numeric_basis_expansion: Numeric basis expansion for functional variable data
In MECfda: Scalar-on-Function Regression with Measurement Error Correction

numeric_basis_expansion

R Documentation

Numeric basis expansion for functional variable data

Description

For a function f(t), t\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 we use here is numerically represented by the value of basis functions at some points in the domain.

Usage

numeric_basis_expansion(object, num_basis)

## S4 method for signature 'functional_variable,numeric_basis'
numeric_basis_expansion(object, num_basis)

Arguments

`object`	a `functional_variable` class object. The minimum and maximum of the slot `t_points` should be respectively equal to the slot `t_0` and slot `t_0` plus slot `period`.
`num_basis`	a `numeric_basis` class object, representing the function basis. See `numeric_basis`.

Value

Returns a numeric matrix, (b_{ik})_{n\times p}, with an extra attribute numeric_basis, which is the numeric_basis object input by the argument num_basis.