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 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).

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)


[Package FunctionalCalibration version 1.0.0 Index]