• Communications for Statistical Applications and Methods
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• v.26 no.2
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• pp.91-102
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• 2019

In this paper, we propose a new estimation method based on a weighted linear regression framework to obtain some estimators for unknown parameters in a two-parameter Rayleigh distribution under a progressive Type-II censoring scheme. We also provide unbiased estimators of the location parameter and scale parameter which have a nuisance parameter, and an estimator based on a pivotal quantity which does not depend on the other parameter. The proposed weighted least square estimator (WLSE) of the location parameter is not dependent on the scale parameter. In addition, the WLSE of the scale parameter is not dependent on the location parameter. The results are compared with the maximum likelihood method and pivot-based estimation method. The assessments and comparisons are done using Monte Carlo simulations and real data analysis. The simulation results show that the estimators ${\hat{\mu}}_u({\hat{\theta}}_p)$ and ${\hat{\theta}}_p({\hat{\mu}}_u)$ are superior to the other estimators in terms of the mean squared error (MSE) and bias.

• 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 Korean Journal of Applied Statistics
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• v.24 no.3
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• pp.445-453
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• 2011

Almost all small area estimations are obtained by minimizing the mean squared error. Recently relative error prediction methods have been developed and adapted to small area estimation. Usually the estimators obtained by using relative error prediction is called a shrinkage estimator. Especially when data set consists of large range values, the shrinkage estimator is known as having good statistical properties and an easy interpretation. In this paper we study the shrinkage estimators based on logistic regression type estimators for small area estimation. Some simulation studies are performed and the Economically Active Population Survey data of 2005 is used for comparison.

• Communications for Statistical Applications and Methods
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• v.26 no.4
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• pp.347-357
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• 2019

We propose new classes of estimators of population mean under non-response using bivariate auxiliary information. Some improved regression (or difference) type estimators have been proposed in four different situations of non response along with their properties and the expressions for the bias and mean square errors of the proposed estimators are derived under double (two-stage) sampling scheme. The properties of the suggested class of estimators are studied and it is observed that the proposed estimators performed better when compared to conventional estimators proposed by Singh and Kumar (Journal of Statistical Planning and Inference, 140, 2536-2550, 2010b), Shabbir and Khan (Communications in Statistics - Theory and Methods, 42, 4127-4145, 2013) and Bhushan and Naqvi (Journal of Statistics and Management Systems, 18, 573-602, 2015). A comparative study is also conducted both theoretically as well as empirically in order to support the results.

• Journal of the Korean Statistical Society
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• v.35 no.1
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• pp.1-23
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• 2006

In this paper we consider an estimation of the discontinuous variance function in nonparametric heteroscedastic random design regression model. We first propose estimators of the change point in the variance function and then construct an estimator of the entire variance function. We examine the rates of convergence of these estimators and give results for their asymptotics. Numerical work reveals that using the proposed change point analysis in the variance function estimation is quite effective.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.288-295
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• 1995

In this paper a hypotheses test procedure based on the least absolute deviation estimators for the unknown parameters in nonlinear regression models is investigated. The asymptotic distribution of the proposed likelihood ratio test statistic are established voth under the null hypotheses and a sequence of local alternative hypotheses. The asymptotic relative efficiency of the proposed test with classical test based on the least squares estimator is also discussed.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.15-27
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• 2001

One proposal is made for constructing nonparametric estimator of slope parameters in a regression model under symmetric error distributions. This estimator is based on the use of idea of Johns for estimating the center of the symmetric distribution together with the idea of regression quantiles and regression trimmed mean. This nonparametric estimator and some other L-estimators are studied by Monte Carlo.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.709-717
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• 2008

The difference of two one-sided kernel estimators is usually used to detect the location of the discontinuity points of regression function. The large absolute value of the statistic imply discontinuity of regression function, so we may use the difference of two one-sided kernel estimators as the test statistic for testing null hypothesis of a smooth regression function. The problem is, however, we only know the asymptotic distribution of the test statistic under $H_0$ and we hardly expect the good performance of test if we rely solely on the asymptotic distribution for determining the critical points. In this paper, we show that if we adjust the bias of test statistic properly, the asymptotic rules hold for even small sample size situation.

• Journal of the Korean Statistical Society
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• v.29 no.2
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• pp.201-217
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• 2000

The method of generalized estimating equations (GEE) has become very popular for the analysis of longitudinal data. We extend this work to the use of M-estimators; the resultant regression estimates are robust to heavy tailed errors and to outliers. The proposed method does not require correct specification of the dependence structure between observation, and allows for heterogeneity of the error. However, an estimate of the dependence structure may be incorporated, and if it is correct this guarantees a higher efficiency for the regression estimators. A goodness-of-fit test for checking the adequacy of the assumed M-estimation regression model is also provided. Simulation studies are conducted to show the finite-sample performance of the new methods. The proposed methods are applied to a real-life data set.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.951-959
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• 2014

Recently Hazelton and Turlach (2009) proposed a weighted kernel density estimator for the deconvolution problem. In the case of Gaussian kernels and measurement error, they argued that the weighted kernel density estimator is a competitive estimator over the classical deconvolution kernel estimator. In this paper we consider weighted kernel density estimators when sample observations are contaminated by double exponentially distributed errors. The performance of the weighted kernel density estimators is compared over the classical deconvolution kernel estimator and the kernel density estimator based on the support vector regression method by means of a simulation study. The weighted density estimator with the Gaussian kernel shows numerical instability in practical implementation of optimization function. However the weighted density estimates with the double exponential kernel has very similar patterns to the classical kernel density estimates in the simulations, but the shape is less satisfactory than the classical kernel density estimator with the Gaussian kernel.