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Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...
We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...
Inst Mathematical Statistics-Ims2024
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The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the covariance, even ...
TAYLOR & FRANCIS INC2022
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We consider the problem of estimating the autocorrelation operator of an autoregressive Hilbertian process. By means of a Tikhonov approach, we establish a general result that yields the convergence rate of the estimated autocorrelation operator as a funct ...
ELSEVIER2022
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We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of Double-struck capital R. An order-1 autoregressive model in this context is to be understood as a Markov chain, where ...
Hoboken2024
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Nonparametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these issues in the de ...
TAYLOR & FRANCIS INC2022
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We present a framework for performing regression when both covariate and response are probability distributions on a compact interval. Our regression model is based on the theory of optimal transportation, and links the conditional Frechet mean of the resp ...
OXFORD UNIV PRESS2022
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Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address ...
Is it possible to detect if the sample paths of a stochastic process almost surely admit a finite expansion with respect to some/any basis? The determination is to be made on the basis of a finite collection of discretely/noisily observed sample paths. We ...
We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...
