• Journal of the Korean Statistical Society
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• 제30권4호
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• pp.551-561
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• 2001

This paper deals with the asymptotic properties for statistical inferences of the parameters in nonlinear regression models. As an optimal criterion for robust estimators of the regression parameters, the regression quantile method is proposed. This paper defines the regression quintile estimators in the nonlinear models and provides simple and practical sufficient conditions for the asymptotic normality of the proposed estimators when the parameter space is compact. The efficiency of the proposed estimator is especially well compared with least squares estimator, least absolute deviation estimator under asymmetric error distribution.

• Journal of the Korean Statistical Society
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• 제32권1호
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• pp.47-64
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• 2003

In this paper, we consider the asymptotic properties of asymmetric least squares estimators for nonlinear regression models. This paper provides sufficient conditions for strong consistency and asymptotic normality of the proposed estimators and derives asymptotic relative efficiency of the pro-posed estimators to the regression quantile estimators. We give some examples and results of a Monte Carlo simulation to compare the asymmetric least squares estimators with the regression quantile estimators.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.373-384
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• 2003

In this paper, we consider the asymptotic properties of regression quantile estimators for the nonlinear regression model when dependent variables are subject to censoring time, and propose the sufficient conditions which ensure consistency and asymptotic normality for regression quantile estimators in censored nonlinear regression model. Also, we drive the asymptotic relative efficiency of the censored regression model with respect to the ordinary regression model.

• Journal of the Korean Statistical Society
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• 제25권1호
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• pp.25-37
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• 1996

In this paper, we propose regression estimators based on a partial replacement sampling scheme over two successive occasions and derive the minimum variances of them. PPSWR, RHC, $\pi$PS and PPSWOR schemes are considered to select unequal probability samples on two occasions. Simulation results over four populations are given for comparison of composite estimators and regression estimators.

• Journal of the Korean Data and Information Science Society
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• 제13권1호
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• pp.157-164
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• 2002

In this paper, we consider the strong consistency of the regression quantiles estimators for the nonlinear regression models when dependent variables are subject to censoring, and provide the sufficient conditions which ensure the strong consistency of proposed estimators of the censored regression models. one example is given to illustrate the application of the main result.

• Journal of the Korean Data and Information Science Society
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• 제14권2호
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• pp.153-165
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• 2003

This paper considers the likelihood ratio test statistic based on nonlinear regression quantiles estimators in order to test of hypothesis about the regression parameter $\theta_o$ and derives asymptotic distribution of proposed test statistic under the null hypothesis and a sequence of local alternative hypothesis. The paper also investigates asymptotic relative efficiency of the proposed test to the test based on the least squares estimators or the least absolute deviation estimators and gives some examples to illustrate the application of the main result.

• 대한수학회논문집
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• 제20권1호
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• pp.145-159
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• 2005

In this paper we consider the problem of testing statistical hypotheses for unknown parameters in nonlinear regression models and propose three asymptotically equivalent tests based on regression quantiles estimators, which are Wald test, Lagrange Multiplier test and Likelihood Ratio test. We also derive the asymptotic distributions of the three test statistics both under the null hypotheses and under a sequence of local alternatives and verify that the asymptotic relative efficiency of the proposed test statistics with classical test based on least squares depends on the error distributions of the regression models. We give some examples to illustrate that the test based on the regression quantiles estimators performs better than the test based on the least squares estimators of the least absolute deviation estimators when the disturbance has asymmetric and heavy-tailed distribution.

• Journal of the Korean Statistical Society
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• 제33권4호
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• pp.411-433
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• 2004

The shrinkage preliminary test ridge regression estimators (SPTRRE) based on Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests for estimating the regression parameters of the multiple linear regression model with multivariate Student's t error distribution are considered in this paper. The quadratic biases and risks of the proposed estimators are compared under both null and alternative hypotheses. It is observed that there is conflict among the three estimators with respect to their risks because of certain inequalities that exist among the test statistics. In the neighborhood of the restriction, the SPTRRE based on LM test has the smallest risk followed by the estimators based on LR and W tests. However, the SPTRRE based on W test performs the best followed by the LR and LM based estimators when the parameters move away from the subspace of the restrictions. Some tables for the maximum and minimum guaranteed efficiency of the proposed estimators have been given, which allow us to determine the optimum level of significance corresponding to the optimum estimator among proposed estimators. It is evident that in the choice of the smallest significance level to yield the best estimator the SPTRRE based on Wald test dominates the other two estimators.

• 대한수학회보
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• 제36권3호
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• pp.451-457
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• 1999

This paper provides sufficient conditions which ensure the strong consistency of regression quantiles estimators of nonlinear regression models. The main result is supported by the application of an asymptotic property of the least absolute deviation estimators as a special case of the proposed estimators. some example is given to illustrate the application of the main result.

• Journal of the Korean Statistical Society
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• 제29권2호
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• pp.187-199
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• 2000

In this paper, we deal with the asymptotic properties of the least absolute deviation estimators in the nonlinear time series regression model. For the sinusodial model which frequently appears in a time series analysis, we study the strong consistency and asymptotic normality of least absolute deviation estimators. And using the derived limiting distributions we show that the least absolute deviation estimators is more efficient than the least squared estimators when the error distribution of the model has heavy tails.