functional_calibration_wavelets {FunctionalCalibration} | R Documentation |
Functional Data Calibration with Wavelets
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 wavelet decomposition.
In matrix notation, the model is represented as:
A = \alpha y + e
Usage
functional_calibration_wavelets(
data,
weights,
wavelet = "DaubExPhase",
method = "bayesian",
tau = 1,
p = NULL,
sigma = NULL,
MC = FALSE,
type = "soft",
singular = FALSE,
x = NULL
)
Arguments
data |
A matrix |
weights |
A matrix |
wavelet |
A string indicating the wavelet family to be used in the Discrete Wavelet Transform (DWT). |
method |
A string specifying the shrinkage method applied to the empirical wavelet coefficients. Options are: "bayesian", "universal", "sure", "probability", or "cv". |
tau |
A numeric value for the |
p |
A numeric value for the |
sigma |
A numeric value for the |
MC |
A logical evaluating to |
type |
A string indicating whether the thresholding should be "soft" or "hard" (applies only when the method is not "bayesian"). |
singular |
A logical evaluating to |
x |
A numeric vector of values at which the function is evaluated. If |
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
dos Santos Sousa, A. R. (2024). A wavelet-based method in aggregated functional data analysis. Monte Carlo Methods and Applications, 30(1), 19-30.
Examples
functional_calibration_wavelets(simulated_data$data, simulated_data$weights)
functional_calibration_wavelets(simulated_data$data, simulated_data$weights,
tau = 5, p = 0.95, sigma = 0.1, x = simulated_data$x)
functional_calibration_wavelets(simulated_data$data, simulated_data$weights,
method = "universal")