• Communications for Statistical Applications and Methods
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• 제5권1호
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• pp.55-67
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• 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.

• Communications for Statistical Applications and Methods
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• 제28권2호
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• pp.189-204
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• 2021

In a regression analysis, a single best model is usually selected among several candidate models. However, it is often useful to combine several candidate models to achieve better performance, especially, in the prediction viewpoint. Model combining methods such as stacking and Bayesian model averaging (BMA) have been suggested from the perspective of averaging candidate models. When the candidate models include a true model, it is expected that BMA generally gives better performance than stacking. On the other hand, when candidate models do not include the true model, it is known that stacking outperforms BMA. Since stacking and BMA approaches have different properties, it is difficult to determine which method is more appropriate under other situations. In particular, it is not easy to find research papers that compare stacking and BMA when regression model assumptions are violated. Therefore, in the paper, we compare the performance among model averaging methods as well as a single best model in the linear regression analysis when standard linear regression assumptions are violated. Simulations were conducted to compare model averaging methods with the linear regression when data include outliers and data do not include them. We also compared them when data include errors from a non-normal distribution. The model averaging methods were applied to the water pollution data, which have a strong multicollinearity among variables. Simulation studies showed that the stacking method tends to give better performance than BMA or standard linear regression analysis (including the stepwise selection method) in the sense of risks (see (3.1)) or prediction error (see (3.2)) when typical linear regression assumptions are violated.

• Communications for Statistical Applications and Methods
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• 제10권2호
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• pp.277-289
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• 2003

We propose modified exact inferential methods in logistic regression model. Exact conditional distribution in logistic regression model is often highly discrete, and ordinary exact inference in logistic regression is conservative, because of the discreteness of the distribution. For the exact inference in logistic regression model we utilize the modified P-value. The modified P-value can not exceed the ordinary P-value, so the test of size $\alpha$ based on the modified P-value is less conservative. The modified exact confidence interval maintains at least a fixed confidence level but tends to be much narrower. The approach inverts results of a test with a modified P-value utilizing the test statistic and table probabilities in logistic regression model.

• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.419-437
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• 1995

Given the specific mean shift outlier model, several standard approaches to obtaining test statistic for outliers are discussed. Each of these is developed in detail for the nonlinear regression model, and each leads to an equivalent distribution. The geometric interpretations of the statistics and accuracy of linear approximation are also presented.

• Journal of the Korean Statistical Society
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• 제28권3호
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• pp.311-324
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• 1999

The problem of 'outliers', observations which look suspicious in some way, has long been one of the most concern in the statistical structure to experimenters and data analysts. We propose a model for an outlier problem and also analyze it in linear regression model using a Bayesian approach. Then we use the mean-shift model and SSVS(George and McCulloch, 1993)'s idea which is based on the data augmentation method. The advantage of proposed method is to find a subset of data which is most suspicious in the given model by the posterior probability. The MCMC method(Gibbs sampler) can be used to overcome the complicated Bayesian computation. Finally, a proposed method is applied to a simulated data and a real data.

• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.805-814
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• 2001

The problem of 'outliers', observations which look suspicious in some way, has long been one of the most concern in the statistical structure to experimenters and data analysts. We propose a model for outliers problem and also analyze it in linear regression model using a Bayesian approach with the variance-inflation model. We will use Geweke's(1996) ideas which is based on the data augmentation method for detecting outliers in linear regression model. The advantage of the proposed method is to find a subset of data which is most suspicious in the given model by the posterior probability The sampling based approach can be used to allow the complicated Bayesian computation. Finally, our proposed methodology is applied to a simulated and a real data.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.1-9
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• 2007

A three-state Markov logistic regression model is suggested to forecast the probability of tomorrow's precipitation based on the current meteorological situation. The suggested model turns out to be better than Markov regression model in the sense of the mean squared error of forecasting for the rainfall data of Seoul area.

• Communications for Statistical Applications and Methods
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• 제17권4호
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• pp.551-560
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• 2010

This paper considers a Bayesian approach to modeling a flexible regression function under structural measurement error model. The regression function is modeled based on semiparametric regression with penalized splines. Model fitting and parameter estimation are carried out in a hierarchical Bayesian framework using Markov chain Monte Carlo methodology. Their performances are compared with those of the estimators under structural measurement error model without a semiparametric component.

• Communications for Statistical Applications and Methods
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• 제9권2호
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• pp.459-471
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• 2002

In applications using a linear regression model with nested error structure, one might be interested in making inferences concerning variance components. This article proposes approximate confidence intervals on the variance component of the primary level in a simple linear regression model with an unbalanced nested error structure. The intervals are compared using computer simulation and recommendations are provided for selecting an appropriate interval.

• Journal of the Korean Statistical Society
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• 제29권2호
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• pp.187-199
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• 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.