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

Venue: | ANN. STATIST |

Citations: | 89 - 45 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}

}

### Years of Citing Articles

### 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...

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Citation Context ...u, Bates, Chen and Wahba (1989), Chen, Gu and Wahba (1989), Gu (1992b), Gu and Wahba (1991a,b, 1993a,b), Chen(1991,1993), and others, discuss further various aspects of these models. The code RKPACK (=-=Gu 1989-=-, available from statlib@lib.stat.cmu.edu) will fit specified SS-ANOVA models given Gaussian data. O'Sullivan (1983), O'Sullivan, Yandell and Raynor (1986), in the d = 1 case, proposed penalized log l... |

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Citation Context ...: 12:5 25 37:5 50 62:5 75 87:5 dur (years) : 3:3 5:4 7:1 9:2 11:5 15:3 21:6 gly (%) : 9:6 10:7 11:5 12:2 13:2 14:1 15:4 bmi (kg=m 2 ) : 18:7 20:6 21:7 22:9 23:9 25:2 27:0 (6.2) As previously reported(=-=Klein et al 1988-=-), increases in glycosylated hemoglobin at baseline are associated with increases in the risk of progression of diabetic retinopathy over the first four years of the study. At most durations of diabet... |

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