• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.77-91
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• 2002

This paper considers a functional regression model with truncated errors in explanatory variables. We show that the ordinary least squares (OLS) estimators produce bias in regression parameter estimates under misspecified models with ignored errors in the explanatory variable measurements, and then propose methods for analyzing the functional model. Fully parametric frequentist approaches for analyzing the model are intractable and thus Bayesian methods are pursued using a Markov chain Monte Carlo (MCMC) sampling based approach. Necessary theories involved in modeling and computation are provided. Finally, a simulation study is given to illustrate and examine the proposed methods.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.233-237
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• 2003

An asymptotic property of the ordinary least squares estimator of the disturbance variance is considered in the regression model with correlated errors. It is shown that the convergence in probability of S$^2$ is equivalent to the asymptotic unbiasedness. Beyond the assumption on the design matrix or the variance-covariance matrix of disturbances error, the result is quite general and simplify the earlier results.

• Journal of the Korean Statistical Society
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• v.36 no.4
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• pp.447-456
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• 2007

On the basis of marginal likelihood of the residual vector which is free of nuisance mean parameters, we propose new Lagrange Multiplier seasonal unit root tests in seasonal autoregressive process. The limiting null distribution of the tests is the standardized ${\chi}^2-distribution$. A Monte-Carlo simulation shows the new tests are more powerful than the tests based on the ordinary least squares (OLS) estimator, especially for large number of seasons and short time spans.

• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.105-112
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• 1990

Let (X, Y) be a pair random variables and let f denote the regression function of the response Y on the measurement variable X. Let K(f) denote a derivative of f. The least squares method is used to obtain a tensor spline estimator $\hat{f}$ of f based on a random sample of size n from the distribution of (X, Y). Under some mild conditions, it is shown that $K(\hat{f})$ achieves the optimal rate of convergence for the estimation of K(f) in $L_2$ and $L_{\infty}$ norms.

• Journal of the Korean Statistical Society
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• v.11 no.1
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• pp.59-68
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• 1982

We propose that, in order to control the inflation and general instability associated with the least squares estimates, we can use the ridge estimator $$ \hat{B}^* = (X'X+kI)^{-1}X'Y : k \leq 0$$ for the regression coefficients B in multivariate regression. Our hope is that by accepting some bias, we can achieve a larger reduction in variance. We show that such a k always exists and we derive the formula obtaining k in multivariate ridge regression.

• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.43-56
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• 2005

In this study, a robust estimation method for the first-order autocorrelation coefficient in the time series model following AR(l) process with additive outlier(AO) is investigated. We propose the L-type trimmed least squares estimation method using the preliminary estimator (PE) suggested by Rupport and Carroll (1980) in multiple regression model. In addition, using Mallows' weight function in order to down-weight the outlier of X-axis, the bounded-influence PE (BIPE) estimator is obtained and the mean squared error (MSE) performance of various estimators for autocorrelation coefficient are compared using Monte Carlo experiments. From the results of Monte-Carlo study, the efficiency of BIPE(LAD) estimator using the generalized-LAD to preliminary estimator performs well relative to other estimators.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.185-198
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• 2016

Regression analysis is an analyzing method of regression model to explain the statistical relationship between explanatory variable and response variables. This paper propose a fuzzy regression analysis applying Theils method which is not sensitive to outliers. This method use medians of rate of increment based on randomly chosen pairs of each components of ${\alpha}$-level sets of fuzzy data in order to estimate the coefficients of fuzzy regression model. An example and two simulation results are given to show fuzzy Theils estimator is more robust than the fuzzy least squares estimator.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.395-409
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• 2014

Data limited, partial, or incomplete are known as an ill-posed problem. If the data with ill-posed problems are analyzed by traditional statistical methods, the results obviously are not reliable and lead to erroneous interpretations. To overcome these problems, we propose a dual generalized maximum entropy (dual GME) estimator for panel data regression models based on an unconstrained dual Lagrange multiplier method. Monte Carlo simulations for panel data regression models with exogeneity, endogeneity, or/and collinearity show that the dual GME estimator outperforms several other estimators such as using least squares and instruments even in small samples. We believe that our dual GME procedure developed for the panel data regression framework will be useful to analyze ill-posed and endogenous data sets.

• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.95-103
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• 1993

Necessary and sufficient conditions for the equality between the best linear unbiased estimators in two linear models with different covariance matrices, $V_1 and V_2$, say, are derived. Various applications of this discovery are also given. Necessary and sufficient conditions for the equality between the best linear unbiased estimator and the ordinary least squares estimator are discussed related to this topic.

• Journal of Korean Society for Quality Management
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• v.25 no.1
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• pp.69-79
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• 1997

We consider the semiparametric linear errors-in-variables model: yi=(${\alpha}+{\beta}ui+{\varepsilon}i$, xi=ui＋${\varepsilon}i$ i=1, …, n where (xi, yi) stands for an observation vector, (ui) denotes a set of incidental nuisance parameters, (${\alpha}$ , ${\beta}$) is a vector of regression parameters and (${\varepsilon}i$, ${\delta}i$) are mutually uncorrelated measurement errors with zero mean and finite variances but otherwise unknown distributions. On the basis of a simple small-sample low-noise a, pp.oximation, we propose a new method of comparing the mean squared errors(MSE) of the various competing estimators of the true regression parameters ((${\alpha}$ , ${\beta}$). Then we show that a class of estimators including the classical least squares estimator and the maximum likelihood estimator are consistent and first-order efficient within the class of all regular consistent estimators irrespective of type of measurement errors.