Shahin Tavakoli

University of Geneva | UNIGE · Institute of Statistics (ISTAT)

Tensor-based morphometry (TBM) aims at showing local differences in brain volumes with respect to a common template. TBM images are smooth but they exhibit (especially in diseased groups) higher values in some brain regions called lateral ventricles. More specifically, our voxelwise analysis shows both a mean-variance relationship in these areas an...

In this paper, which consists of two parts (Part I: representation results; Part II: estimation and forecasting methods), we set up the theoretical foundations for a high‐dimensional functional factor model approach in the analysis of large cross‐sections (panels) of functional time series (FTS). In Part I, we establish a representation result stat...

This paper is the second one in a set of two laying the theoretical foundations for a high‐dimensional functional factor model approach in the analysis of large cross‐sections (panels) of functional time series (FTS). Part I establishes a representation result by which, under mild assumptions on the covariance operator of the cross‐section, any FTS...

The sound of our speech is influenced by the places we come from. Great Britain contains a wide variety of distinctive accents which are of interest to linguistics. In particular, the "a" vowel in words like "class" is pronounced differently in the North and the South. Speech recordings of this vowel can be represented as formant curves or as Mel-f...

Prediction of subject age from brain anatomical MRI has the potential to provide a sensitive summary of brain changes, indicative of different neurodegenerative diseases. However, existing studies typically neglect the uncertainty of these predictions. In this work we take into account this uncertainty by applying methods of functional data analysi...

Prediction of subject age from brain anatomical MRI has the potential to provide a sensitive summary of brain changes, indicative of different neurodegenerative diseases. However, existing studies typically neglect the uncertainty of these predictions. In this work we take into account this uncertainty by applying methods of functional data analysi...

Dialect variation is of considerable interest in linguistics and other social sciences. However, traditionally it has been studied using proxies (transcriptions) rather than acoustic recordings directly. We introduce novel statistical techniques to analyze geolocalized speech recordings and to explore the spatial variation of pronunciations continu...

In this paper, we set up theoretical foundations for high-dimensional functional factor models for the analysis of large panels of functional time series (FTS). We first establish a representation result stating that if the first $r$ eigenvalues of the covariance operator of the cross-section of $N$ FTS are unbounded as $N$ diverges and if the $(r+...

The assumption of separability of the covariance operator for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible, either for computational reasons, or due to a small sample size. However, inferential tools to verify this assu...

We consider the problem of testing for separability in nonparametric covariance operators of multidimensional functional data is considered. We cast the problem in a tensor product of Hilbert space framework, where the role of the partial trace operator is emphasized, and the tests proposed are computationally tractable. An applications to acoustic...

The book Mr. Tickle is a childhood favourite for many. But this fantastical story of a man with “extraordinary long arms” is helping statisticians derive a more realistic understanding of the differences in regional accents. By Marius A. Tirlea, Shahin Tavakoli, Davide Pigoli and John A. D. Aston

Dialect variation is of considerable interest in linguistics and other social sciences. However, traditionally it has been studied using proxies (transcriptions) rather than acoustic recordings directly. We introduce novel statistical techniques to analyse geolocalised speech recordings and to explore the spatial variation of pronunciations continu...

Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of localizing any inferred differences in frequency and along curvelength. The approach we take is one of Fourier analysis, where the...

The assumption of separability of covariance operators in the different directions for a random image or hypersurface can be of substantial use in applications, especially in situations where the accurate estimation of the full covariance structure is unfeasible, either for computational reasons or due to a small sample size. However, inferential t...

This work is about time series of functional data (functional time series), and consists of three main parts. In the first part (Chapter 2), we develop a doubly spectral decomposition for functional time series that generalizes the Karhunen–Loève expansion. In the second part (Chapter 3), we develop the theory of estimation for the spectral density...

We develop a doubly spectral representation of a stationary functional time series, and study the properties of its empirical version. The representation decomposes the time series into an integral of uncorrelated frequency components (Cramér representation), each of which is in turn expanded in a Karhunen–Loève series. The construction is based on...

We develop the basic building blocks of a frequency domain framework for drawing statistical inferences on the second-order structure of a stationary sequence of functional data. The key element in such a context is the spectral density operator, which generalises the notion of a spectral density matrix to the functional setting, and characterises...