• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.593-604
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• 2003

In this paper we introduce the integral type Lupas-$B{\acute{e}}zier$ operator $\tilde{B}_{n,{\alpha}}$, which is a new approximation operator of probabilistic type. We study the rate of pointwise convergence of the operators $\tilde{B}_{n,{\alpha}}$ for local bounded functions and get an asymptotically estimate by means of some methods and techniques of probability theory.

• 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.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.3
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• pp.142-147
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• 2003

We consider a single-input-single-output nonlinear system which can be represented in a normal form. The nonlinear system has a modeling uncertainties including the input coefficient uncertainty. A high-gain observer is used to estimate the states variables to reject a modeling uncertainty. A globally bounded output feedback integral sliding mode control is proposed to stabilize the closed loop system. The proposed integral sliding mode control can asymptotically stabilize the closed loop system in the presence of input coefficient uncertainty.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.159-171
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent ; that is, the power of the test will not approach 1 as the sample size increases. Hence we give a test based on the ratio of two asymptotically efficient estimates of scale. We also have conducted a power study to compare the test procedures, using Monte Carlo samples from a wide range of alternatives. It is found that the suggested statistics have higher power for the alternatives with the coefficient of variation greater that or equal to 1.

• Communications for Statistical Applications and Methods
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• v.9 no.3
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• pp.629-637
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• 2002

Shapiro and Wilk(1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test based on the statistic is inconsistent Kim(2001a) proposed a modified Shapiro-Wilk's test statistic using the ratio of two asymptotically efficient estimators of scale. In this paper, we study the consistency of the proposed test.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.473-481
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent. Kim(2001) proposed a modified Shapiro-Wilk's test statistic based on the ratio of tow asymptotically efficient estimates of scale. In this paper, we study the asymptotic behavior of the statistic using the approximation of the quantile process by a sequence of Brownian bridges and represent the limit null distribution as an integral of a Brownian bridge.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.101-113
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• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.351-363
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• 2016

In this paper, we consider the entropy-based goodness of fit test (Vasicek's test) for a composite hypothesis. The test measures the discrepancy between the nonparametric entropy estimate and the parametric entropy estimate obtained from an assumed parametric family of distributions. It is shown that the proposed test is asymptotically normal under regularity conditions, but is affected by parameter estimates. As a remedy, a bootstrap version of Vasicek's test is proposed. Simulation results are provided for illustration.

• Communications for Statistical Applications and Methods
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• v.3 no.3
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• pp.113-123
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• 1996

Data-dependent (adaptive) choice of asymptotically efficient score functions for rank estimators and M-estimators of regression parameters in a linear regression model with left-truncated and right-censored data are developed herein. The locally adaptive smoothing techniques of Muller and Wang (1990) and Uzunogullari and Wang (1992) provide good estimates of the hazard function h and its derivative h' from left-truncated and right-censored data. However, since we need to estimate h'/h for the asymptotically optimal choice of score functions, the naive estimator, which is just a ratio of estimated h' and h, turns out to have a few drawbacks. An altermative method to overcome these shortcomings and also to speed up the algorithms is developed. In particular, we use a subroutine of the PPR (Projection Pursuit Regression) method coded by Friedman and Stuetzle (1981) to find the nonparametric derivative of log(h) for the problem of estimating h'/h.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.3
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• pp.130-135
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• 2001

In this paper, an observer-based adaptive controller is proposed to control the longitudinal motion of vehicles. The standard gradient method will be used to estimate the vehicle parameters, mass, time constant, etc. The nonlinear model between the driving force and the vehicle acceleration will be chosen to design the state observer for the vehicle velocity and acceleration. It will be shown that the proposed observer is exponentially stable, and that the adaptive controller proposed on this paper is stable. It will be proved that the errors of the relative distance, velocity and acceleration converge to zero asymptotically fast, and that the overall system is also asymptotically stable. The simulation results are presented to investigate the effectiveness of the proposed method.