arXiv subjects

Tianbo Chen

Publications and source records attributed to Tianbo Chen.

7 recordsLinked to original sources

arXiv2026

Expectile Periodograms

This paper introduces a novel periodogram-like function, called the expectile periodogram, for modeling spectral features of time series and detecting hidden periodicities. The expectile periodogram is constructed from trigonometric expectile regression, in which a specially designed check function is used to substitute the squared $l_2$ norm that leads to the ordinary periodogram. The expectile periodogram retains the key properties of the ordinary periodogram as a frequency-domain representation of serial dependence in time series, while offering a more comprehensive understanding by examining the data across the entire range of expectile levels. We establish the asymptotic theory and investigate the relationship between the expectile periodogram and the so called expectile spectrum. Simulations demonstrate the efficiency of the expectile periodogram in the presence of hidden periodicities. Finally, by leveraging the inherent two-dimensional nature of the expectile periodogram, we train a deep learning (DL) model to classify earthquake waveform data. Remarkably, our approach outperforms alternative periodogram-based methods in terms of classification accuracy.

stat.ME↗

arXiv2025

Asymmetric Huber Periodogram

This paper introduces a novel spectral M-estimator, called the asymmetric Huber periodogram (AHP), as a generalization of the ordinary periodogram (PG), the quantile periodogram (QP), and the Huber periodogram (HP). The AHP is constructed via trigonometric asymmetric Huber regression (AHR), in which a specially designed loss function replaces the squared $\ell_2$ loss used to define the PG. Relative to the QP, the AHP can be more computationally efficient, and relative to the HP and PG, it provides a more comprehensive characterization by examining the data across the range of the asymmetry parameter. We establish the theoretical properties of the AHP and investigate its relationship with the corresponding asymmetric Huber spectrum (AHS). Building on the asymptotic theory, we develop confidence intervals (CIs) for the AHS and propose a Fisher-type test. Simulation studies and two applications further demonstrate the AHP's effectiveness in detecting hidden periodicities, robustness to outliers, and utility for time series clustering.

stat.ME↗

arXiv2025

Robust Functional Ward's Linkages with Applications in EEG data Clustering

This paper proposes two new distance measures, called functional Ward's linkages, for functional data clustering that are robust against outliers. Conventional Ward's linkage defines the distance between two clusters as the increase in sum of squared errors (SSE) upon merging, which can be interpreted graphically as an increase in the diameter. Analogously, functional Ward's linkage defines the distance of two clusters as the increased width of the band delimited by the merged clusters. To address the limitations of conventional Ward's linkage in handling outliers and contamination, the proposed linkages focus exclusively on the most central curves by leveraging magnitude-shape outlyingness measures and modified band depth, respectively. Simulations and real-world electroencephalogram (EEG) data analysis demonstrate that the proposed methods outperform other competitive approaches, particularly in the presence of various types of outliers and contamination.

stat.ME↗

arXiv2020

Clustering Brain Signals: A Robust Approach Using Functional Data Ranking

In this paper, we analyze electroencephalograms (EEG) which are recordings of brain electrical activity. We develop new clustering methods for identifying synchronized brain regions, where the EEGs show similar oscillations or waveforms according to their spectral densities. We treat the estimated spectral densities from many epochs or trials as functional data and develop clustering algorithms based on functional data ranking. The two proposed clustering algorithms use different dissimilarity measures: distance of the functional medians and the area of the central region. The performance of the proposed algorithms is examined by simulation studies. We show that, when contaminations are present, the proposed methods for clustering spectral densities are more robust than the mean-based methods. The developed methods are applied to two stages of resting state EEG data from a male college student, corresponding to early exploration of functional connectivity in the human brain.

stat.ME↗

arXiv2020

Collective Spectral Density Estimation and Clustering for Spatially-Correlated Data

In this paper, we develop a method for estimating and clustering two-dimensional spectral density functions (2D-SDFs) for spatial data from multiple subregions. We use a common set of adaptive basis functions to explain the similarities among the 2D-SDFs in a low-dimensional space and estimate the basis coefficients by maximizing the Whittle likelihood with two penalties. We apply these penalties to impose the smoothness of the estimated 2D-SDFs and the spatial dependence of the spatially-correlated subregions. The proposed technique provides a score matrix, that is comprised of the estimated coefficients associated with the common set of basis functions representing the 2D-SDFs. {Instead of clustering the estimated SDFs directly, we propose to employ the score matrix for clustering purposes, taking advantage of its low-dimensional property.} In a simulation study, we demonstrate that our proposed method outperforms other competing estimation procedures used for clustering. Finally, to validate the described clustering method, we apply the procedure to soil moisture data from the Mississippi basin to produce homogeneous spatial clusters. We produce animations to dynamically show the estimation procedure, including the estimated 2D-SDFs and the score matrix, which provide an intuitive illustration of the proposed method.

stat.ME↗

arXiv2019

A Semi-Parametric Estimation Method for the Quantile Spectrum with an Application to Earthquake Classification Using Convolutional Neural Network

In this paper, a new estimation method is introduced for the quantile spectrum, which uses a parametric form of the autoregressive (AR) spectrum coupled with nonparametric smoothing. The method begins with quantile periodograms which are constructed by trigonometric quantile regression at different quantile levels, to represent the serial dependence of time series at various quantiles. At each quantile level, we approximate the quantile spectrum by a function in the form of an ordinary AR spectrum. In this model, we first compute what we call the quantile autocovariance function (QACF) by the inverse Fourier transformation of the quantile periodogram at each quantile level. Then, we solve the Yule-Walker equations formed by the QACF to obtain the quantile partial autocorrelation function (QPACF) and the scale parameter. Finally, we smooth QPACF and the scale parameter across the quantile levels using a nonparametric smoother, convert the smoothed QPACF to AR coefficients, and obtain the AR spectral density function. Numerical results show that the proposed method outperforms other conventional smoothing techniques. We take advantage of the two-dimensional property of the estimators and train a convolutional neural network (CNN) to classify smoothed quantile periodogram of earthquake data and achieve a higher accuracy than a similar classifier using ordinary periodograms.

stat.ME↗

arXiv2017

Nonparametric collective spectral density estimation with an application to clustering the brain signals

In this paper, we develop a method for the simultaneous estimation of spectral density functions (SDFs) for a collection of stationary time series that share some common features. Due to the similarities among the SDFs, the log-SDF can be represented using a common set of basis functions. The basis shared by the collection of the log-SDFs is estimated as a low-dimensional manifold of a large space spanned by a pre-specified rich basis. A collective estimation approach pools information and borrows strength across the SDFs to achieve better estimation efficiency. Also, each estimated spectral density has a concise representation using the coefficients of the basis expansion, and these coefficients can be used for visualization, clustering, and classification purposes. The Whittle pseudo-maximum likelihood approach is used to fit the model and an alternating blockwise Newton-type algorithm is developed for the computation. A web-based shiny App found at "https://ncsde.shinyapps.io/NCSDE" is developed for visualization, training and learning the SDFs collectively using the proposed technique. Finally, we apply our method to cluster similar brain signals recorded by the electroencephalogram for identifying synchronized brain regions according to their spectral densities.

stat.ME↗