• Journal of the Korean Statistical Society
• /
• 제32권1호
• /
• 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 for Statistical Applications and Methods
• /
• 제18권4호
• /
• pp.527-535
• /
• 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
• /
• 제30권4호
• /
• pp.551-561
• /
• 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
• /
• 제18권4호
• /
• pp.477-483
• /
• 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.

• 응용통계연구
• /
• 제19권1호
• /
• pp.81-96
• /
• 2006

본 연구에서는 분포를 알 수 없고 비대칭인 공정자료에 실용적으로 적용할 수 있는 간단한 관리도법을 제안하였다. 비대칭 분포를 따르는 공정자료에 정규성 가정에 기초한 슈하르트 관리도를 그대로 적용하면 비대칭성이 증가할수록 제 1종 오류를 범할 확률이 증가할 가능성이 높아지며 변동을 관리하는데 효율성이 떨어지게 된다. 이러한 문제를 해결하기 위해 본 연구에서 제시한 관리도는 관리한계선을 사분위수에 기초하여 정하는 방안을 제시하고 있다. 이러한 방법으로 관리한계선을 그릴 경우 제 1종 오류도 감소하게 되고, 비대칭분포를 하는 공정자료에 대하여 매우 실용적이라고 하겠다.

• 응용통계연구
• /
• 제24권6호
• /
• pp.1033-1043
• /
• 2011

본 논문에서는 KOSPI지수와 원-달러 환율의 로그수익률을 사용하여 비대칭 이분산성에 대해 연구한다. 커널 density plot과 상승기와 하강기의 평균, 분산을 검토하여 이들 시계열의 변동의 비대칭성에 대한 윤곽을 파악하고 GARCH군의 여러 비대칭 모형을 적합하여 비대칭성을 실증적으로 파악한다. 또한 최종선택 모형인 EGARCH 모형을 바탕으로 부트스트래핑을 사용하여 미래 시점의 변동성인 조건부 분산의 기대치를 예측하고 예측표준오차를 구해본다.

• Communications for Statistical Applications and Methods
• /
• 제25권1호
• /
• pp.43-60
• /
• 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
• /
• 제9권1호
• /
• pp.101-113
• /
• 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.

• 한국시뮬레이션학회논문지
• /
• 제9권3호
• /
• pp.43-51
• /
• 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.

• 한국시뮬레이션학회:학술대회논문집
• /
• 한국시뮬레이션학회 2000년도 추계학술대회 논문집
• /
• pp.6-10
• /
• 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.