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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 ...
Ricardo Barros Lourenço's user avatar
2 votes
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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 ...
cgmil's user avatar
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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 ...
T07072014's user avatar
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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 ...
Palantir's user avatar
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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: ...
Mark Wexler's user avatar
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1 answer
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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 ...
MSKO's user avatar
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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 ...
s5s's user avatar
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1 answer
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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 ...
MSKO's user avatar
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Convergence of variational posterior

Let $q_\lambda(z)\in\mathcal Q$ be the variational posterior approximation of $p(z|y)$. Note that the optimal $\lambda^*$ is approximated by the following recursive sequence $$ \lambda^{(k+1)}=\lambda^...
KNN's user avatar
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3 votes
1 answer
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Simulating iid mean zero Matérn processes

I'm currently learning FDA (functional data analysis), following "Introduction to Functional Data Analysis" by Kokoszka & Reimherr. Here it is exercice 1.5: 1.5 The Matérn covariance ...
eloi navarro diaz's user avatar
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Covariance of functional data object

This is a follow-up question on my earlier question Functional Regression in R: Functional Response Regressed on Scalar Covariate. I have a functional response $Y(t)$ (i.e., a stochastic process) ...
Quertiopler's user avatar
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1 answer
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Empirical basis functions

Preliminary Consider $n$ individuals each with observed data $ Z_i, i = 1, \ldots, n$. For each individual $i$, the longitudinal predictor $Z_i = \{Z_i(t_{i1}), \ldots, Z_i(t_{i,R_i})\}$ is measured ...
ADAM's user avatar
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Functional Principal Component Analysis - Explaining Functional Principal Component Scores

I was wondering if someone can help with explaining Functional Principal Component Scores? I am working with a dataset which reflects participants in a weight loss management trial (longitudinal data)....
Data_Science_Mick's user avatar
3 votes
1 answer
92 views

Functional Regression in R: Functional Response Regressed on Scalar Covariate

I have a functional response $Y(t)$ (i.e., a stochastic process) which I regress on a set of scalar explanatory variables $X_1$ ($=1$, i.e., $X_1$ is a constant term), $X_2$, and $X_3$. The equation I ...
Quertiopler's user avatar
1 vote
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Functional Data Analysis with Missing Data

I am trying to analyze a dataset containing several observations for n = 27. Unfortunately, not every participant answered the question every time, i.e., when plotting the graph it has holes in it. I ...
Soph's user avatar
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3 votes
1 answer
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Generate survival data with functional data using R

I am reading this article here and trying to regenerate their simulation study. Here is this scenario here, among others, but if I can figure out one, the rest follow. That is, Simulation set-up we ...
ADAM's user avatar
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Simulating models for longitudinal and survival data

This simulation study is taken from this [article] (https://pubmed.ncbi.nlm.nih.gov/35574725/). I am trying to generate this simulation Theoretical Set up Define the set of true basis functions, \...
ADAM's user avatar
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Does anyone know how to model selection for function on function linear model to find the best subset of functional covariate in R [closed]

Does anyone know how to model selection for function on function linear model to find the best subset of functional covariate in R
Sky Sha's user avatar
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Influence function of conditional quantile

I'm trying to derive the influence function of the estimand $\Psi$ $$\Psi(P) = P(Y > y | X = x)$$ Following tutorials for deriving the influence function of the average treatment effect here. Has ...
dogs4ever's user avatar
3 votes
1 answer
387 views

Functional analysis in R with fda

I'm working with time series data for drug response. And, I wanted to as is there are some alternative ways to analyse it since the FDA package in R is not working in my case. The type of my data is ...
Rosa Maria's user avatar
1 vote
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truncated Functional data analysis + identify subgroups?

I have intensive longitudinal data about heartbeat rates, movement activity measured by actiwatch, respiration rates etc... collected from about 100 patients at a terminal care. For each patient, data ...
ReiMon's user avatar
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Is there a substitute for an "average" which best inherently represents data, rather than reducing it to one or another aspect?

I was thinking about the arithmetic average as a type of metric or a representation of data. Maybe there is a mathematical argument for the non-arbitrariness of that function. I think something like ...
Julius Hamilton's user avatar
2 votes
2 answers
81 views

Curve quantification

I have some longitudinal measurement data of 15,000. I smoothed that data with B-spline smoothing and got the following curve. I then want to quantify this curve and extract features for clustering ...
NakataKoo's user avatar
1 vote
0 answers
41 views

How to combine dissimilar curves into a single "average"?

With relevance to "functional data analysis", I am looking for some approach which can give an intermediate function among these five different function plots, where this "average ...
Superunknown's user avatar
1 vote
0 answers
83 views

Statistical method for finding homogeneous groups of curves

I need to divide a set of 100 or more response curves into groups. These curves are formed by backscattering intensity along a range of frequencies. Basically, each curve represents the intensity in ...
il nibbio's user avatar
1 vote
0 answers
60 views

Forecasting using functional data analysis with parametric models for the functions

I have collected data at regularly spaced time intervals, and at each time, the observed data is commonly fit by a simple parametric functional form involving several parameters. A naive approach to ...
Barry's user avatar
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204 views

Reproducing kernel hilbert space norm as smoothness functional

Let $K:X \times X \rightarrow \mathbb{R}$ be a Mercer kernel with an associated RKHS $H$ then the norm $|f|_H^2$ can be used as a way to ensure that $f$ is smooth in $H$. If i understand correctly, ...
endeavor's user avatar
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1 answer
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Estimating the standard deviation

I have data of a function $f(t)$, where I always have just a single data point per $t$. It is known that the data is affected by noise, where the noise itself is also a function of $t$. Now I want to ...
Johny Dow's user avatar
3 votes
1 answer
55 views

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 ...
fool's user avatar
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2 votes
1 answer
58 views

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 ...
Lefty's user avatar
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1 answer
363 views

Fitting an functional autoregressive model in R with mgcv

I'm working with the 'mgcv' package in R and I just want to know if I am going about the right way of fitting a functional autoregressive (FAR) model. The FAR model is represented as $$Y=f_1(x.1)x.1+...
Warhawk1987's user avatar
19 votes
2 answers
3k views

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 ...
KaRJ XEN's user avatar
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0 answers
163 views

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 ...
Jakob J's user avatar
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2 votes
1 answer
59 views

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 ...
fool's user avatar
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1 vote
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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 ...
fool's user avatar
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0 answers
77 views

Approximating RKHS norm with samples

I have a function $f'$, sampled from a Gaussian process prior with a known kernel $f' \sim N(0,K)$. Is it possible to find/approximate a solution for $min_w||f_w-f'||^2_H$ if I can calculate both $...
Cat-with-a-pipe's user avatar
1 vote
0 answers
18 views

Covariance kernel: understanding the term within groups and between groups terms of a two-way functional ANOVA

I was studying the paper "Multilevel Functional Principal Component Analysis" by Chong-Zhi Di et. al. To find the functional PCA for functional data with group factor, it is suggested to use ...
Hoàng Đình Thịnh's user avatar
1 vote
1 answer
237 views

Is panel data the same as functional data?

Panel data is defined in wikipedia as: In statistics and econometrics, panel data and longitudinal data are both multi-dimensional data involving measurements over time. Panel data is a subset of ...
Alberto Perez Martinez's user avatar
1 vote
0 answers
40 views

What kind of machine learning models fit data of this kind?

I have been working with a manufacturing process. It would be very efficient to build a machine learning model for the kind of data that I have. So, my dataset has typically three inputs. VAl_1 VAl_2 ...
Siva Teja's user avatar
1 vote
0 answers
29 views

Functional Autoregressive Process - Predictive Factors

Let $X_1,...,X_N$ be random functions on an Hilbert space $\mathbb{H}$, following a Functional Autoregressive process of order 1: $$ X_{t+1} = \Psi X_t + \varepsilon_t $$ Where $\Psi$ is a linear ...
Niccolò Ajroldi's user avatar
7 votes
1 answer
276 views

What are the simplest examples of nonlinear statistical functionals?

I am reading Wasserman's book "All of Statistics" in which he defines a statistical functional as any function $T(F)$ of the cumulative distribution function $F(x)$ that outputs a real ...
Peaceful's user avatar
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1 vote
0 answers
111 views

Functional time series forecasting

I am working in hourly multivariate time series forecasting, so due to big data, I made the forecasting through functional time series. The model that I am using is the functional autoregressive model ...
faheem's user avatar
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1 vote
0 answers
57 views

Functional PCA for stationary signal

I just came across this technique: https://en.wikipedia.org/wiki/Functional_principal_component_analysis As far as I understand, if projects a signal onto a functional subspace that describe the "...
Thomas's user avatar
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2 votes
1 answer
924 views

Square root transformation of Poisson process. How $\small Var[\sqrt{P(\lambda)}] \approx \frac{1}{4}$

I am working on Kaggle Neural data challenge. I am trying to understand the transformation applied on the neural spiking data. A number of spikes given a stimulus are Poisson distributed as $$Y_i \...
Saranraj Nambusubramaniyan's user avatar
2 votes
0 answers
193 views

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 ...
Cm7F7Bb's user avatar
  • 309
1 vote
0 answers
60 views

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(...
Abhishek Singh's user avatar
5 votes
1 answer
688 views

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 ...
Lefty's user avatar
  • 499
1 vote
0 answers
105 views

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, <...
Lefty's user avatar
  • 499
0 votes
0 answers
33 views

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. ...
Lefty's user avatar
  • 499
1 vote
0 answers
114 views

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 ...
faheem jan's user avatar