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Interval-valued data regression using nonparametric additive models
임창원 한국통계학회 2016 Journal of the Korean Statistical Society Vol.45 No.3
Interval-valued data are observed as ranges instead of single values and frequently appear with advanced technologies in current data collection processes. Regression analysis of interval-valued data has been studied in the literature, but mostly focused on parametric linear regression models. In this paper, we study interval-valued data regression based on nonparametric additive models. By employing one of the current methods based on linear regression, we propose a nonparametric additive approach to properly analyze intervalvalued data with a possibly nonlinear pattern. We demonstrate the proposed approach using a simulation study and a real data example, and also compare its performance with those of existing methods.
On knot placement for penalized spline regression
Fang Yao,Thomas C.M. Lee 한국통계학회 2008 Journal of the Korean Statistical Society Vol.37 No.3
This paper studies the problem of knot placement in penalized regression spline fitting. Given a pre-specified number of knots, most existing knot placement methods allocate the knots in an equally spaced fashion. This paper proposes a simple knot placement scheme for improving such “equally spaced methods”. This new scheme first identifies locations of local extrema in the target function, and then it places additional knots in such places. The rationale behind this is that quite often such local extrema coincide with the critical locations for placing knots. The proposed scheme is shown to be superior in a simulation study.
Bayesian Curve-Fitting in Semiparametric Small Area Models with Measurement Errors
Hwang, Jinseub,Kim, Dal Ho The Korean Statistical Society 2015 Communications for statistical applications and me Vol.22 No.4
We study a semiparametric Bayesian approach to small area estimation under a nested error linear regression model with area level covariate subject to measurement error. Consideration is given to radial basis functions for the regression spline and knots on a grid of equally spaced sample quantiles of covariate with measurement errors in the nested error linear regression model setup. We conduct a hierarchical Bayesian structural measurement error model for small areas and prove the propriety of the joint posterior based on a given hierarchical Bayesian framework since some priors are defined non-informative improper priors that uses Markov Chain Monte Carlo methods to fit it. Our methodology is illustrated using numerical examples to compare possible models based on model adequacy criteria; in addition, analysis is conducted based on real data.