weight_estimation

Estimates the weights associated with the functional coefficients
$\alpha_l(x)$ using the using Ordinary Least Squares.
The problem can be formulated as:
$$A(x) = \displaystyle \sum_{l=1}^{L} y_l \alpha_l(x)$$
where $A(x)$ is the aggregated function evaluated at each point $x$,
$\alpha_l(x)$ are the functional coefficients, and $y_l$ are the weights to be estimated.

Implements methods for calibrating an aggregated functional data model using
wavelets or splines. Each aggregated curve is modeled as a linear combination of
component functions and known weights. The component functions are estimated using
wavelets or splines. The package is based on dos Santos Sousa (2024) <doi:10.1515/mcma-2023-2016>
and Saraiva and Dias (2009) <doi:10.47749/T/UNICAMP.2009.471073>.

Vitor Perrone

FunctionalCalibration

Aggregated Functional Data Calibration using Splines and
Wavelets

Alex Sousa

weight_estimation function

<dl><dt>data</dt>
<dd>A numeric vector representing one sample of the aggregated function $A(x)$, evaluated at a grid of points $x$.</dd>
<dt>alpha</dt>
<dd>A numeric matrix where each column represents the values of a function $\alpha_l(x)$ evaluated at the same grid of points as <code>data</code>.</dd></dl>

Arguments

Weight Estimation — weight_estimation

<dl>

<dt>data</dt>
<dd>A numeric vector representing one sample of the aggregated function $A(x)$, evaluated at a grid of points $x$.</dd>


<dt>alpha</dt>
<dd>A numeric matrix where each column represents the values of a function $\alpha_l(x)$ evaluated at the same grid of points as <code>data</code>.</dd>

</dl>

weight_estimation: Weight Estimation

Description

Usage

Value

Arguments

Examples