Existence and Uniqueness of Penalized Least Square Estimation for Smoothing Spline Nonlinear Nonparametric Regression Models
نویسندگان
چکیده
where Ni are known nonlinear functionals, g = (g1, · · · , gr) are unknown functions, and 2i iid ∼ N(0, σ) are random errors. Without loss of generality, we assume that r = 2. As in O’Sullivan (1990), we express design points x explicitly in the functional Ni: Ni(g1, g2) = η(g1, g2; xi), where η is a known nonlinear functional. In the following sections, η(g1, g2; x) is sometimes also represented by η(g1, g2) or η when the meaning is clear. g1 and g2 are estimated as minimizers of the following penalized least squares (PLS)
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