• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.543-554
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• 1997

A family of some capability indices { $C_{p}$(.alpha.,.beta.); .alpha..geq.0, .beta..geq.0}, containing the indices $C_{p}$, $C_{{pk}}$, $C_{{pm}}$, and $C_{{pmk}}$, has been defined by Vannman(1993) for the case of two-sided specification interval. By varying the parameters of the family various capability indices with suitable properties are obtained. We derive tha asymptotic distribution of the family { $C_{p}$(.alpha.,.beta.); .alpha..geq.0,.beta..geq.0} under general proper conditions. It is also shown that the bootstrap approximation to the distribution of the estimator $C_{p}$(.alpha., .beta.) is vaild for almost all sample sequences. These asymptotic distributions would be used in constructing some bootstrap confidence intervals.tervals.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.337-346
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• 1996

The chi-squared type statistic generated from the empirical process can be used for testing the goodness of fit hypothesis on iid random sample. Lee (1995) showed that under some conditions, the chi-squared type statistic is asymptotically maximin in the sense of Strasser (1985). Since the chi-squared type statistic depends on the choice of *points in the unit interval, it is worth investigating the points yielding more efficient tests. Motivated by this viewpoint, we are led to study the asymptotic relative efficiency of chi-squared type tests in the same setting of Lee (1995). Some examples are given for illustration.

• Journal of the Korean Statistical Society
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• v.36 no.1
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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.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.303-312
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• 1995

We consider the following type of general semi-parametric non-linear regression model : $y_i = f_i(\theta) + \epsilon_i, i=1, \cdots, n$ where ${f_i(\cdot)}$ represents the set of non-linear functions of the unknown parameter vector $\theta' = (\theta_1, \cdots, \theta_p)$ and ${\epsilon_i}$ represents the set of measurement errors with unknown distribution. Under suitable finite-sample, small-dispersion asymptotic framework, we derive a general lower bound for the asymptotic mean squared error (AMSE) matrix of the Gauss-consistent estimator of $\theta$. We then prove the fundamental result that the general non-linear least squares estimator (NLSE) is an optimal estimator within the class of all regular Gauss-consistent estimators irrespective of the type of the distribution of the measurement errors.

• Proceedings of the Korean Reliability Society Conference
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• 2004.07a
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• pp.167-175
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• 2004

A nonparametric procedure is proposed to test the exponentiality against the hypothesis that one life distribution has a greater residual life times than the other life distribution. Such a hypothesis turns out to be equivalent to the one that one failure rate is greater than the other and so the proposed test works as a competitor to more IFR tests by Kochar (1979, 1981) and Cheng (1985). Our test statistic utilizes the U-statistics theory and a large sample nonpara metric test is established. The power of the proposed test is discussed by calculating the Pitman asymptotic relative efficiencies against several alter native hypotheses. A numerical example is presented to exemplify the proposed test.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.10
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• pp.848-855
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• 1989

The asymptotic properties of the Overdetermined Yule-Walker (OYW) estimators were studied. A formula was derived for the asymptotic covariance matrix of the estimation errors. It verified the experimentally observed fact that the frequency estimation accuracy is generally improved as the number of Yule-Walker equations is increased. The asymptotic estimation accuracies of the OYW method were compared with the Cramer-Rao low bound.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.235-245
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• 2000

In this paper, we consider the Regression Quantiles Estimators in nonlinear regression models. This paper provides the sufficient conditions for strong consistency and asymptotic normality of proposed estimation and drives asymptotic relative efficiency of proposed estimatiors with least square estimation. We give some examples and results of Monte Carlo simulation to compare least square and regression quantile estimators.

• International Journal of Reliability and Applications
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• v.11 no.2
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• pp.139-151
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• 2010

The main objective of this study is to present a new approach to obtain moment inequalities for the new better than renewal used (NBRU) class of life distributions. In order to achieve our main objective, the moment inequalities for NBRU class of life distribution using the new approach has been derived and then a new test for testing exponentiality against NBRU class based on these inequalities has been constructed. Then we calculate the Pitman asymptotic efficiency for the proposed test using some alternative distributions and comparing it with the other tests. Moreover, we make a comparison between Pittman asymptotic efficiencies (PAE's) and PAE's of some other tests. A simulation study is conducted to calculate the upper critical values and the power estimate of the proposed test for some common alternatives. Finally, we apply the suggested test to some real data.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.858-863
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• 2010

In this paper, we study the asymptotic behavior of solutions for the delay semilinear fuzzy integrodifferential systems on $E^1_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E^1_N$.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.6
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• pp.554-557
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• 2008

We analyze the stability property of a class of nonlinear time-delay systems with time-varying delays. We present a time-delay independent sufficient condition for the global asymptotic stability. In order to prove the sufficient condition, we exploit the inherent property of the considered systems instead of applying the Krasovskii or Razumikhin stability theory that may cause the mathematical difficulty of analysis. We prove the sufficient condition by constructing two sequences that represent the lower and upper bound variations of system state in time, and showing the two sequences converge to an identical point, which is the equilibrium point of the system. The simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.