Questions tagged [functional-data-analysis]

Functional Data Analysis defines a framework where the fundamental units of analysis are functions.

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Forecasting a series that comes with uncertainty

I have a time series resulting from a spatiotemporal aggregation on the spatial domain. As a result, I have a central measurement (let's say mean average) and a dispersion (let's say standard ...
30 views

To what extent can likelihood methods be used for functional responses?

Let's suppose that we are working with a functional data set, $Y_i(t)$, $Y_i\in L^2[0,1]$, $1\le i\le n$. If we were working with univariate or even multivariate data set, likelihood methods would ...
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Is there a statistical test to compare two heatmaps/response surfaces or two curves?

I am conducting a series of experiments in which I analyse the effect of the order of treatment of bacterial cells with different concentrations of two compounds (Drug 1 and Drug 2). The values in the ...
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Why does FPCA not use scaling as PCA?

Functional principal component analysis (FPCA), according to the original paper, does not use scaling before FPCA, as in PCA. Instead, it uses a covariance matrix to compute the eigen-components. I ...
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Is the FPCA just a PCA on coefficients?

Is functional principal-components analysis (FPCA) on basis representations just a PCA on the component coefficients? The following seems to indicate that yes, it is: ...
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Error function of Functional Principal Component Regression is itself a curve. Why?

I have data indexed from 0 to 54. Using 6 principal components that explains 99% variation of data I was not expecting the error function to exhibit such a clear shape? By error function from ...
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Functional Data Analysis - minimum points per curve?

I am embarking on a project for which I'd like to use functional Data Analysis (FDA). I have several thousand discrete curves objects on which I'd like to fit continuous time curves. These discrete ...
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How can I use functional time series or functional principal component regression for forecasting this type of data?

Lets say I have this type of data. For one of the series, I observed data until day 300. Can I use functional principal component regression to forecast next 50 observations? What is the best way to ...
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Why is Functional Data Analysis (FDA) not as popular?

I am interested in FDA (data perceived as functions), as someone from a pure mathematics background and I think it can help provide solutions to some major challenges in data analysis (also data ...
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Fourier Basis with even number of basis functions (R, FDA package)

For a project on scalar-on-function regression using a truncated basis expansion of the coefficient function, I am trying to understand why an even number of Fourier basis functions is only useful in ...
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Two sample hypothesis tests for functional (curve) data

Suppose I have two samples of functional data or curves $x_i(t), i \in \{1,\dots,n_1\}$ and $y_i(t)\in\{1,\dots,n_2\}$ for $t\in\{1,\dots,T\}$. What tests are suitable for testing the null hypothesis ...
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Principles in experiment design for functional data analysis

The goal or objective of "standard"$^†$ experiment design is to design a data collection scheme (for a finite budget) such that linear models$^†$ can be applied and inference results can be ...
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Generalized additive models vs. functional data models

I am not sure I understand the difference between functional data analysis (FDA) and GAM. Or in short, I was reading about GAM and I found the following model which seems like an FDA model (there is a ...
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Coefficients in Functional Regression

I would like to estimate the effect of DoE factors in my response which is a function. For this reason, I tried to apply the Functional Data Analysis method. As example, I have a 12 treatment DoE, <...
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