| Popis: |
We propose a nonlinear regression model that uses basis expansion for the case where the underlying regression function has inhomogeneous smoothness. In this case, conventional nonlinear regression models tend to over- or underfit where the function is smoother or less smooth, respectively. We begin by roughly approximating the underlying regression function with a locally linear function. We then extend the fused lasso signal approximator and thereby develop a fast and efficient algorithm. We next use the residuals between the locally linear functions and the data to adaptively prepare the basis functions. Finally, using a regularization method, we construct a nonlinear regression model with these basis functions. To select the optimal value of the tuning parameter for the regularization method, we provide an explicit form of the generalized information criterion. The validity of our proposed method is then demonstrated through several numerical examples. |
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