• Bulletin of the Korean Mathematical Society
• /
• v.36 no.3
• /
• 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.

• Communications for Statistical Applications and Methods
• /
• v.8 no.1
• /
• pp.229-235
• /
• 2001

Let {X$\_$n/, n$\geq$1] be a stationary sequence of negatively associated random variables with distribution function F(x)=P(X$_1$$\leq$x). The empirical distribution function F$\_$n/(x) based on X$_1$, X$_2$,....., X$\_$n/ is proposed as an estimator for F$\_$n/(x). Strong consistency and asymptotic normality of F$\_$n/(x) are studied. We also apply these ideas to estimation of the survival function.

• Journal of the Korean Data and Information Science Society
• /
• v.10 no.2
• /
• pp.341-357
• /
• 1999

Greenwich and Jahr-Schaffrath(1995) considered a new process incapability index(PII) $C_{pp}$, which modified the useful index $C^{\ast}_{pm}{$ for detecting assignable causes. The new index $C_{pp}$ provides an uncontaminated separation between information concerning the process accuracy and precision while this kind of information separation is not available with the $C^{\ast}_{pm}$ index. In this paper, we will study about the index $C_{pp}$ based on the bootstrap. First, we will prove the consistency of bootstrap deriving the bootstrap asymptotic distribution for our index $C_{pp}$. Moreover, with the consistency of bootstrap, we will construct six bootstrap confidence intervals and compare their performances. Some simulation results, comparison and analysis are provided. In particular, two STUD and ABC bootstrap methods perform significantly better.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.14-14
• /
• 2003

Given a sequence ｛ $X_{n}$｝ of independent and identically distributed random variables with F, a sequential procedure for the p-th quantile ξ$_{P}$= $F^{-1}$ (P), 0$\beta$-protection. Some asymptotic properties for the proposed procedure and of an involved stopping time are proved: asymptotic consistency, asymptotic efficiency and asymptotic normality. From one of the results an effect of smoothing based on kernel functions is discussed. The results are also extended to the contaminated case.e.e.

• Communications for Statistical Applications and Methods
• /
• v.4 no.1
• /
• pp.111-117
• /
• 1997

The ordinary least squares estimator $S^2$ for the variance of the disturbances is considered in the linear regression model with sutocorrelated disturbances. It is proved that the OLS-estimator of disturbance variance is asymptotically unbiased and weakly consistent, when the distrubances are generated by an MA(q) process. In particular, the asymptotic unbiasedness and consistency of $S^2$ is satisfied without any restriction on the regressor matrix.

• Journal of the Korean Data and Information Science Society
• /
• v.6 no.2
• /
• pp.65-76
• /
• 1995

The importance of left truncated and right censoring cases has considered for better information in medical follow-up and engineering life testing studies. We propose some estimation procedure for the mean residual life function with consistency and asymptotic normality on the left truncated and right censoring model. And then, the comparision with Kaplan-Meier estimator ignoring the left truncated effect and the small sample properities are investigated by asymptotic biases and M.S.E.'s thresh Monte Carlo study.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.889-905
• /
• 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.

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

• Journal of the Korea Society for Simulation
• /
• v.9 no.3
• /
• 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.

• Journal of the Korean Data and Information Science Society
• /
• v.15 no.1
• /
• pp.273-284
• /
• 2004

Bayes estimation of parameters is considered for two independent exponential distributions with ordered means. Order restricted Bayes estimators for means are obtained with respect to inverted gamma, noninformative prior and uniform prior distributions, and their asymptotic properties are established. It is shown that the maximum likelihood estimator, restricted maximum likelihood estimator, unrestricted Bayes estimator, and restricted Bayes estimator of the mean are all consistent and have the same limiting distribution. These estimators are compared with the corresponding unrestricted Bayes estimators by Monte Carlo simulation.