functional_calibration_splines {FunctionalCalibration} | R Documentation |
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)
Arguments
data |
A matrix |
weights |
A matrix |
x |
A numeric vector of values at which the function is evaluated. |
n_functions |
Number of spline basis functions to be used for estimating |
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)
.
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)