• Communications for Statistical Applications and Methods
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• 제20권4호
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• pp.247-257
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• 2013

A variety of practical problems can be addressed in the framework of rotation (successive) sampling. The present work presents a sample rotation pattern where sampling units are drawn on two successive occasions. The problem of estimation of population variance on current (second) occasion in two - occasion successive (rotation) sampling has been considered. A class of estimators has been proposed for population variance that includes many estimators as a particular case. Asymptotic properties of the proposed class of estimators are discussed. The proposed class of estimators is compared with the sample variance estimator when there is no matching from the previous occasion. Optimum replacement policy is discussed. Results are supported with the empirical means of comparison.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권2호
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• pp.123-135
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• 2016

This article deals with the pricing of Asian options under a constant elasticity of variance (CEV) model as well as a stochastic elasticity of variance (SEV) model. The CEV and SEV models are underlying asset price models proposed to overcome shortcomings of the constant volatility model. In particular, the SEV model is attractive because it can characterize the feature of volatility in risky situation such as the global financial crisis both quantitatively and qualitatively. We use an asymptotic expansion method to approximate the no-arbitrage price of an arithmetic average Asian option under both CEV and SEV models. Subsequently, the zero and non-zero constant leverage effects as well as stochastic leverage effects are compared with each other. Lastly, we investigate the SEV correction effects to the CEV model for the price of Asian options.

• Journal of the Korean Statistical Society
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• 제36권1호
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• pp.57-76
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• 2007

Kriging is a nonparametric regression method used in geostatistics for estimating curves and surfaces for spatial data. It may come as a surprise that the Kriging estimator, normally derived as the best linear unbiased estimator, is also the solution of a particular variational problem. Thus, Kriging estimators can also be interpreted as generalized smoothing splines where the roughness penalty is determined by the covariance function of a spatial process. We build off the early work by Silverman (1982, 1984) and the analysis by Cox (1983, 1984), Messer (1991), Messer and Goldstein (1993) and others and develop an equivalent kernel interpretation of geostatistical estimators. Given this connection we show how a given covariance function influences the bias and variance of the Kriging estimate as well as the mean squared prediction error. Some specific asymptotic results are given in one dimension for Matern covariances that have as their limit cubic smoothing splines.

• International Journal of Reliability and Applications
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• 제17권2호
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• pp.107-119
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• 2016

A new concept of aging classes namely new better (worse) than used at age $t_0$ in moment generating function order, $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$) is introduced. For the classes $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$), preservation under convolution, mixture, mixing and the homogeneous Poisson shock model are studied. In the sequel, nonparametric test is proposed, the asymptotic normality of the class is established and the asymptotic null variance is estimated. The percentiles and powers of this test are tabulated. The asymptotic efficiencies for some alternatives distributions are derived. Finally sets of real data are used as examples to elucidate the use of the proposed test in practical application.

• Communications for Statistical Applications and Methods
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• 제24권3호
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• pp.291-301
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• 2017

It is well known in a small sample that the maximum likelihood (ML) approach for variance components in the general linear model yields estimates that are biased downward. The ML estimate of residual variance tends to be downwardly biased. The underestimation of residual variance, which has implications for the estimation of marginal effects and asymptotic standard error of estimates, seems to be more serious in some limited dependent variable models, as shown by some researchers. An alternative frequentist's approach may be restricted or residual maximum likelihood (REML), which accounts for the loss in degrees of freedom and gives an unbiased estimate of residual variance. In this situation, the REML estimator is derived in a censored regression model. A small sample the REML is shown to provide proper inference on regression coefficients.

• Communications for Statistical Applications and Methods
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• 제17권4호
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• pp.575-589
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• 2010

Exponential L$\acute{e}$evy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.

• 한국통신학회논문지
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• 제30권11C호
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• pp.1116-1124
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• 2005

We investigated the mean and variance of the MSE and the MI-based image registration methods that have been widely applied for image registration. By using the first order Taylor series expansion, we have approximated the mean and the variance for one-dimensional image registration. The asymptotic results show that the MSE based method is unbiased and efficient for the same image registration problem while the MI-based method shows larger variance. However, for the different modality image registration problem, the MSE based method is largely biased while the MI based method still achieves registration. The results imply that the MI based method achieves robustness to the different image modalities at the cost of inefficiency. The analytical results are supported by simulation results.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 추계학술대회논문집A
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• pp.693-698
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• 2000

Aspects of classical information theory, such as rate distortion theory, investigate how to encode and decode information from an independently identically distributed source so that the asymptotic distortion rate between the source and its quantized representation is minimized. However, in most natural dynamics, the source state is highly corrupted by disturbances, and the measurement contains the noise. In recent coder-estimator sequence is developed for state estimation problem based on observations transmitted with finite communication capacity constraints. Unlike classical estimation problems where the observation is a continuous process corrupted by additive noises, the condition is that the observations must be coded and transmitted over a digital communication channel with finite capacity. However, coder-estimator sequence does not provide such a quantitative analysis as a variance for estimation error. In this paper, under the assumption that the estimation error is Gaussian distribution, a variance for coder-estimation sequence is proposed and its fitness is evaluated through simulations with a simple example.

• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.603-613
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• 2001

A test based on score statistic is derived for detecting homoscedasticity of errors in unbalanced random effects linear model. A small simulation study is performed to investigate the finite sample behaviour of the test statistic which is known to have an asymptotic chi-square distribution under the null hypothesis.

• Journal of the Korean Statistical Society
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• 제25권2호
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• pp.217-233
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• 1996

This paper gives a rigorous proof of an asymptotic result about bias and variance for a transformation-based nonparametric regression estimator proposed by Park et al (1995).