• Journal of the Korean Statistical Society
• /
• v.29 no.2
• /
• pp.187-199
• /
• 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
• /
• v.27 no.1
• /
• pp.101-112
• /
• 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 Data and Information Science Society
• /
• v.14 no.2
• /
• pp.153-165
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.373-384
• /
• 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 Mathematical Society
• /
• v.51 no.4
• /
• pp.735-749
• /
• 2014

This paper studies the asymptotic behavior of the finite-time ruin probability in a jump-diffusion risk model with constant force of interest, upper tail asymptotically independent claims and a general counting arrival process. Particularly, if the claim inter-arrival times follow a certain dependence structure, the obtained result also covers the case of the infinite-time ruin probability.

• Journal of the Korean Statistical Society
• /
• v.26 no.4
• /
• pp.467-476
• /
• 1997

The two-sample t-test is not expected to be optimal when the two samples are not drawn from normal populations. According to Box and Cox (1964), the transformation is estimated to enhance the normality of the tranformed data. We investigate the asymptotic relative efficiency of the ordinary t-test versus t-test applied transformation introduced by Yeo and Johnson (1997) under Pitman local alternatives. The theoretical and simulation studies show that two-sample t-test using transformed date gives higher power than ordinary t-test for location-shift models.

• Steel and Composite Structures
• /
• v.4 no.2
• /
• pp.133-147
• /
• 2004

This paper deals with the asymptotic analysis of Mohr-Coulomb and Drucker-Prager soft thin layers bonded with elastic solids. In the first part, a mathematical analysis shows how to obtain an interface law that replaces mechanically and geometrically the thin layer. This law is strongly non-linear and couples microscopic and macroscopic scales. In the second part of the paper, the microscopic terms are quantified numerically, and it is shown that they can be neglected.

• Journal of the Korean Statistical Society
• /
• v.32 no.1
• /
• pp.47-64
• /
• 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.

• Communications of the Korean Mathematical Society
• /
• v.11 no.1
• /
• pp.131-137
• /
• 1996

In this paper, we give a necessary and sufficient condition for the weak convergence of trajectories of non-lipschitzian asymptotically nonexpansive mappings.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.40 no.7
• /
• pp.1217-1233
• /
• 2015

The paper studies characteristics of the minimum mean-square error symmetric scalar quantizers for the generalized gamma, Bucklew-Gallagher and Hui-Neuhoff probability density functions. Toward this goal, asymptotic formulas for the inner- and outermost thresholds, and distortion are derived herein for nonuniform quantizers for the Bucklew-Gallagher and Hui-Neuhoff densities, parallelling the previous studies for the generalized gamma density, and optimal uniform and nonuniform quantizers are designed numerically and their characteristics tabulated for integer rates up to 20 and 16 bits, respectively, except for the Hui-Neuhoff density. The assessed asymptotic formulas are found consistently more accurate as the rate increases, essentially making their asymptotic convergence to true values numerically acceptable at the studied bit range, except for the Hui-Neuhoff density, in which case they are still consistent and suggestive of convergence. Also investigated is the uniqueness problem of the differentiation method for finding optimal step sizes of uniform quantizers: it is observed that, for the commonly studied densities, the distortion has a unique local minimizer, hence showing that the differentiation method yields the optimal step size, but also observed that it leads to multiple solutions to numerous generalized gamma densities.