• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.183-196
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• 2005

In this paper we studied the saddlepoint approximations to the distribution of non-homogeneous quadratic forms in normal variables. The results are the extension of Kuonen's which provide the same approximations to homogeneous quadratic forms. The CGF of interested statistics and related properties are derived for applications of saddlepoint techniques. Simulation results are also provided to show the accuracy of saddlepoint approximations.

• Communications for Statistical Applications and Methods
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• v.17 no.3
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• pp.367-376
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• 2010

Recently various methods were suggested and reviewed for estimating diffusion processes. Out of suggested estimation method, we mainly concerns on the estimation method using saddlepoint approximation method, and we suggest a term saddlepoint approximation(ASP) method which is the simplest saddlepoint approximation method. We will show that ASP method provides fast estimator as much as Euler approximation method(EAM) in computing, and the estimator also has good statistical properties comparable to the maximum likelihood estimator(MLE). By simulation study we compare the properties of ASP estimator with MLE and EAM, for Ornstein-Uhlenbeck diffusion processes.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1171-1180
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• 2014

We considered saddlepoint approximations to VaR (value at risk) and ES (expected shortfall) which frequently encountered in finance and insurance as the measures of risk management. In this paper we supposed univariate and multivariate skew-normal distributions, instead of traditional normal class distributions, as underlying distribution of linear portfolios. Simulation results are provided and showed the suggested saddlepoint approximations are very accurate than normal approximations.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1211-1219
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• 2013

Recently, the usage of skew-normal distribution, instead of classical normal distribution, is rising up in many statistical theories and applications. In this paper, we deal with saddlepoint approximation for the distribution function of sample mean of skew-normal distribution. Comparing to normal approximation, saddlepoint approximation provides very accurate results in small sample sizes as well as for large or moderate sample sizes. Saddlepoint approximations related to the skew-normal distribution, suggested in this paper, can be used as a approximate approach to the classical method of Gupta and Chen (2001) and Chen et al. (2004) which need very complicate calculations. Through simulation study, we verified the accuracy of the suggested approximation and applied the approximation to Robert's (1966) twin data.

• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.959-967
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• 2016

Distributional assumptions on equity returns play a key role in valuation theories for derivative securities. Elberlein and Keller (1995) investigated the distributional form of compound returns and found that some of standard assumptions can not be justified. Instead, Generalized Hyperbolic (GH) distribution fit the empirical returns with high accuracy. Hu and Kercheval (2007) also show that the normal distribution leads to VaR (Value at Risk) estimate that significantly underestimate the realized empirical values, while the GH distributions do not. We consider saddlepoint approximations to estimate the VaR and the ES (Expected Shortfall) which frequently encountered in finance and insurance as measures of risk management. We supposed GH distributions instead of normal ones, as underlying distribution of linear portfolios. Simulation results show the saddlepoint approximations are very accurate than normal ones.

• The Korean Journal of Applied Statistics
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• v.27 no.5
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• pp.809-818
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• 2014

Multivariate skew-normal distribution(distribution that includes multivariate normal distribution) has been recently applied to many application areas. We consider saddlepoint approximation for a statistic of linear combination based on a multivariate skew-normal distribution. This approach can be regarded as an extension of Na and Yu (2013) that dealt saddlepoint approximation for the distribution of a skew-normal sample mean for a linear statistic and multivariate version. Simulations results and examples with real data verify the accuracy and applicability of suggested approximations.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.571-579
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• 2016

Most of studies related to the distributions of quadratic forms are conducted under the assumption of multivariate normal distribution. In this paper, we suggested an approximation to the distribution of quadratic forms based on multivariate skew-normal distribution as alternatives for multivariate normal distribution. Saddlepoint approximations are considered and the accuracy of the approximations are verified through simulation studies.

• Proceedings of the Korean Statistical Society Conference
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• 2005.05a
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• pp.209-213
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• 2005

본 논문에서는 1차 자기회귀모형에서 자기회귀계수에 대한 여러 가지 추정량들의 분포함수에 대한 근사적추론 방법에 대해 연구하였다. 이차형식에 대한 안장점근사의 결과를 이용한 이 근사법은 여러 형태의 추정량들에 대해 근사분포의 유도과정이 불필요하며, 소표본은 물론 통계적 추론의 주요 관심영역에서의 근사정도가 매우 뛰어난 장점을 가지고 있다. 모의실험을 통해 Edgeworth근사를 비롯한 기존의 여러 근사법보다 효율이 뛰어남을 확인하였다.

• The Korean Journal of Applied Statistics
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• v.22 no.1
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• pp.171-179
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• 2009

In this paper we studied the effective approximations to the distribution of the sum of products of normal variables. Based on the saddlepoint approximations to the quadratic forms, the suggested approximations are very accurate and easy to use. Applications to the FSK (Frequency Shift Keying) communication are also considered.

• The Korean Journal of Applied Statistics
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• v.20 no.1
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• pp.103-115
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• 2007

In this paper we studied the small sample asymptotic inference for the autoregressive coefficient in AR(1) model. Based on saddlepoint approximations to the distribution of quadratic forms, we suggest a new approximation to the distribution of the estimators of the noncircular autoregressive coefficients. Simulation results show that the suggested methods are very accurate even in the small sample sizes and extreme tail area.