• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.235-245
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• 2000

In this paper, we consider the Regression Quantiles Estimators in nonlinear regression models. This paper provides the sufficient conditions for strong consistency and asymptotic normality of proposed estimation and drives asymptotic relative efficiency of proposed estimatiors with least square estimation. We give some examples and results of Monte Carlo simulation to compare least square and regression quantile estimators.

• Journal of the Korean Statistical Society
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• v.8 no.1
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• pp.23-36
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• 1979

In the multiple linear regression model a class of weighted least absolute error estimaters, which minimize the sum of weighted absolute residuals, is proposed. It is shown that the weighted least absolute error estimators with Wilcoxon scores are equivalent to the Koul's Wilcoxon type estimator. Therefore, the asymptotic efficiency of the proposed estimator with Wilcoxon scores relative to the least squares estimator is the same as the Pitman efficiency of the Wilcoxon test relative to the Student's t-test. To find the estimates the iterative weighted least squares method suggested by Schlossmacher is applicable.

• The Korean Journal of Applied Statistics
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• v.9 no.1
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• pp.139-152
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• 1996

In this paper we propose nonparametric tests using optimal weights for umbrella alternatives in a randomized block design. We obtain the optimal weights by maximizing the asymptotic relative efficiency of the proposed test statistics with respect to Mack and Wolf(1981) type test statistic, and investigate asymptotic relative efficiencies of the proposed test statistics using these optimal weights relative to Mack and Wolfe type statistics and linear rank statistic. Throughout simulations for small samples, the proposed test statistic has good powers rather than the other two tests when the block sizes are different.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.123-133
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• 2015

In this paper, the problem of testing exponentiality against net decreasing variance residual lifetime (NDVRL) classes of life distributions is investigated. For this property a nonparametric test is presented based on kernel method. The test is presented for complete and right censored data. Furthermore, Pitman's asymptotic relative efficiency (PARE) is discussed to assess the performance of the test with respect to other tests. Selected critical values are tabulated. Some numerical simulations on the power estimates are presented for proposed test. Finally, numerical examples are presented for the purpose of illustrating our test.

• 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.9 no.1
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• pp.101-113
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• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• Journal of the Korean Statistical Society
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• v.7 no.1
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• pp.17-26
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• 1978

For testing $\beta_i=\beta, i=1,...,k$, in the regression model $Y_{ij} = \alpha_i + \beta_ix_{ij} + e_{ij}, j=1,...,n_i$, a simple and robust test based on Kendall's tau is proposed. Its asymptotic distribution is proved to be chi-square under the null hypthesis and noncentral chi-square under an appropriate sequence of alternatives. For the optimal designs, the asymptotic relative efficiency of the proposed procedure with respect to the least squares procedure is the same as that of the Wilcoxon test with respect to the t-test.

• ETRI Journal
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• v.18 no.3
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• pp.207-213
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• 1996

This paper proposes a new nonparametric test for testing the null hypothesis that the MRL is constant against the alternative hypothesis that the MRL is decreasing (increasing) for ramdomly censored data. The proposed test statistic is a L-statistic, and we use L-statistic theory to establish its asymptotic normality of the test statistic. We discuss the efficiency loss due to censoring and also calculate the asymptotic relative efficiencies of our test statistic with respect to the Chen, Hollander and Langberg's test for several alternatives.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.141-153
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• 2006

In this paper, we present the U-Statistic test for testing exponentiality against new renewal better than used (NRBU) based on a goodness of fit approach. Selected critical values are tabulated for sample sizes n=5(1)30(10)50. The asymptotic Pitman relative efficiency relative to (NRBU) test given in the work of Mahmoud et all (2003) is studied. The power estimates of this test for some commonly used life distributions in reliability are also calculated. Some of real examples are given to elucidate the use of the proposed test statistic in the reliability analysis. The problem in case of right censored data is also handled.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.251-264
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• 1998

When the LRT is not feasible, we define quasi-LRT(QLRT) as a modification of the LRT Under some appropriate conditions the QLRT shares Bahadur optimality and Bartlett Adjustability with the LRT. When we can find maximum likelihood estimator under the null parameter space but not under the unrestricted parameter space, our QLRT is Bahadur optimal as is the LRT We suggest the stopping rule of the Newton-Raphson iterations for constructing the QLRT statistics which are Bartlett adjustable.