• Genomics & Informatics
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• v.20 no.1
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• pp.9.1-9.6
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• 2022

Mendelian randomization (MR) uses genetic variation as a natural experiment to investigate the causal effects of modifiable risk factors (exposures) on outcomes. Two-sample Mendelian randomization (2SMR) is widely used to measure causal effects between exposures and outcomes via genome-wide association studies. 2SMR can increase statistical power by utilizing summary statistics from large consortia such as the UK Biobank. However, the first-order term approximation of standard error is commonly used when applying 2SMR. This approximation can underestimate the variance of causal effects in MR, which can lead to an increased false-positive rate. An alternative is to use the second-order approximation of the standard error, which can considerably correct for the deviation of the first-order approximation. In this study, we simulated MR to show the degree to which the first-order approximation underestimates the variance. We show that depending on the specific situation, the first-order approximation can underestimate the variance almost by half when compared to the true variance, whereas the second-order approximation is robust and accurate.

• Management Science and Financial Engineering
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• v.19 no.2
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• pp.37-42
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• 2013

This paper suggests a numerical method for valuation of European and American options under the two L$\acute{e}$vy Processes, Normal Inverse Gaussian Model and the Variance Gamma model. The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the existing numerical method, the lattice-based method.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.4
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• pp.15-23
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• 1995

In this paper, we evaluate the performance of a transient queueing approximation when it is applied to modeling computer communication networks. An operational computer network that uses the ISO IS-IS(Intermediate System-Intermediate System) routing protocol is modeled as a Jackson network. The primary goal of the approximation pursued in the study was to provide transient queue statistics comparable in accuracy to the results from conventional Monte Carlo simulations. A closure approximation of the M/M/1 queueing system was extended to the general Jackson network in order to obtain transient queue statistics. The performance of the approximation was compared to a discrete event simulation under nonstationary conditions. The transient results from the two simulations are compared on the basis of queue size and computer execution time. Under nonstationary conditions, the approximations for the mean and variance of the number of packets in the queue erer fairly close to the simulation values. The approximation offered substantial speed improvements over the discrete event simulation. The closure approximation provided a good alternative Monte Carlo simulation of the computer networks.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.383-395
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• 1997

This paper proves that the standard bootstrap approximation for the least absolute deviation (LAD) estimate of .beta. in AR(1) processes with infinite variance error terms is asymptotically valid in probability when the bootstrap resample size is much smaller than the original sample size. The theoretical validity results are supported by simulation studies.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.625-636
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• 2011

This paper proposes two parametric entropy estimators, the minimum variance unbiased estimator and the maximum likelihood estimator, for the lognormal distribution for a comparison of the properties of the two estimators. The variances of both estimators are derived. The influence of the bias of the maximum likelihood estimator on estimation is analytically revealed. The distributions of the proposed estimators obtained by the delta approximation method are also presented. Performance comparisons are made with the two estimators. The following observations are made from the results. The MSE efficacy of the minimum variance unbiased estimator appears consistently high and increases rapidly as the sample size and variance, n and ${\sigma}^2$, become simultaneously small. To conclude, the minimum variance unbiased estimator outperforms the maximum likelihood estimator.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.10A
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• pp.1566-1575
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• 2000

This paper studies mismatched scalar quantization of a generalized gamma source by a quantizer that is optimally (in the mean square error sense) designed for another generalized gamma source. Specifically, it considers variance-mismatched quantization which occurs when the variance of the source to be quantized differs from tat of the designed-for source. The main result is the two distortion formulas derived from Bennett's integral. The first formula is an approximation expression that uses the outermost threshold of an optimum scalar quantizer, and the second formula, in turn, uses an approximation formula for this outermost threshold. Numerical results are obtained for Laplacian sources, which are example of a generalized gamma source, and comparisons are made between actual mismatched distortions and the two formulas. These numerical results show that the two formulas become more accurate, as the number of quantization points gets larger and the ratio of the source variance to that of the designed-for source gets bigger. For example, the formulas are within 2~4% of the actual distortion for approximately 64 quantization points or more. In conclusion, the proposed approximation formulas are considered to have contribution as closed formulas and for their accuracy.

• East Asian mathematical journal
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• v.34 no.3
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• pp.239-248
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• 2018

In this paper, we derive a closed-form formula of a second-order approximation for a European corrected option price under stochastic elasticity of variance model mentioned in Kim et al. (2014) [1] [J.-H. Kim, J Lee, S.-P. Zhu, S.-H. Yu, A multiscale correction to the Black-Scholes formula, Appl. Stoch. Model. Bus. 30 (2014)]. To find the explicit-form correction to the option price, we use Mellin transform approaches.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.170-177
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• 1998

In this paper, a unified solution of Hankel norm approximation problem is proposed by $\delta$-operator. To derive the main result, all-pass property is derived from the inner and co-inner property in the $\delta$-domain. The solution of all-pass becomes an optimal Hankel norm approximation problem in .delta.-domain through LLFT(Low Linear Fractional Transformation) inserting feedback term $\phi(\gamma)$, which is a free design parameter, to hold the error bound desired against the variance between the original model and the solution of Hankel norm approximation problem. The proposed solution does not only cover continuous and discrete ones depending on sampling interval but also plays a key role in robust control and model reduction problem. The verification of the proposed solution is exemplified via simulation for the zero-order Hankel norm approximation problem and the model reduction problem applied to a 16th order MIMO system.

• Journal of Korean Society for Quality Management
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• v.33 no.3
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• pp.149-155
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• 2005

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.135-141
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• 2006

Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.