fourier_basis_expansion: Fourier basis expansion for functional variable data

In MECfda: Scalar-on-Function Regression with Measurement Error Correction

Fourier basis expansion for functional variable data

Description

For a function f(x), x\in\Omega, and a basis function sequence \{\rho_k\}_{k\in\kappa}, basis expansion is to compute \int_\Omega f(t)\rho_k(t) dt. Here we do basis expansion for all f_i(t), t\in\Omega = [t_0,t_0+T] in functional variable data, i=1,\dots,n. We compute a matrix (b_{ik})_{n\times p}, where b_{ik} = \int_\Omega f(t)\rho_k(t) dt. The basis used here is the Fourier basis,

\frac{1}{2},\ \cos(\frac{2\pi}{T}k[x-t_0]),\ \sin (\frac{2\pi}{T}k[x-t_0])

where x\in[t_0,t_0+T] and k = 1,\dots,p_f.

Usage

fourier_basis_expansion(object, order_fourier_basis)

## S4 method for signature 'functional_variable,integer'
fourier_basis_expansion(object, order_fourier_basis)

Arguments

object	a functional_variable class object.
order_fourier_basis	the order of Fourier basis, p_f.

Value

Returns a numeric matrix, (b_{ik})_{n\times p}, where b_{ik} = \int_\Omega f(t)\rho_k(t) dt.

Author(s)

Heyang Ji

MECfda documentation built on April 3, 2025, 10:07 p.m.