• Communications for Statistical Applications and Methods
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• v.6 no.3
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• pp.929-938
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• 1999

We propose a criterion for testing homogeneity of diagonal covariance matrices of K multivariate normal populations. It is based on a factorization of usual likelihood ratio intended to propose and develop a criterion that makes use of properties of structures of the diagonal convariance matrices. The criterion then leads to a simple test as well as to an accurate asymptotic distribution of the test statistic via general result by Box (1949).

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.557-587
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• 2005

This paper elucidates the limiting Gaussian distribution of a class of rank order statistics {$T_N$} for two sample problem pertaining to empirical processes of the squared residuals from two independent samples of GARCH processes. A distinctive feature is that, unlike the residuals of ARMA processes, the asymptotics of {$T_N$} depend on those of GARCH volatility estimators. Based on the asymptotics of {$T_N$}, we empirically assess the relative asymptotic efficiency and effect of the GARCH specification for some GARCH residual distributions. In contrast with the independent, identically distributed or ARMA settings, these studies illuminate some interesting features of GARCH residuals.

• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.121-132
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• 1995

In this paper we consider optimal designs of partially step-stress life testing which is deviced for k-component series systems with the considerably long life time. Test items are first run simultaneously at use condition for a specified time, and the surviving items are then run at accelerated condition until a predetermined censoring time. The optimal criterion for the change time to accelerated condition is to minimized either the generalized asymptotic variance of maximum likelihood estimators of the hazard rates at use condition and the acceleration factors or the asymptotic variance of the maximum likelihood estimators of the acceleration factors.

• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.167-178
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• 1994

To estimate coefficient matrix in autoregressive model, usually ordinary least squares estimator or unconditional maximum likelihood estimator is used. It is unknown that for univariate AR(p) model, unconditional maximum likelihood estimator gives better power property that ordinary least squares estimator in testing for unit root with mean estimated. When autoregressive model contains multiple unit roots and unconditional likelihood function is used to estimate coefficient matrix, the seperation of nonstationary part and stationary part of the eigen-values in the estimated coefficient matrix in the limit is developed. This asymptotic property may give an idea to test for multiple unit roots.

• The Korean Journal of Applied Statistics
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• v.7 no.1
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• pp.103-112
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• 1994

An asymptotic property of the estimated eigenvalues for multivariate AR(p) process which consists of vector of nonstationary process and vector of stationary process is developed. All components of the nonstationary process are assumed to reveal random walk behavior. The asymptotic property is helpful in understanding multiple unit roots. In this paper we show the stationay part in multivariate AR(p) process does not affect the limiting distribution of estimated eigenvalues associated with the nonstationary process. A test statistic based on the ordinary least squares estimator for testing a certain number of multiple unit roots is suggested.

• International Journal of Reliability and Applications
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• v.7 no.1
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• pp.1-11
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• 2006

The better mean residual life at $t_0\;(BMRL-t_0)$ class of life distribution is introduced by Kulasekara and Park (1987). They proved that the $BMRL-t_0$ class contains the DMRL class, but it is a proper subclass of the NBUE class. In this paper we develop a new family of tests for testing exponentiality against the $BMRL-t_0\;(WMRL-t_0)$ alternatives based on the goodness of fit approach. It is shown that the suggested test is better than the one introduced by Kulasekara and Park (1987) in the sense of Pitman asymptotic efficiency values.

• 한국전산유체공학회:학술대회논문집
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• 2004.10a
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• pp.7-14
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• 2004

It is well known that preconditioning methods are efficient for convergence acceleration at compressible low Mach number flows. In this study, the original Euler equations and three preconditioners nondimensionalized differently are implemented in two dimensional inviscid bump flows using the 3rd order MUSCL and DADI schemes as flux discretization and time integration respectively. The multigrid and local time stepping methods are also used to accelerate the convergence. The test case indicates that a properly modified local preconditioning technique involving concepts of a global preconditioning one produces Mach number independent convergence. Besides, an asymptotic analysis for properties of preconditioning methods is added.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.217-227
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• 2009

Assuming that a given nonlinear function f : $\mathbf{R}{\rightarrow}\mathbf{R}$ has a zero $\alpha$with integer multiplicity $m{\geq}1$ and is sufficiently smooth in a small neighborhood of $\alpha$, we define extended leap-frogging Newton's method. We investigate the order of convergence and the asymptotic error constant of the proposed method as a function of multiplicity m. Numerical experiments for various test functions show a satisfactory agreement with the theory presented in this paper and are throughly verified via Mathematica programming with its high-precision computability.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.1
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• pp.177-196
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• 1997

In this paper, statistically optimal accelerated life test(ALT) plans considering statistical efficiency only and new compromise ALT plans to sacrifice some statistical efficiency in return for improved overall properties including estimobility probability and robustness for the model assumptions are developed under the assumptions of constant stress, intermittent inspection, Type I censoring and lognormal failure distribution which has been one of the popular choices of failure distributions in the extensive engineering applications of ALT. Computational experiments are conducted to compare with four ALT plans including two proposed ones under continuous and intermittent inspections over a range of parameter values in terms of asymptotic variance, sensitivities for guessed input values, and proportion of estimable samples, etc. The small and moderate sample properties for the proposed ALT plans designed under asymptotic criterion are also investigated by Monte Carlo simulation.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.159-171
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• 1994

Some rank score tests are proposed for testing the equality of all sampling distribution functions against umbrella location-scale alternatives in k-sample problem. Only the case of known peak $\ell$ is considered. Under the null hypothesis and a contiguous sequence of unbrella location-scale alternatives, the asymptotic properties of the proposed test statistics are investigated. Also, the asymptotic local powers are compared with each others. The results show that the tests based on the Chen-Wolfe rank analogue statistic are more powerful than others for unequally spaced umbrella location-scale alternatives and robust.