Questions tagged [functional-data-analysis]
Functional Data Analysis defines a framework where the fundamental units of analysis are functions.
141
questions
2
votes
0
answers
29
views
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^...
- 153
3
votes
1
answer
52
views
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 ...
0
votes
0
answers
16
views
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) ...
- 83
0
votes
0
answers
36
views
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 ...
- 129
2
votes
0
answers
27
views
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)....
3
votes
1
answer
44
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 ...
- 83
1
vote
0
answers
48
views
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 ...
- 11
2
votes
1
answer
132
views
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 ...
- 129
1
vote
1
answer
147
views
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,
\...
- 129
0
votes
0
answers
22
views
What are the advantages of using Functional Data Analysis (FDA) over traditional Time Series or Stochastic Process approaches?
In the case where the curves (functions) are defined on a time interval.
- 441
1
vote
0
answers
12
views
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
- 11
0
votes
0
answers
45
views
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 ...
2
votes
1
answer
165
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 ...
- 203
1
vote
0
answers
12
views
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 ...
- 21
1
vote
0
answers
34
views
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 ...
- 111
2
votes
1
answer
30
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 ...
- 33
1
vote
0
answers
40
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 ...
- 111
0
votes
0
answers
41
views
How to do an A/B test with sampling distribution when the values are not boolean?
I have a dataset that looks similar to this
...
1
vote
0
answers
58
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 ...
- 11
1
vote
0
answers
49
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 ...
- 261
0
votes
0
answers
139
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, ...
- 153
1
vote
1
answer
64
views
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 ...
- 35
3
votes
1
answer
51
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 ...
- 2,386
1
vote
1
answer
55
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 ...
- 337
0
votes
1
answer
263
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+...
- 499
20
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 ...
- 303
1
vote
0
answers
124
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 ...
- 43
2
votes
1
answer
51
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 ...
- 2,386
1
vote
0
answers
44
views
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 ...
- 2,386
0
votes
0
answers
50
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 $...
1
vote
0
answers
17
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 ...
1
vote
1
answer
174
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 ...
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
...
- 11
1
vote
0
answers
26
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 ...
7
votes
1
answer
248
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 ...
- 603
1
vote
0
answers
84
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 ...
- 11
1
vote
0
answers
51
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 "...
- 840
2
votes
1
answer
678
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
$$Y_i \...
2
votes
0
answers
162
views
Roughness penalty matrix for the Fourier basis functions
I am trying to understand how the roughness penalty matrix for the Fourier basis functions is calculated in R using the fda ...
- 269
1
vote
0
answers
57
views
Prove that $K(x_{1},x_{2})=f(x_{1})K_{1}(x_{1},x_{2})f(x_{2})$ is symmetric positive definite if $K_{1}(x_{1},x_{2})$ is symmetric positive definite
I have been trying to prove this 5th proposition on the 25th slide
We can prove that $ K(x_{1},x_{2}) $ will be a valid kernel as:
\begin{align}
K(x_{1},x_{2}) = & \; f(x_{1})K_{1}(x_{1},x_{2})f(...
5
votes
1
answer
482
views
Generalized additive models vs. functional data models
I am not sure I understand the difference between functional data analysis (FDA) and GAM.
Or in short, I was reading about GAM and I found the following model which seems like an FDA model (there is a ...
- 337
1
vote
0
answers
95
views
Coefficients in Functional Regression
I would like to estimate the effect of DoE factors in my response which is a function.
For this reason, I tried to apply the Functional Data Analysis method.
As example,
I have a 12 treatment DoE,
<...
- 337
0
votes
0
answers
33
views
Predict parameters of another model
I would like to make a model to predict the parameters of another model.
As example,
By using design of experiment I made some trials and I measured the temperature (response).
e.g.
...
- 337
1
vote
0
answers
103
views
How to Generalize functional Autoregressive model
I am working with the multivariate hourly electricity price data, data consist of six years hourly electricity data in which the first five years are use as testing set and the last year as validation ...
- 41
6
votes
0
answers
77
views
Asymptotic properties of functional models
When working in Functional Data Analysis, a classical "preprocessing" step is to represent the "observations" using a B-spline expansion:
$$
X_i(t) \approx \sum_{j=1}^J \lambda_{ij}...
- 530
1
vote
0
answers
58
views
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, ...
- 41
6
votes
2
answers
480
views
How to express descriptive statistics as statistical functionals - and why?
I'm reading through class notes explaining statistical functionals and came across the following expressions with little explanation how they were derived:
Mean $=T(F)=\int xdF(x)$
Variance $=T(F)=\...
- 5,442
1
vote
0
answers
29
views
A space of functions and their Fourier Transforms?
Conjugate variables and the Fourier transform are often used to analyze different states of a single object. For example in Quantum Mechanics it can be used to describe changing information about ...
- 11
1
vote
0
answers
75
views
Comparing curve fits
I have imaging data where I imaged different instances of the (somewhat) same phenomenon (2 different experimental conditions). I have already settled on the equations I use for curve fitting and ...
- 11
1
vote
1
answer
129
views
Functional Linear Regression without Orthonormal Basis for Prediction
What do you do in functional linear regression when for whatever reason you don't want to use an orthonormal basis expansion? In functional linear regression for scalar on function regression, one may ...
- 492