scam (version 1.1-5)

gcv.ubre_grad: The GCV/UBRE score value and its gradient

Description

For the estimation of the SCAM smoothing parameters the GCV/UBRE score is optimized outer to the Newton-Raphson procedure of the model fitting. This function returns the value of the GCV/UBRE score and calculates its first derivative with respect to the log smoothing parameter using the method of Wood (2009). The function is not normally called directly, but rather service routines for bfgs_gcv.ubre.

Usage

gcv.ubre_grad(rho, G, gamma, ee, eb, esp, 
                             check.analytical, del)

Arguments

rho

log of the initial values of the smoothing parameters.

G

a list of items needed to fit a SCAM.

gamma

A constant multiplier to inflate the model degrees of freedom in the GCV or UBRE/AIC score.

ee

Get the enviroment for the model coefficients.

eb

Get the enviroment for the model coefficients derivatives.

esp

Get the enviroment for the smoothing parameter.

check.analytical

If this is TRUE then finite difference derivatives of GCV/UBRE score will be calculated, otherwise NULL.

del

A positive scalar (default is 1e-4) giving an increment for finite difference approximation when check.analytical=TRUE, otherwise NULL.

Value

• A list is returned with the following items:
• dgcv.ubre
  The value of GCV/UBRE gradient.
• gcv.ubre
  The GCV/UBRE score value.
• scale.est
  The value of the scale estimate.
• object
  The elements of the fitting procedure monogam.fit for a given value of the smoothing parameter.
• dgcv.ubre.check
  If check.analytical=TRUE this returns the finite-difference approximation of the gradient.
• check.grad
  If check.analytical=TRUE this returns the relative difference (in and finite differenced derivatives.

References

Pya, N. (2010) Additive models with shape constraints. PhD thesis. University of Bath. Department of Mathematical Sciences Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press. Wood, S.N. (2011) Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society: Series B. 73(1): 1--34

See Also

scam, bfgs_gcv.ubre