FunctionalCalibration (version 1.0.0)

functional_calibration_splines: Functional Data Calibration with Splines

Description

This function performs functional calibration based on the following model:

$$A_i(x_m) = \displaystyle \sum_{l=1}^{L} y_{il} \alpha_l(x_m) + e_i(x_m), \quad i = 1,...,I, \quad m = 1,...,M = 2^J$$

where the functions \(\alpha_l(x)\) are estimated using spline basis functions.

In matrix notation, the model is represented as:

$$A = \alpha y + e$$

Usage

functional_calibration_splines(data, weights, x, n_functions = 10)

Value

The function returns a list containing two objects.

alpha

A matrix with the estimated functional coefficients \(\alpha\).

Plots

A list of plot objects, each representing the corresponding function \(\alpha_l(x)\).

Arguments

data

A matrix \(M\) x \(I\) where each column represents one sample of the aggregated function — the matrix \(A\) in the model.

weights

A matrix \(L\) x \(I\) representing the weight values associated with each sample — the matrix \(y\) in the model.

x

A numeric vector of values at which the function is evaluated.

n_functions

Number of spline basis functions to be used for estimating \(\alpha_l(x)\).

References

Saraiva, M. A., & Dias, R. (2009). Analise não-parametrica de dados funcionais: uma aplicação a quimiometria (Doctoral dissertation, Master’s thesis, Universidade Estadual de Campinas, Campinas).

Examples

functional_calibration_splines(simulated_data$data, simulated_data$weights, simulated_data$x)
functional_calibration_splines(simulated_data$data, simulated_data$weights, simulated_data$x, 12)