• The Korean Journal of Applied Statistics
• /
• v.8 no.2
• /
• pp.187-200
• /
• 1995

This paper is concerned with a regression model with nonlinear time series errors. Testing procedures for linearity of error terms are studied. To this end, large-sample properties of estimators of regression parameters and autoregression parameter are obtained. These results are then used to develop test statistics for testing linearity of errors. Some simulation studies are shown.

• Communications for Statistical Applications and Methods
• /
• v.4 no.2
• /
• pp.453-463
• /
• 1997

Nonparametric kernel regression has recently gained widespread acceptance as an attractive method for the nonparametric estimation of the mean function from noisy regression data. Also, the practical implementation of kernel method is enhanced by the availability of reliable rule for automatic selection of the bandwidth. In this article, we propose a method for automatic selection of the bandwidth that minimizes the asymptotic mean square error. Then, the estimated bandwidth by the proposed method is compared with the theoretical optimal bandwidth and a bandwidth by plug-in method. Simulation study is performed and shows satisfactory behavior of the proposed method.

• Journal of the Korean Statistical Society
• /
• v.31 no.2
• /
• pp.229-235
• /
• 2002

A generalized Stein-rule estimator of the vector of regression coefficients in linear regression model is considered and its properties are analyzed according to the criterion of Pitman nearness. A comparative study shows that the generalized Stein-rule estimator representing a class of estimators contains particular members which are better than the usual Stein-rule estimator according to the Pitman closeness.

• Communications for Statistical Applications and Methods
• /
• v.13 no.3
• /
• pp.479-490
• /
• 2006

Francis Gallon (1822-1911) introduced the term 'regression' and 'correlation' in the study on human inheritance of the stature from parents to their children. In almost every statistics textbook, superficial attentions have been given to him just as the inventor of the term 'regression'. Rereading his books and papers, we investigated problems he had tried to solve and the methods he had used to solve the problems. In addition, we tried to find the motivation that had led Gallon to take attention to the variation rather than the central tendency of observational data that had fascinated his forerunner Adloph Quetelet.

• The Korean Journal of Applied Statistics
• /
• v.25 no.2
• /
• pp.321-330
• /
• 2012

In this paper we study some basic statistics in quantile regression. In particular, we investigate the residual, goodness-of-fit statistic and the effect of one or few observations on estimates of regression coefficients. In addition, we compare the proposed goodness-of-fit statistic with the statistic considered by Koenker and Machado (1999). An illustrative example based on real data sets is given to see the numerical performance of the proposed basic statistics.

• Journal of applied mathematics & informatics
• /
• v.3 no.2
• /
• pp.205-216
• /
• 1996

The field of nonparametrics has shown its appeal in re-cent years with anarray of new tools for statistical analysis. As one of those tools nonparametric regression has become a prominent statis-tical research topic and also has been well established as a useful tool. In this article we investigate the biased cross-validation selector, BCV, which is proposed by Oh et al. (1995) for a less smoothing regression function. In the simulation study BCV selector is shown to perform well in parctice with respect to ASE ratio.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.247-257
• /
• 2007

Consider the heteroscedastic regression model $Y_i=g(x_i)+{\sigma}_i\;{\epsilon}_i=(1{\leq}i{\leq}n)$, where ${\sigma}^2_i=f(u_i)$, the design points $(x_i,\;u_i)$ are known and nonrandom, and g and f are unknown functions defined on closed interval [0, 1]. Under the random errors $\epsilon_i$ form a sequence of NA random variables, we study the asymptotic normality of wavelet estimators of g when f is a known or unknown function.

• Journal of the Korean Data and Information Science Society
• /
• v.18 no.4
• /
• pp.847-857
• /
• 2007

This paper provides a statistical algorithm which detects COD (chemical oxygen demand) measurement machine error on real-time. For this we propose to use regression model fitting and check its validity against the current observations. The main idea is that the normal regression relation between COD measurement and other parameters inside the machine will be violated when the machine is out of order.

• Communications for Statistical Applications and Methods
• /
• v.5 no.1
• /
• pp.55-67
• /
• 1998

Recent work by Shin and Sarkar (1996) examines model misspecification problems for nonstationary time series. Shin and Sarkar introduce a general regression model with integrated errors and one system of integrated regressors and discuss the limiting distributions of the OLS estimators and the usual OLS statistics such as $\hat{\sigma^2}$t, DW and $R^2$. We analyze three different model misspecification problems through a Monte Carlo study and investigate each model misspecification problem. Our Monte Carlo experiments show that DW and $R^2$ can be in general used as diagnostic tools to detect spurious regression, misspecification of nonstationary autoregressive and polynomial regression models.

• Journal of the Korean Statistical Society
• /
• v.29 no.2
• /
• pp.187-199
• /
• 2000

In this paper, we deal with the asymptotic properties of the least absolute deviation estimators in the nonlinear time series regression model. For the sinusodial model which frequently appears in a time series analysis, we study the strong consistency and asymptotic normality of least absolute deviation estimators. And using the derived limiting distributions we show that the least absolute deviation estimators is more efficient than the least squared estimators when the error distribution of the model has heavy tails.