• Journal of the Korean Statistical Society
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• v.32 no.1
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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.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.527-535
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• 2011

This study proposes a modified definition about $C_{pk}$ based on median as the centering parameter in order to more easily control the process since the mean does not represent any quantile of the asymmetric process distribution. Then we consider an estimate and derive the asymptotic normality for the estimate of the modified $C_{pk}$. In addition, we provide an example with asymmetric distributions and discuss the estimation for the limiting variance that are followed by some concluding remarks.

• Journal of the Korean Statistical Society
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• v.30 no.4
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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.

• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.477-483
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• 2011

This article is concerned with a class of threshold-asymmetric GARCH models both for stationary case and for non-stationary case. We investigate large sample properties of estimators from QML(quasi-maximum likelihood) and QL(quasilikelihood) methods. Asymptotic distributions are derived and it is interesting to note for non-stationary case that both QML and QL give asymptotic normal distributions.

• The Korean Journal of Applied Statistics
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• v.19 no.1
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• pp.81-96
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• 2006

This paper proposes a simple control chart method which can be practically used for asymmetric process data where the distribution is unknown. If we use the Shewhart type control charts which are based on normality assumption for the asymmetric process data, the type I error could increase as the asymmetry increases and the effectiveness of control chart to control variation decreases. To solve such problems, this paper suggests to calculate the control limits based on the quartiles. If we obtain the control limits by such quartile method, the type I error could decrease and it looks much more practical for asymmetric distributed process data.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1033-1043
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• 2011

In this paper, we use a nested family of models of Generalized Autoregressive Conditional Heteroscedasticity(GARCH) to verify asymmetric conditional heteroscedasticity in the KOSPI and Won-Dollar exchange rate. This study starts from an investigation of whether time series data have asymmetric features not explained by standard GARCH models. First, we use kernel density plot to show the non-normality and asymmetry in data as well as to capture asymmetric conditional heteroscedasticity. Later, we use three representative asymmetric heteroscedastic models, EGARCH(Exponential Garch), GJR-GARCH(Glosten, Jagannathan and Runkle), APARCH(Asymmetric Power Arch) that are improved from standard GARCH models to give a better explanation of asymmetry. Thereby we highlight the fact that volatility tends to respond asymmetrically according to positive and/or negative values of past changes referred to as the leverage effect. Furthermore, it is verified that how the direction of asymmetry is different depending on characteristics of time series data. For the KOSPI and Korean won-US dollar exchange rate, asymmetric heteroscedastic model analysis successfully reveal the leverage effect. We obtained predictive values of conditional volatility and its prediction standard errors by using moving block bootstrap.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.43-60
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• 2018

This paper considers the use of classical and Bayesian inference methods to analyze data generated by variables whose natural behavior can be modeled using asymmetric distributions in the presence of left censoring. Our approach used a $L{\grave{e}}vy$ distribution in the presence of left censored data and covariates. This distribution could be a good alternative to model data with asymmetric behavior in many applications as lifetime data for instance, especially in engineering applications and health research, when some observations are large in comparison to other ones and standard distributions commonly used to model asymmetry data like the exponential, Weibull or log-logistic are not appropriate to be fitted by the data. Inferences for the parameters of the proposed model under a classical inference approach are obtained using a maximum likelihood estimators (MLEs) approach and usual asymptotical normality for MLEs based on the Fisher information measure. Under a Bayesian approach, the posterior summaries of interest are obtained using standard Markov chain Monte Carlo simulation methods and available software like SAS. A numerical illustration is presented considering data of thyroglobulin levels present in a group of individuals with differentiated cancer of thyroid.

• 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 Korea Society for Simulation
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• v.9 no.3
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• pp.43-51
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• 2000

In regression model, we estimate the unknown parameters by using various methods. There are the least squares method which is the most general, the least absolute deviation method, the regression quantile method and the asymmetric least squares method. In this paper, we will compare each others with two cases: firstly the theoretical comparison in the asymptotic sense and then the practical comparison using Monte Carlo simulation for a small sample size.

• Proceedings of the Korea Society for Simulation Conference
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• 2000.11a
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• pp.6-10
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• 2000

In regression model we estimate the unknown parameters using various methods. There are the least squares method which is the most general, the least absolute deviation, the regression quantile and the asymmetric least squares method. In this paper, we will compare each others with two case: to begin with the theoretical comparison in the asymptotic sense, and then the practical comparison using Monte Carlo simulation for a small sample size.