smooth.construct.sp.smooth.spec: Slepian projection smoothers in GAMs

In spsmooth: spsmooth: An Extension Package for 'mgcv'.

Description

gam can use arbitrary smooths, specified via terms like s(x, bs="XX"). This extension package allows for use of the term s(x, bs="sp") which specifies a non-penalized Slepian (discrete prolate spheroidal sequence) projection smoother.

Usage

## S3 method for class 'sp.smooth.spec'
smooth.construct(object, data, knots) 

Arguments

object	A smooth specification object, usually generated by a term s(..., bs="sp", xt=c(W=w, mask=UserMask), ...), where the user-specified W is the standardized bandwidth and UserMask is a logical vector corresponding to data availability for the GAM.
data	A list containing just the data required by this term, typically an index series corresponding to time. Name should correspond to object$term. If data does not consist of a contiguous index series (in time), element mask must be included as part of object. This is done by including xt=c(mask=UserMask) as a parameter to the s function call. See the example in spsmooth.
knots	Object should be NULL, and is functionally ignored. Only included for compatibility with gam framework.

Details

The constructor is not normally called directly, but is rather used internally by gam.

As a subspace projection operator, this smoother does not use knots: each basis vector has full support.

Suggests that a bandwidth parameter be set, 0 < W < 0.5. This bandwidth parameter is directly equivalent to the band-pass of the resulting projection operator. This parameter is standardized to be in units of cycles/timeStep, where timeStep is the dT time step for the data being smoothed, i.e. 1 hour, 1 day, etc..

In the case of missing data, requires a mask vector be passed as an extra parameter via the s(..., xt=c(mask=UserMask)) in gam in order to accurately compute the basis matrix.

Value

An object of class sp.smooth. In addition to the usual elements of a smooth class documented under smooth.construct, this object will contain:

v	Full-length basis matrix, before sub-selecting for missing data.
N	Length of full (including NA) index series.
k	Number of basis vectors used, typically floor(2NW) - 1.
W	Time-Bandwidth parameter, strictly bounded 0 < W < 0.5.
C	Defaulted to 1, removing centering constraints. These constraints tamper with the innate orthonormality of the basis vectors.

Author(s)

Wesley Burr

References

Slepian, D. (1978) Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty – V: The Discrete Cases. Bell Systems Technical Journal, V. 57, pp. 1371-1429.

spsmooth documentation built on April 15, 2017, 2:51 a.m.