• Journal of the Korean Data and Information Science Society
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• v.26 no.3
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• pp.749-754
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• 2015

This article presents Bayesian approach to regression splines with knots on a grid of equally spaced sample quantiles of the independent variables under functional measurement error model.We consider small area model by using penalized splines of non-linear pattern. Specifically, in a basis functions of the regression spline, we use radial basis functions. To fit the model and estimate parameters we suggest a hierarchical Bayesian framework using Markov Chain Monte Carlo methodology. Furthermore, we illustrate the method in an application data. We check the convergence by a potential scale reduction factor and we use the posterior predictive p-value and the mean logarithmic conditional predictive ordinate to compar models.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.167-170
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• 2003

We develop semiparametric methods for matched case-control studies using regression splines. Three methods are developed: an approximate crossvalidation scheme to estimate the smoothing parameter inherent in regression splines, as well as Monte Carlo Expectation Maximization (MCEM) and Bayesian methods to fit the regression spline model. We compare the approximate cross-validation approach, MCEM and Bayesian approaches using simulation, showing that they appear approximately equally efficient, with the approximate cross-validation method being computationally the most convenient. An example from equine epidemiology that motivated the work is used to demonstrate our approaches.

• Communications for Statistical Applications and Methods
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• v.26 no.1
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• pp.69-78
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• 2019

A structured model with both single-index and varying coefficients is a powerful tool in modeling high dimensional data. It has been widely used because the single-index can overcome the curse of dimensionality and varying coefficients can allow nonlinear interaction effects in the model. For high dimensional index vectors, variable selection becomes an important question in the model building process. In this paper, we propose an efficient estimation and a variable selection method based on a smoothing spline approach in a partially linear single-index-coefficient regression model. We also propose an efficient algorithm for simultaneously estimating the coefficient functions in a data-adaptive lower-dimensional approximation space and selecting significant variables in the index with the adaptive LASSO penalty. The empirical performance of the proposed method is illustrated with simulated and real data examples.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1295-1309
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• 2016

This paper is to reproduce the result of Kim et al. (2014) by deriving a benchmark dose lower bound (BMDL) of lead based on the 2005 cohort data set of Children's Health and Environmental Research (CHEER) data set. The ADHD rating scales in the 2005 cohort were not consistent along the three follow-ups since two different ADHD rating scales were used in the cohort. We first unified the ADHD rating scales in the 2005 cohort by deriving a conversion formula using a penalized linear spline. We then constructed two linear mixed models for the 2005 cohort which reflected the longitudinal characteristics of the data set. The first model introduced the random intercept and the random slope terms and the second model assumed the first order autoregressive structure of the error term. Using these two models, we derived the BMDLs of lead and reconfirmed the "regression to the mean" nature of the ADHD score discovered by Kim et al. (2014). We also noticed that there was a definite difference between the sampling distributions of the two cohorts. As a result, taking this difference into account, we were able to obtain the consistent result with Kim et al. (2014).

• The Korean Journal of Applied Statistics
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• v.32 no.4
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• pp.543-559
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• 2019

Data often include missing values due to various reasons. If the missing data mechanism is not MCAR, analysis based on fully observed cases may an estimation cause bias and decrease the precision of the estimate since partially observed cases are excluded. Especially when data include many variables, missing values cause more serious problems. Many imputation techniques are suggested to overcome this difficulty. However, imputation methods using parametric models may not fit well with real data which do not satisfy model assumptions. In this study, we review imputation methods using nonlinear models such as kernel, resampling, and spline methods which are robust on model assumptions. In addition, we suggest utilizing imputation classes to improve imputation accuracy or adding random errors to correctly estimate the variance of the estimates in nonlinear imputation models. Performances of imputation methods using nonlinear models are compared under various simulated data settings. Simulation results indicate that the performances of imputation methods are different as data settings change. However, imputation based on the kernel regression or the penalized spline performs better in most situations. Utilizing imputation classes or adding random errors improves the performance of imputation methods using nonlinear models.