• Journal of the Korean Statistical Society
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• 제26권1호
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• pp.1-22
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• 1997

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.

• Water Engineering Research
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• 제3권3호
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• pp.195-202
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• 2002

The mean is generally used as a point estimator in water-quality data. Unfortunately, the nonnormal and skewed distributions of data hinder the direct application of the mean, which is inappropriate statistics in this case. The use of robust statistics such as L, M, and R-estimators are recommended and become more efficient. The median (L-estimator), the biweight (M-estimator), and the Hodges-Lehmann method (R-estimator) are briefly introduced and applied in this paper. From the actual data analyses, it is known that the median does not guarantee robustness for a small number of data sets, and robust measures of location or the arithmetic mean without outliers are highly recommended if the distribution has tails or outliers. Care must be taken to measure the location because water quality level within a water body can change depending on the selected point estimator.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.653-657
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• 2005

Eigenstructure of a spatial design matrix of Matheron's variogram estimator in $R^1$ is derived. It is shown that the spatial design matrix in $R^1$ with n/2$\le$h < n has a nice spectral decomposition. The mean, variance, and covariance of this estimator are obtained using the eigenvalues of a spatial design matrix. We also found that the lower bound and the upper bound of the normalized Matheron's variogram estimator.

• 품질경영학회지
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• 제15권2호
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• pp.27-37
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• 1987

In life testing problem, many authors obtained the minimum variance unbiased estimator of $P_r$[X>Y] for the exponential family generally and conceptually. In this paper, we study the maximum likelihood estimator and minimum variance unbiased estimator of $P_r$[X>Y] in exponential X and normal Y.

• International Journal of Reliability and Applications
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• 제12권1호
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• pp.61-77
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• 2011

One of the most important problems in the estimation of the parameter of the failure model, is the cost of experimental sampling units, which can be reduced by using any prior information available about ${\theta}$, and devising a two-stage pooling shrunken estimation procedure. We have proposed an estimator of the reliability function (R(t)) of the exponential model using two-stage time censored data when a prior value about the unknown parameter (${\theta}$) is available from the past. To compare the performance of the proposed estimator with the classical estimator, computer intensive calculations for bias, mean squared error, relative efficiency, expected sample size and percentage of the overall sample size saved expressions, were done for varying the constants involved in the proposed estimator (${\tilde{R}}$(t)).

• International Journal of Reliability and Applications
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• 제1권2호
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• pp.123-131
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• 2000

This paper concerns with the consistent estimator for the fuzzy expectation of a random variable taking values in the space F($R^p$) of upper semicontinuous convex fuzzy subsets of $R^p$ with compact support. We introduce the concept of a fuzzy sample mean and show that the fuzzy sample mean is a strong consistent estimator for the fuzzy expectation. Some examples are given to illustrate the main result.

• 대한수학회논문집
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• 제11권4호
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• pp.1187-1192
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• 1996

It is known that an unbiased estimator of f(p) for binomial B(n,p) exists if and only if f is a polynomial of degree at most n, in which case the unbiased estimator of a real-valued function $f(p), p = (p_0,p_1,\cdots,p_r)$ is unique. In general, this estimator has the serious fault of not being range preserving; that is, its value may fall outside the range of f(p). In this article, a condition on a real-valued function f is derived that is necessary for the unbiased estimator to be range preserving that this is sufficient when n is large enough.

• Journal of the Korean Statistical Society
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• 제31권2호
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• pp.229-235
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• 2002

A generalized Stein-rule estimator of the vector of regression coefficients in linear regression model is considered and its properties are analyzed according to the criterion of Pitman nearness. A comparative study shows that the generalized Stein-rule estimator representing a class of estimators contains particular members which are better than the usual Stein-rule estimator according to the Pitman closeness.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2000년도 추계학술대회 학술발표 논문집
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• pp.39-43
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• 2000

In this paper, we show that the fuzzy sample mean is a strong consistent estimator for the expectation of a fuzzy random set taking values in the space F(R$\^$/p) of upper semicontinuous convex fuzzy subsets of R$\^$/p with compact support.

• 응용통계연구
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• 제28권3호
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• pp.417-427
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• 2015

표본의 대표성을 측정하기 위한 척도로 응답률이 사용된다. 즉 높은 응답률일수록 표본의 대표성을 더 잘 나타낸다고 할 수 있다. 그러나 높은 응답률이라 할지라도 무응답이 존재하는 것이므로 표본의 대표성을 설명하기에는 한계가 있는 경우가 발생한다. 그래서 Schouten 등 (2009)에서는 R-indicator라는 새로운 척도를 제시하여 표본의 대표성을 더 설명할 수 있게 하였다. 본 논문에서는 R-indicator도 표본에 의해 추정되어야 한다는 것에 착안하여 그것에 관한 새로운 추정량을 제시한다. 또한 여러 모의실험하에 R-indicator의 대표성으로써의 설명력과 제안된 추정량의 편향과 효율을 기존의 추정량과 비교분석하며 실제자료에도 제안한 추정량을 적용하여 표본의 대표성을 설명한다.