pwcv {refund}

Pointwise cross-validation for function-on-scalar regression

Description

Estimates prediction error for a function-on-scalar regression model by leave-one-function-out cross-validation (CV), at each of a specified set of points.

Usage

pwcv(
  fdobj,
  Z,
  L = NULL,
  lambda,
  eval.pts = seq(min(fdobj$basis$range), max(fdobj$basis$range), length.out = 201),
  scale = FALSE
)

Arguments

fdobj

a functional data object (class fd) giving the functional responses.

Z

the model matrix, whose columns represent scalar predictors.

L

a row vector or matrix of linear contrasts of the coefficient functions, to be restricted to equal zero.

lambda

smoothing parameter: either a nonnegative scalar or a vector, of length ncol(Z), of nonnegative values.

eval.pts

argument values at which the CV score is to be evaluated.

scale

logical value or vector determining scaling of the matrix Z (see scale, to which the value of this argument is passed).

Details

Integrating the pointwise CV estimate over the function domain yields the cross-validated integrated squared error, the standard overall model fit score returned by lofocv.

It may be desirable to derive the value of lambda from an appropriate call to fosr, as in the example below.

Value

A vector of the same length as eval.pts giving the CV scores.

Author(s)

Philip Reiss [e-mail]

References

Reiss, P. T., Huang, L., and Mennes, M. (2010). Fast function-on-scalar regression with penalized basis expansions. International Journal of Biostatistics, 6(1), article 28. Available at https://pubmed.ncbi.nlm.nih.gov/21969982/

See Also

fosr, lofocv