• Journal of the Korean Statistical Society
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• 제36권1호
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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.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.243-248
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• 1995

The problem of optimal design for a nonparametric regression with binary data is considered. The aim of the statistical analysis is the estimation of a quantal response surface in two dimensions. Bias, variance and IMSE of kernel estimates are derived. The optimal design density with respect to asymptotic IMSE is constructed.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 1998년도 The 12th Asia Quality Management Symposium* Total Quality Management for Restoring Competitiveness
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• pp.309-315
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• 1998

Process Capability can be expressed with a process index which indicates the incapability of a process to meet its specifications. This index is regarded as a process capability index(PCI) or more precisely as a process incapability index(PII). It is obtained from a simple transformation of a PCI. Greenwich and Jahr-Schaffrath(1995) considered the PII $C_{pp}$ which could be obtained from the transformation to the PCI, $C_{pm}$, and they provided the asymptotic distribution for $C_{pp}$ which was useful unless the process characteristic was normally distributed. However, some statistical inferences based on the asymptotic distribution need a large sample size. There are some processes which process engineers could not help obtaining sufficiently a large sample size. Thus, we have derived its corresponding bootstrap asymptotic distribution since bootstrapping would be a helpful technique for the PII, $C_{pp}$ which was nonparametric or free from assumptions of the distribution of the characteristic X. Moreover, we have constructed six bootstrap confidence intervals used in reducing bias of estimations based on the bootstrap asymptotic distribution and simulated their performances for $C_{pp}$,

• Journal of the Korean Data and Information Science Society
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• 제5권2호
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• pp.19-27
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• 1994

It is known that the maximum likelihood method does not provide explicit estimator for the scale parameter of the Weibull distribution based on Type-II censored samples. In this paper we provide an approximate maximum likelihood estimator (AMLE) of the scale parameter of the Weibull distribution with Type-II censoring. We obtain the asymptotic variance and simulate the values of the bias and the variance of this estimator based on 3000 Monte Carlo runs for n = 10(10)30 and r,s = 0(1)4. We also simulate the absolute biases of the MLE and the proposed AMLE for complete samples. It is found that the absolute bias of the AMLE is smaller than the absolute bias of the MLE.

• 응용통계연구
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• 제6권2호
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• pp.341-353
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• 1993

여러 개의 종으로 구성된 모집단에서 일정 크기의 표본을 추출하였을 경우, 다음차례에 뽑힐 종이 새로운 종이 될 조건부확률의 추정량으로서 가장 널리 사용되어 온 것은 Good(1953)이 경험적 베이지안 접근법을 사용하여 제안한 비모수추정량이다. Clayton과 Frees(1987)는 Good의 추정량에 대한 대안으로서 비모수최우추정량을 제안하고, 시뮬레이션을 통해 모집단이 비교적 불균일할 경우 자신들이 제안한 추정량이 Good의 추정량보다 평균제곱오차가 작음을 보여 주었고, Lee(1989)는 모집단이 균등분포에 비교적 가깝지 않은 절단기하분포를 따를 때 이를 점근적으로 규명하였다. 그러나 비모수최우추정량은 상당한 편의를 지니고 있는데, 본 연구에서는 이 편의의 일부를 보정한 새로운 추정량이 대부분의 모집단분포 형태에 있어 비모수최우추정량보다 평균제곱오차가 작으며, 모집단이 균일분포에 아주 가까운 경우를 제외하고는 Good의 추정량보다도 평균제곱오차가 작음을 점근적으로 규명하고, 이를 소표본 시뮬레이션을 통하여 확인하였다.

• 응용통계연구
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• 제25권4호
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• pp.681-695
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• 2012

In this paper, a family of estimators for the finite population variance investigated by Srivastava and Jhajj (1980) is studied under two different situations of random non-response considered by Tracy and Osahan (1994). Asymptotic expressions for the biases and mean squared errors of members of the proposed family are obtained; in addition, an asymptotic optimum estimator(AOE) is also identified. Estimators suggested by Singh and Joarder (1998) are shown to be members of the proposed family. A correction to the Singh and Joarder (1998) results is also presented.

• Journal of the Korean Data and Information Science Society
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• 제16권4호
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• pp.1159-1165
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• 2005

Basu et al. (1998) proposed a new density-based estimator, called the minimum density power divergence estimator (MDPDE), which avoid the use of nonparametric density estimation and associated complication such as bandwidth selection. Woodward et al. (1995) examined the minimum Hellinger distance estimator (MHDE), proposed by Beran (1977), in the case of estimation of the mixture proportion in the mixture of two normals. In this article, we introduce the MDPDE for a mixture proportion, and show that both the MDPDE and the MHDE have the same asymptotic distribution at a model. Simulation study identifies some cases where the MHDE is consistently better than the MDPDE in terms of bias.

• Wind and Structures
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• 제16권4호
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• pp.355-372
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• 2013

The Gringorten estimator has been extensively used in extreme value analysis of wind speed records to obtain unbiased estimates of design wind speeds. This paper reviews the derivation of the Gringorten estimator for the mean plotting position of extremes drawn from parents of the exponential type and demonstrates how it eliminates most of the bias caused by the classical Weibull estimator. It is shown that the coefficients in the Gringorten estimator are the asymptotic values for infinite sample sizes, whereas the estimator is most often used for small sample sizes. The principles used by Gringorten are used to derive a new Consistent Linear Unbiased Estimator (CLUE) for the mean plotting positions for the Fisher Tippett Type 1, Exponential and Weibull distributions and for the associated standard deviations. Analytical and Bootstrap methods are used to calibrate the bias error in each of the estimators and to show that the CLUE are accurate to better than 1%.

• Communications for Statistical Applications and Methods
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• 제22권6호
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• pp.655-664
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• 2015

A nonresponse adjusted raking ratio estimator that consists of weighting adjustment using estimated response probability and raking procedure is often used to reduce the nonresponse bias and keep the calibration property of the estimator. We investigated asymptotic properties of nonresponse adjusted raking ratio estimator and proposed a variance estimator. A simulation study is used to examine the performance of suggested estimators.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.27-32
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• 2000

To overcome boundary problems with wavelet regression, we propose a simple method that reduces bias at the boundaries. It is based on a combination of wavelet functions and low-order polynomials. The utility of the method is illustrated with simulation studies and a real example. Asymptotic results show that the estimators are competitive with other nonparametric procedures.