Questions tagged [functional-data-analysis]

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

Functional Data Analysis (FDA) defines a framework where the fundamental units of analysis are functions. A dataset is assumed to hold observations from an underlying smoothly varying stochastic process. Typical functional datasets are collections of curves and shapes, but also surfaces, general three dimensional objects or even more high-dimensional objects are increasingly considered.

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Functional principal component analysis (FPCA): what is it all about?

Functional principal component analysis (FPCA) is something I have stumbled upon and never got to understand. What is it all about? See "A survey of functional principal component analysis" by Shang, 2011, and I'm citing: PCA runs into serious…
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Is there an unbiased estimator of the Hellinger distance between two distributions?

In a setting where one observes $X_1,\ldots,X_n$ distributed from a distribution with density $f$, I wonder if there is an unbiased estimator (based on the $X_i$'s) of the Hellinger distance to another distribution with density $f_0$,…
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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 science), compared to the ordinary perspective in…
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From a statistical perspective: Fourier transform vs regression with Fourier basis

I am trying to understand whether discrete Fourier transform gives the same representation of a curve as a regression using Fourier basis. For example, library(fda) Y=daily$tempav[,1] ## my data length(Y) ## =365 ## create Fourier basis and…
qoheleth
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When/where to use functional data analysis?

I am very new to functional data analysis (FDA). I am reading: Ramsay, James O., and Silverman, Bernard W. (2006), Functional Data Analysis, 2nd ed., Springer, New York. However, I am still not very clear where/when to use FDA? Could someone…
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How to simulate functional data?

I'm trying to test various functional data analysis approaches. Ideally, i'd like to test the panel of approaches i have on simulated functional data. I've tried to generate simulated FD using an approach based on a summing Gaussian noises (code…
user603
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Dynamic Time Warping and normalization

I'm using Dynamic Time Warping to match a "query" and a "template" curve and having reasonable success thus far, but I have some basic questions: I'm assessing a "match" by assessing whether the DTW result is less than some threshold value that I…
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What is the difference between functional data analysis and high dimensional data analysis

There are a lot of references in the statistic literature to "functional data" (i.e. data that are curves), and in parallel, to "high dimensional data" (i.e. when data are high dimensional vectors). My question is about the difference between the…
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Predicting response from new curves using fda package in R

Basically all I want to do is predict a scalar response using some curves. I've got as far as doing a regression (using fRegress from the fda package) but have no idea how to apply the results to a NEW set of curves (for prediction). I have N=536…
dcl
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Forecasting of density function

I am doing some research about forecasting time series of probability density functions. We are aiming to forecast a PDF given historically observed (usually, estimated) PDF. The forecasting method we are developing performs pretty well in…
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How to map a trajectory to a vector?

I have a series of data points in this form (timestamp, lat, long) for a set of users. Each user has a trajectory when he travels from point A to point B. There might be any number of points from A to B. They are ordered data points based on time…
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Learning from unordered tuples?

EDIT: I reduced my problem to a more specific question: https://math.stackexchange.com/questions/26573/ But I am still interested in other ideas. Let's say our data is generated by $$Y_i = f(X_i) + \epsilon_i$$ where $X_i$ are observed vectors, and…
charles.y.zheng
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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 number. Then he goes on to define a 'linear statistical…
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Illustration of functional gradient descent

I'm trying to understand boosting as gradient descent (GD) in functional space. I've followed the argument in the classic paper on the subject, but would characterize my understanding as tenuous at best. Proceeding by the way of analogy, I'll make…
RDK
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Estimating speed from position updates with uncertain time intervals

I have 2 alternative methods to solve a problem, and I was just wondering what people who know the math better than I think, and if there is a better method to use for this type of problem. The problem: I have a list of lat/lon positions and a value…
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