• Journal of the Korean Data and Information Science Society
• /
• 제13권1호
• /
• pp.157-164
• /
• 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
• /
• 제14권2호
• /
• 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.

• 대한수학회보
• /
• 제36권3호
• /
• pp.451-457
• /
• 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.

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

• 응용통계연구
• /
• 제25권5호
• /
• pp.793-802
• /
• 2012

One proposal is made to construct a nonparametric estimator of slope parameters in a regression model under symmetric error distributions. This estimator is based on the use of the idea of minimizing approximate variance of a proposed estimator using regression quantiles. This nonparametric estimator and some other L-estimators are studied and compared with well known M-estimators through a simulation study.

• Journal of the Korean Data and Information Science Society
• /
• 제11권2호
• /
• pp.235-245
• /
• 2000

두 변수간의 함수관계를 연구하는 회귀분석에서 모수를 추정하기 위하여 가장 널리 사용되는 방법은 최소자승법이다. 그러나 최소자승법은 표본 평균처럼 약간의 이상치에도 민감하게 반응하여 강인성(robustness)을 만족하지 못함으로 새로운 추정량이 필요하다. 본 논문에서는 최소분위추정량과 최소분위추정량에 근거한 일차결합추정량의 점근적 성질을 연구하였다. 또한 최소자승추정량에 대해 제시된 추정량의 점근적 효율성을 구하고 모의실험을 통하여 최소분위추정량의 효율성을 조사하였다.

• Communications for Statistical Applications and Methods
• /
• 제12권3호
• /
• pp.807-818
• /
• 2005

In this paper we propose an estimation method for regression quantiles with left-truncated and right-censored data. The estimation procedure is based on the weight determined by the Kaplan-Meier estimate of the distribution of the response. We show how the proposed regression quantile estimators perform through analyses of Stanford heart transplant data and AIDS incubation data. We also investigate the effect of censoring on regression quantiles through simulation study.

• Communications for Statistical Applications and Methods
• /
• 제10권3호
• /
• pp.859-871
• /
• 2003

In this paper we introduce some adaptive M-estimators using selector statistics to estimate the slope of regression model under the symmetric and continuous underlying error distributions. This selector statistics is based on the residuals after the preliminary fit L$_1$ (least absolute estimator) and the idea of Hogg(1983) and Hogg et. al. (1988) who used averages of some order statistics to discriminate underlying symmetric distributions in the location model. If we use L$_1$ as a preliminary fit to get residuals, we find the asymptotic distribution of sample quantiles of residual are slightly different from that of sample quantiles in the location model. If we use the functions of sample quantiles of residuals as selector statistics, we find the suitable quantile points of residual based on maximizing the asymptotic distance index to discriminate distributions under consideration. In Monte Carlo study, this adaptive M-estimation method using selector statistics works pretty good in wide range of underlying error distributions.

• Journal of the Korean Data and Information Science Society
• /
• 제4권
• /
• pp.13-30
• /
• 1993

We propose the ordered least squares estimators(OLSE's) of the parameters and the p-th quantiles for the two-parameter Weibull regression model under the Type II censoring, The Monte Carlo simulations are performed to compare the proposed estimators with the maximum likelihood estimators(MLE's), and it is shown that the proposed estimators are slightly better than MLE's as the censoring rate goes up.

• Communications for Statistical Applications and Methods
• /
• 제30권6호
• /
• pp.531-550
• /
• 2023

The estimation of extreme quantiles is one of the main objectives of statistics of extremes (which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regression model. The proposed estimator was compared with two estimators of extreme quantiles in the literature in a simulation study. The results show that the proposed estimator is stable to the choice of the number of top order statistics and show lesser bias and mean square error compared to the existing extreme quantile estimators. Practical application of the proposed estimator is illustrated with data from the pedochemical and insurance industries.