# Questions tagged [functional-data-analysis]

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

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### Efficient storage of functional data

I have access to a sample (size $N$) of functional data. Each observation corresponds to $C$ functions. Each function $f_{n,c}$ is represented by $T_n$ points for $1\geq n \geq N, 1\geq c \geq C$. All ...
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### Methods for modelling distributions?

As predictor X I have particle size distributions and I would like to run a model y ~ X. I.e. each trial has a response ...
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### Roughness penalty matrix for the Fourier basis functions

I am trying to understand how the roughness penalty matrix for the Fourier basis functions is calculated in R using the fda ...
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### Prove that $K(x_{1},x_{2})=f(x_{1})K_{1}(x_{1},x_{2})f(x_{2})$ is symmetric positive definite if $K_{1}(x_{1},x_{2})$ is symmetric positive definite

I have been trying to prove this 5th proposition on the 25th slide We can prove that $K(x_{1},x_{2})$ will be a valid kernel as: \begin{align} K(x_{1},x_{2}) = & \; f(x_{1})K_{1}(x_{1},x_{2})f(...
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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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### Predict parameters of another model

I would like to make a model to predict the parameters of another model. As example, By using design of experiment I made some trials and I measured the temperature (response). e.g. ...
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### How to Generalize functional Autoregressive model

I am working with the multivariate hourly electricity price data, data consist of six years hourly electricity data in which the first five years are use as testing set and the last year as validation ...
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### Asymptotic properties of functional models

When working in Functional Data Analysis, a classical "preprocessing" step is to represent the "observations" using a B-spline expansion:  X_i(t) \approx \sum_{j=1}^J \lambda_{ij}...
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### functional principle components is retransform to original data

I am working with multivariate time series hourly data of five years, I use the first four years as testing set and last one year as validation set. My objective is to obtain one year hourly forecast, ...
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### Control of type I error rate in functional ANOVA F-test

I am following how to compare curves via functional data analysis, specifically functional ANOVA. This video makes sense in describing it as being a lot like vanilla ANOVA...up to a point. When we do ...
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### Reference request: Modulus of continuity of the map from parameter space to the space of probability measures

I am thinking of the following condition in my research: Let $\Theta \subset \mathbb R$ be the parameter space and $\mathbb P_\theta$ be the probability measure on sample space $\mathbb X$ ...
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### How to prove properties about mixed (discrete and continuous inputs) function spaces?

I am using Gaussian Processes for data with mixed inputs (discrete and continuous input variables) i.e. $𝑥=[𝑥_𝑐,𝑥_𝑑]$ where $𝑥_𝑐 \in \Re$ and $x_d \in \mathbb{Z}$. There is a lot of work on ...
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