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Abstract:
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It is well known that Free-knot spline introduces flexible location parameters in the polynomial splines in order to capture the nonlinear trend and distinct structure changes. The free location unknowns bring advantages to capture marked data pattern precisely and also unavoidable lethargy and heavy computational cost. In this paper, we proposed a penalized free-knot spline and bootstrapping algorithms for confidence bands with a focus on likelihood function maximization for model computation. To optimize the non-linear objective functions, we borrow the Automatic Differentiation Model Builders proposed by Skaug and Fourier (2006) to approximate general likelihood functions. With satisfied performance and improved computation power, the proposed methods have been applied in the a wide range of models including Gaussian, Generalized Linear Model, and Quasi-likelihood functions in simulation studies and real data analysis.
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