R: Constructors for functional data in basis representation

tfb {tf}

R Documentation

Constructors for functional data in basis representation

Description

Various constructors for tfb-vectors from different kinds of inputs.

Usage

tfb(data = data.frame(), basis = c("spline", "fpc", "wavelet"), ...)

tfb_wavelet(data, ...)

as.tfb(data, basis = c("spline", "fpc"), ...)

Arguments

`data`	a `matrix`, `data.frame` or `list` of suitable shape, or another `tf`-object containing functional data.
`basis`	either "`spline`" (see `tfb_spline()`, the default) or "`fpc`" (see `tfb_fpc()`). (`wavelet` not implemented yet)
`...`	further arguments for `tfb_spline()` or `tfb_fpc()`

Details

tfb is a wrapper for functions that set up spline-, principal component- or wavelet-based representations of functional data. For all three, the input data x_i(t) are represented as weighted sums of a set of common basis functions B_k(t); k = 1,\dots, K identical for all observations and weight or coefficient vectors b_i = (b_{i1}, \dots, b_{iK}) estimated for each observation: x_i(t) \approx \sum_k B_k(t) b_{ik}. Depending on the value of basis, the basis functions B(t) will either be spline functions or the first few estimated eigenfunctions of the covariance operator of the x(t) (fpc) or wavelets (wavelet).

See tfb_spline() for more details on spline basis representation (the default). See tfb_fpc() for using an functional principal component representation with an orthonormal basis estimated from the data instead.

Value