test statistics with classical test based on least squares depends on the error distributions of the regression models. We give some examples to illustrate that the test based on the regression quantiles estimators performs better than the test based on the least squares estimators of the least absolute deviation estimators when the disturbance has asymmetric and heavy-tailed distribution.

• 응용통계연구
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• 제7권1호
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• pp.19-34
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• 1994

본 논문에서는 K개의 회귀직선에서 기울기들의 우산형 대립가설에 대한 평행성을 검정하는 비모수 검정법을 제안하고 제안된 검정법의 점근적 성질들을 고찰하고자 한다. 정점을 알고 있는 경우와 모르고 있는 경우로 구분하여 검정법을 제시하고 몇몇 분포에 대해 모의 실험을 해본 결과 제안된 검정통계량이 꼬리가 두터운 분포에서 우도비 검정법들보다 검정력이 우수함을 보였다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 합동 추계학술대회 논문집 정보 및 제어부문
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• pp.26-29
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• 2001

In a target tracking problem the radar glint noise has non-Gaussian heavy-tailed distribution and will seriously affect the target tracking performance. In most nonlinear situations an Extended Robust Kalman Filter(ERKF) can yield acceptable performance as long as the noises are white Gaussian. However, an Extended Robust $H_{\infty}$ Filter (ERHF) can yield acceptable performance when the noises are Laplacian. In this paper, we use the Interacting Multiple Model(IMM) estimator for the problem of target tracking with glint noise. In the IMM method, two filters(ERKF and ERHF) are used in parallel to estimate the state. Computer simulations of a real target tracking shows that hybrid filter used the IMM algorithm has superior performance than a single type filter.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2007년도 심포지엄 논문집 정보 및 제어부문
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• pp.14-16
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• 2007

The statistics for the Gaussian noise mixed with impulsive noise are modelled. The denoising algorithm called amplitude-limited sample average filter is derived, which is optimal in terms of minimizing mean square errors under the assumption that contaminating noise is heavy-tailed Gaussian distributed. Its performance is shown to be excellent when image is corrupted mainly with Gaussian noise. However, it shows visually grainy output as the amount of impulsive noise increases. In order to overcome such problems, it is combined with the myriad filter to propose an amplitude-limited myriad filter. Simulation shows it effectively removes both Gaussian and impulsive noise, not blurring edges severey.