Constructors for functional data in basis representation

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()

Value

a tfb-object (or a data.frame/matrix for the conversion functions, obviously.)

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.

See also

Other tfb-class: fpc_wsvd(), tfb_fpc(), tfb_spline()

Other tfb-class: fpc_wsvd(), tfb_fpc(), tfb_spline()