• 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 applied mathematics & informatics
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• 제22권1_2호
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• pp.209-222
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• 2006

Estimation of the spectral measure, covariance and spectral density functions of a strictly stationary r-vector valued time series is considered, under the assumption that some of the observations are missed. The modified periodograms are calculated using data window. The asymptotic normality is studied.

• 대한수학회보
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• 제47권5호
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• pp.889-905
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• 2010

In this paper, a distribution free approach to the parameter estimation of a simple bilinear model with periodic coefficients is presented. The proposed method relies on minimum distance estimator based on the autocovariances of the squared process. Consistency and asymptotic normality of the estimator, as well as hypotheses testing, are derived. Numerical experiments on simulated data sets are presented to highlight the theoretical results.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.117-126
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• 2001

We provide a simple chi-squared test of multivariate normality based on rectangular cells on the spherical data. This test is simple since it is a direct extension of the univariate chi-squared test to multivariate case and the expected cell counts are easily computed. We derive the limiting distribution of the chi-squared statistic via the conditional limit theorems. We study the accuracy in finite samples of the limiting distribution and then compare the poser of our test with those of other popular tests in an application to a real data.

• 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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• 제28권1호
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• pp.57-72
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• 1999

Falk(1994) showed that the asymptotic efficiency of the Pickands estimator of the extreme value index $\beta$ can considerably be improved by a simple convex combination. In this paper we propose an alternative estimator of $\beta$ which is as asymptotically efficient as the optimal convex combination of the Pickands estimators but has a better finite-sample performance. We prove consistency and asymptotic normality of the proposed estimator. Monte Carlo simulations are conducted to compare the finite-sample performances of the proposed estimator and the optimal convex combination estimator.

• 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.

• Journal of the Korean Statistical Society
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• 제27권1호
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• pp.101-112
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• 1998

This paper is concerned with the asymptotic properties of the least absolute deviation estimators for the nonlinear regression model when dependent variables are subject to censoring time, and proposed the simple and practical sufficient conditions for the strong consistency and asymptotic normality of the least absolute deviation estimators in censored regression model. Some desirable asymptotic properties including the asymptotic relative efficiency of proposed model with respect to standard model are given.

• Journal of the Korean Statistical Society
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• 제31권1호
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• pp.109-120
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• 2002

In this paper, we show the weak convergence of U-empirical processes for two sample problem. We use the result to show the asymptotic normality for the generalized dodges-Lehmann estimates with the Bahadur representation for quantifies of U-empirical distributions. Also we consider the asymptotic normality for the test statistics in a simple way.

• Journal of the Korean Statistical Society
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• 제36권4호
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• pp.471-477
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• 2007

In this paper, we provide a new proof to correct the asymptotic normality for the estimate $\hat{C}_{pmk}\;of\;C_{pmk}$, which is one of the well-known definitions of the process capability index. Also we comment briefly on the correction of the limiting distribution for $\hat{C}_{pmk}$ and on the use of re-sampling methods for the inference of $C_{pmk}$. Finally we discuss the concept of asymptotic unbiasedness.