• 한국시뮬레이션학회:학술대회논문집
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• 한국시뮬레이션학회 2000년도 추계학술대회 논문집
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• pp.6-10
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• 2000

In regression model we estimate the unknown parameters using various methods. There are the least squares method which is the most general, the least absolute deviation, the regression quantile and the asymmetric least squares method. In this paper, we will compare each others with two case: to begin with the theoretical comparison in the asymptotic sense, and then the practical comparison using Monte Carlo simulation for a small sample size.

• Journal of the Korean Data and Information Science Society
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• 제18권3호
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• pp.669-678
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• 2007

An algorithm to detect the number of discontinuity points of the variance function in regression model is proposed. The proposed algorithm is based on the left and right one-sided kernel estimators of the second moment function and test statistics of the existence of a discontinuity point coming from the asymptotic distribution of the estimated jump size. The finite sample performance is illustrated by simulated example.

• Communications for Statistical Applications and Methods
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• 제17권3호
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• pp.349-356
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• 2010

The ordinary least squares based estimator of the disturbance variance in a regression model for spatial panel data is shown to be asymptotically unbiased and weakly consistent in the context of SAR(1), SMA(1) and SARMA(1,1)-disturbances when there is measurement error in the regressor matrix.

• Communications for Statistical Applications and Methods
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• 제22권1호
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• pp.81-93
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• 2015

Validity of the stationary bootstrap of Politis and Romano (1994) is proved for U-statistics under strong mixing. Weak and strong consistencies are established for the stationary bootstrap of U-statistics. The theory is applied to a symmetry test which is a U-statistic regarding a kernel density estimator. The theory enables the bootstrap confidence intervals of the means of the U-statistics. A Monte-Carlo experiment for bootstrap confidence intervals confirms the asymptotic theory.

• Journal of the Korean Statistical Society
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• 제26권4호
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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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• 제24권2호
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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.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.109-114
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• 2002

In this paper we propose a change-point estimator with left and right regressions using the sample Fourier coefficients on the orthonormal bases. The asymptotic properties of the proposed change-point estimator are established. The limiting distribution and the consistency of the estimator are derived.

• Communications for Statistical Applications and Methods
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• 제6권2호
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• pp.345-356
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• 1999

This paper deals with the problem of estimating regression coefficients in nonlinear regression model having random regressor. The sufficient conditions for consistency of the $L_1$-estimator with random regressor are given and discussed in this paper. An example is given to illustrate the application of the main results.

• Communications for Statistical Applications and Methods
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• 제7권3호
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• pp.731-739
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• 2000

Conditional least square estimators for the parameters of he NLAR(p) time series models are obtained. it is also shown that these estimators are consistent and asymptotically normal.

• Communications for Statistical Applications and Methods
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• 제10권2호
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• pp.399-422
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• 2003

In actual manufacturing industries, process capability analysis often entails characterizing or assessing processes or products based on more than one engineering specification or quality characteristic. Since these characteristics are related, it is a risky undertaking to represent variation of even a univariate characteristic by a single index. Therefore, the desirability of using vector-valued process capability index(PCI) arises quite naturally. In this paper, some vector-valued ${PCI}_p$ ${C}_p$=(${C}_{px}$, ${C}_{py}$),${C}_{pk}$=(${C}_{pkx}$, ${C}_{pky}$) and ${C}_{pm}$=(${C}_{pmx}$, ${C}_{pmy}$) considering univariate PCIs ${C}_p$,${C}_{pk}$ and ${C}_{pm}$ are studied. First, we propose some asymptotic confidence regions of our vector-valued PCIs with bootstrap. And we examine the performance of asymptotic confidence regions of our vector-valued PCIs ${C}_p$ and ${C}_{pk}$ under the assumption of bivariate normal distribution BN($\mu_{x}$, $\mu_{y}$, $\sigma_{x}^{2}$, $\sigma_{y}^{2}$, $\rho$) and bivariate chi-square distribution Bivariate $x^2$(5,5,$\rho$).