• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.417-426
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• 2001

This paper addresses the nonparametric Bayesian estimation for the exponential populations under type II censoring. The Dirichlet process prior is used to provide nonparametric Bayesian estimates of parameters of exponential populations. In the past, there have been computational difficulties with nonparametric Bayesian problems. This paper solves these difficulties by a Gibbs sampler algorithm. This procedure is applied to a real example and is compared with a classical estimator.

• Journal of the Korean Data and Information Science Society
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• 제9권2호
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• pp.173-177
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• 1998

This paper presents the asymptotic relative efficiency of the nonparametric estimator relative to the parametric maximum likelihood estimator of the reliability function under the proportional hazards model of random censorship. Also we examine the efficiency loss due to censoring proportions and misson times.

• Journal of the Korean Statistical Society
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• 제30권4호
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• pp.645-660
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• 2001

In this paper we propose a goodness-of-fit test statistic for testing the (null) parametric model versus the (alternative) nonparametric model. Most of existing nonparametric test statistics are based on the residuals which are obtained by regressing the data to a parametric model. Our test is based on the bootstrap estimator of the probability that the smoothing parameter estimator is infinite when fitting residuals to cubic smoothing spline. Power performance of this test is investigated and is compared with many other tests. Illustrative examples based on real data sets are given.

• Journal of the Korean Statistical Society
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• 제33권4호
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• pp.435-447
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• 2004

In additive nonparametric regression, Linton and Nielsen (1995) showed that the marginal integration when applied to the local linear smoother produces a rate-optimal estimator of each univariate component function for the case where the dimension of the predictor is two. In this paper we give new formulas for the bias and variance of the marginal integration regression estimators which are valid for boundary areas as well as fixed interior points, and show the local linear marginal integration estimator is in fact rate-optimal when the dimension of the predictor is less than or equal to four. We extend the results to the case of the local polynomial smoother, too.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.111-118
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• 1999

We treat the problem of estimating reliability R(t) = P[Y(t) < X(t)] in the time dependent strength-stress model in which a unit of strength X(t) is subjected to environmental stress Y(t) at time t. In this paper two nonparametric approaches to estimate of R(t) are analyzed and compared with parametric method by simulation.

• Journal of the Korean Statistical Society
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• 제35권1호
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• pp.105-114
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• 2006

In this paper we propose a simple and computationally attractive difference-based variance estimator in nonparametric regression models with multivariate predictors. We show that the estimator achieves $n^{-1/2}$ rate of convergence for regression functions with only a first derivative when d, the dimension of the predictor, is less than or equal to 4. When d > 4, the rate turns out to be $n^{-4/(d+4)}$ under the first derivative condition for the regression functions. A numerical study suggests that the proposed estimator has a good finite sample performance.

• Journal of the Korean Data and Information Science Society
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• 제22권6호
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• pp.1223-1232
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• 2011

Tong and Wang's estimator (2005) is a new approach to estimate the error variance using least squares method such that a simple linear regression is asymptotically derived from Rice's lag- estimator (1984). Their estimator highly depends on the setting of a regressor and weights in small sample sizes. In this article, we propose a new approach via a local quadratic approximation to set regressors in a small sample case. We estimate the error variance as the intercept using a ridge regression because the regressors have the problem of multicollinearity. From the small simulation study, the performance of our approach with some existing methods is better in small sample cases and comparable in large cases. More research is required on unequally spaced points.

• Journal of the Korean Statistical Society
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• 제29권3호
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• pp.307-313
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• 2000

Suppose we have a set of data X1, ···, Xn and employ kernel density estimator to estimate the marginal density of X. in this article bandwith selection problem for kernel density estimator is examined closely. In particular the Kullback-Leibler method (a bandwith selection methods based on average square error (ASE)) is considered.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.111-119
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• 2007

In this paper, we develop a nonparametric Bayesian methodology of estimating an unknown distribution function F at the given survival time with current status data under the assumption of Dirichlet process prior on F. We compare our algorithm with the nonparametric maximum likelihood estimator through application to simulated data and real data.

• 응용통계연구
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• 제25권3호
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• pp.457-464
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• 2012

Small area estimation is a statistical inference method to overcome the large variance due to the small sample size allocated in a small area. Recently some nonparametric estimators have been applied to small area estimation. In this study, we suggest a nonparametric mixed effect small area estimator using kernel smoothing and compare the small area estimators using labor statistics.