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Kernel Regression Estimation for Permutation Fixed Design Additive Models
Baek, Jangsun,Wehrly, Thomas E. The Korean Statistical Society 1996 Journal of the Korean Statistical Society Vol.25 No.4
Consider an additive regression model of Y on X = (X$_1$,X$_2$,. . .,$X_p$), Y = $sum_{j=1}^pf_j(X_j) + $\varepsilon$$, where $f_j$s are smooth functions to be estimated and $\varepsilon$ is a random error. If $X_j$s are fixed design points, we call it the fixed design additive model. Since the response variable Y is observed at fixed p-dimensional design points, the behavior of the nonparametric regression estimator depends on the design. We propose a fixed design called permutation fixed design, and fit the regression function by the kernel method. The estimator in the permutation fixed design achieves the univariate optimal rate of convergence in mean squared error for any p $\geq$ 2.
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.
A Nonparametric Additive Risk Model Based on Splines
Park, Cheol-Yong 한국데이터정보과학회 2007 한국데이터정보과학회지 Vol.18 No.1
We consider a nonparametric additive risk model that is based on splines. This model consists of both purely and smoothly nonparametric components. As an estimation method of this model, we use the weighted least square estimation by Huller and Mckeague (1991). We provide an illustrative example as well as a simulation study that compares the performance of our method with the ordinary least square method.
A Nonparametric Additive Risk Model Based on Splines
박철용 한국데이터정보과학회 2007 한국데이터정보과학회지 Vol.18 No.1
We consider a nonparametric additive risk model that is based on splines. This model consists of both purely and smoothly nonparametric components. As an estimation method of this model, we use the weighted least square estimation by Huffer and McKeague (1991). We provide an illustrative example as well as a simulation study that compares the performance of our method with the ordinary least square method.
Component selection in additive quantile regression models
Hohsuk Noh,이은령 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.3
Nonparametric additive models are powerful techniques for multivariate data analysis. Although many procedures have been developed for estimating additive components bothin mean regression and quantile regression, the problem of selecting relevant componentshas not been addressed much especially in quantile regression. We present a doublypenalizedestimation procedure for component selection in additive quantile regressionmodels that combines basis function approximation with a ridge-type penalty and a variantof the smoothly clipped absolute deviation penalty. We show that the proposed estimatoridentifies relevant and irrelevant components consistently and achieves the nonparametricoptimal rate of convergence for the relevant components. We also provide an accurateand efficient computation algorithm to implement the estimator and demonstrate itsperformance through simulation studies. Finally, we illustrate our method via a real dataexample to identify important body measurements to predict percentage of body fat of anindividual.