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FAST ADAPTIVE PENALIZED SPLINES

• Tatyana Krivobokova, Department of Economics, University of Bielefeld, Bielefeld, Germany
• Ciprian M. Crainiceanu, Johns Hokins Bloomberg School of Public Health, Department of Biostatistics
• Goran Kauermann, Department of Economics, University of Bielefeld, Bielefeld, Germany

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Abstract:

This paper proposes a numerically simple routine for locally adaptive smoothing. The locally heterogeneous regression function is modelled as a penalized spline with a smoothly varying smoothing parameter modelled as another penalized spline. This is being formulated as hierarchical mixed model, with spline coe±cients following a normal distribution, which by itself has a smooth structure over the variances. The modelling exercise is in line with Baladandayuthapani, Mallick & Carroll (2005) or Crainiceanu, Ruppert & Carroll (2006). But in contrast to these papers Laplace's method is used for estimation based on the marginal likelihood. This is numerically simple and fast and provides satisfactory results quickly. We also extend the idea to spatial smoothing and smoothing in the presence of non normal response.

Subject Area:

General Biostatistics

Suggested Citation:

Tatyana Krivobokova, Ciprian M. Crainiceanu, and Goran Kauermann, "FAST ADAPTIVE PENALIZED SPLINES" (March 2007). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 100.
http://www.bepress.com/jhubiostat/paper100