Degrees‐of‐freedom tests for smoothing splines

By Eva Cantoni, Trevor J. Hastie. 2002

66 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanical Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7671fac6e552986a85059ca1e8cd56d360db390d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Ciprian M. Crainiceanu
2. Sylvain Sardy
3. Gerda Claeskens
4. Yuedong Wang
5. Chunlei Ke
6. David Ruppert
7. Paul Tseng
8. Tom A. B. Snijders

In Mechanical Engineering

1. David Ruppert
2. Paul Tseng
3. Gerda Claeskens
4. Ciprian M. Crainiceanu
5. Tom A. B. Snijders
6. Johannes Berkhof

In Statistics and Probability

1. Ciprian M. Crainiceanu
2. Gerda Claeskens
3. David Ruppert
4. Yuedong Wang
5. Paul Tseng
6. Chunlei Ke
7. Sylvain Sardy
8. Tom A. B. Snijders

Citations in the corpus

• Diagnostic Checks for Multilevel Models (2008, methodology): “65] provide some approximate F -tests based on residual sums of squares and Cantoni and Hastie [9] and Guo [22] present likelihood ratio tests for H0 : λ −1 = 0 which is equivalent to H0 : η = 0 (3.”
• Restricted likelihood ratio lack‐of‐fit tests using mixed spline models (2004, background): “Cantoni and Hastie (2002) constructed a likelihood ratio type of statistic in a setting of mixed smoothing splines, thereby reformulating the hypotheses in terms of degrees of freedom.”
• ON SEMIPARAMETRIC REGRESSION WITH O'SULLIVAN PENALIZED SPLINES (2008, unknown): “Nychka & Cummins, 1996; Cantoni & Hastie, 2002; Welham et al., 2007).”
• Semiparametric Nonlinear Mixed-Effects Models and Their Applications (2001, background): “There are several ways which Ofm1 ‹4¢5 can be represented as a mixed model (e.g., Wahba 1978; Speed 1991; Verbyla 1994; Cantoni and Hastie 2000).”
• AMlet, RAMlet, and GAMlet: Automatic Nonlinear Fitting of Additive Models, Robust and Generalized, With Wavelets (2004, background): “The selection of the smoothing parameters also remains an open question (Cantoni and Hastie 2002).”
• Likelihood ratio tests in linear mixed models with one variance component (2003, result): “Cantoni and Hastie (2002) proposed a test (called R in their paper) that is derived from the LRT in the LMM representation of a smoothing spline.”
• Smoothing parameter selection for a class of semiparametric linear models (2009, unknown): “When equation (1) represents the non-parametric regression model (3) or the semiparametric regression model (4), assumption 2 may not hold, and assumption 3 does not hold in many formulations (although Cantoni and Hastie (2002) did make this assumption).”