Variance Reduction in Smoothing Splines |
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Authors: | ROBERT L PAIGE SHAN SUN KEYI WANG |
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Institution: | Department of Mathematics and Statistics, Texas Tech University; Department of Mathematics, University of Texas Arlington; Edwards Lifesciences |
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Abstract: | Abstract. We develop a variance reduction method for smoothing splines. For a given point of estimation, we define a variance-reduced spline estimate as a linear combination of classical spline estimates at three nearby points. We first develop a variance reduction method for spline estimators in univariate regression models. We then develop an analogous variance reduction method for spline estimators in clustered/longitudinal models. Simulation studies are performed which demonstrate the efficacy of our variance reduction methods in finite sample settings. Finally, a real data analysis with the motorcycle data set is performed. Here we consider variance estimation and generate 95% pointwise confidence intervals for the unknown regression function. |
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Keywords: | clustered/longitudinal data non-parametric regression smoothing splines variance reduction |
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