## Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic Retinopathy (1995)

Venue: | ANN. STATIST |

Citations: | 83 - 44 self |

### BibTeX

@ARTICLE{Wahba95smoothingspline,

author = {Grace Wahba and Yuedong Wang and Chong Gu and Ronald Klein and Barbara Klein},

title = {Smoothing Spline ANOVA for Exponential Families, with Application to the Wisconsin Epidemiological Study of Diabetic Retinopathy},

journal = {ANN. STATIST},

year = {1995},

volume = {23},

pages = {1865--1895}

}

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### OpenURL

### Abstract

Let y i ; i = 1; \Delta \Delta \Delta ; n be independent observations with the density of y i of the form h(y i ; f i ) = exp[y i f i \Gammab(f i )+c(y i )], where b and c are given functions and b is twice continuously differentiable and bounded away from 0. Let f i = f(t(i)), where t = (t 1 ; \Delta \Delta \Delta ; t d ) 2 T (1)\Omega \Delta \Delta \Delta\Omega T (d) = T , the T (ff) are measureable spaces of rather general form, and f is an unknown function on T with some assumed `smoothness' properties. Given fy i ; t(i); i = 1; \Delta \Delta \Delta ; ng, it is desired to estimate f(t) for t in some region of interest contained in T . We develop the fitting of smoothing spline ANOVA models to this data of the form f(t) = C + P ff f ff (t ff ) + P ff!fi f fffi (t ff ; t fi ) + \Delta \Delta \Delta. The components of the decomposition satisfy side conditions which generalize the usual side conditions for parametric ANOVA. The estimate of f is obtained as the minimizer...