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Title: Regression Spline via Penalizing Derivatives.
Keywords: Regression Splines, Truncated Power Basis, SCAD, Derivatives, Sparse, Re-parameterize
Issue Date: 7-Jan-2009
Citation: ZHU YEYING (2009-01-07). Regression Spline via Penalizing Derivatives.. ScholarBank@NUS Repository.
Abstract: Regression spline based on a truncated power basis has been proved to be a very useful nonparametric method for fitting a data set generated from the nonparametric regression model, where the underlying function m(t) is unknown. In some situations when the coefficient vector is large dimensional and the pth times derivatives of the regression function are sparse, we attempt to re-parameterize the coefficient vector as a linear function of certain derivative vector, whose last K + 1 components are the pth times derivatives of the regression spline function. Then, the smoothly clipped absolute deviation (SCAD) method of Fan and Li (2001) can be adopted to select and estimate the non-zero components of the transformed coefficients simultaneously. The proposed method is shown to be more efficient than estimating the coefficients by SCAD method directly, especially when the true curve is piecewise with different orders of polynomials at different segments.
Appears in Collections:Master's Theses (Open)

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