arXiv subjects

Dharini Pathmanathan

Publications and source records attributed to Dharini Pathmanathan.

8 recordsLinked to original sources

arXiv2025

Reframing Three-Dimensional Morphometrics Through Functional Data Innovations

This study innovates geometric morphometrics by incorporating functional data analysis, the square-root velocity function (SRVF), and arc-length parameterisation for 3D morphometric data, leading to the development of seven new pipelines in addition to the standard geometric morphometrics (GM) approach.. This enables three-dimensional images to be examined from perspectives that do not neglect curvature, through the combined use of arc-length parameterisation, soft-alignment, and elastic-alignment. A simulation study was conducted to demonstrate the general effectiveness of eight pipelines: geometric morphometrics (GM, baseline), arc-GM, functional data morphometrics (FDM), arc-FDM, soft-SRV-FDM, arc-soft-SRV-FDM, elastic-SRV-FDM, and arc-elastic-SRV-FDM. These pipelines were also applied to distinguish dietary categories of kangaroos (omnivores, mixed feeders, browsers, and grazers) using cranial landmarks obtained from 41 extant species. Principal component analysis was conducted, followed by classification analysis using linear discriminant analysis, multinomial regression and support vector machines with a linear kernel. The results highlight the effectiveness of functional data analysis, together with arc-length and SRVF-based approaches, in opening the door to more robust perspectives for analysing three-dimensional morphometrics, while establishing geometric morphometrics as the baseline for comparison.

stat.AP↗

arXiv2025

Functional regression with randomized signatures: An application to age-specific mortality rates

We propose a novel extension of the Hyndman-Ullah (HU) model to forecast mortality rates by integrating randomized signatures, referred to as the HU model with randomized signatures (HUrs). Unlike truncated signatures, which grow exponentially with order, randomized signatures, based on the Johnson-Lindenstrauss lemma, are able to approximate higher-order interactions in a computationally feasible way. Using mortality data from four countries, we evaluate the performance of the novel HUrs model compared to two alternative HU model versions. Our empirical results show that the proposed HUrs model performs well, particularly for Bulgarian and Japanese data.

stat.ME↗

arXiv2025

Compositional data analysis for modelling and forecasting mortality using the {\alpha}-transformation

Mortality forecasting is crucial for demographic planning and actuarial studies, especially for projecting population ageing and longevity risk. Classical approaches largely rely on extrapolative methods, such as the Lee-Carter (LC) model, which use mortality rates as the mortality measure. In recent years, compositional data analysis (CoDA), which respects summability and non-negativity constraints, has gained increasing attention for mortality forecasting. While the centred log-ratio (CLR) transformation is commonly used to map compositional data to real space, the {\alpha}-transformation, a generalisation of log-ratio transformations, offers greater flexibility and adaptability. This study contributes to mortality forecasting by introducing the {\alpha}-transformation as an alternative to the CLR transformation within a non-functional CoDA model that has not been previously investigated in existing literature. To fairly compare the impact of transformation choices on forecast accuracy, zero values in the data are imputed, although the {\alpha}-transformation can inherently handle them. Using age-specific life table death counts for males and females in 31 selected European countries/regions from 1983 to 2018, the proposed method demonstrates comparable performance to the CLR transformation in most cases, with improved forecast accuracy in some instances. These findings highlight the potential of the {\alpha}-transformation for enhancing mortality forecasting within the non-functional CoDA framework.

stat.AP↗

arXiv2024

Spatial Principal Component Analysis and Moran Statistics for Multivariate Functional Areal Data

The paper introduces a multivariate functional areal spatial principal component analysis (mfasPCA) framework, together with multivariate functional Moran's I statistics, to enable the assessment of spatial autocorrelation and dimension reduction for multivariate functional data observed over areal units. The proposed framework is spatial-functional in scope: the functional argument may represent time, age, wavelength, or another ordered continuum, while spatial dependence is introduced across areal units through a spatial weight matrix. The principal component method is defined through a Moran-type spatially weighted criterion. We propose eigenvalue-based permutation tests to assess the significance of spatially structured components. The testing framework includes omnibus tests, componentwise tests with Holm adjustment, and sequential rank-wise tests based on tail sums of eigenvalues. Simulation studies show that mfasPCA captures positive and negative spatial-functional structures and concentrates them in the leading components under the respective autocorrelation regimes. A real-data application illustrates how mfasPCA identifies spatially structured modes of multivariate functional variation.

stat.ME↗

arXiv2024

Generalized dynamic functional principal component analysis

In this paper, we explore dimension reduction for functional time series. We propose a generalized dynamic functional principal component analysis (GDFPCA) which does not rely on spectral density estimation and demonstrates strong empirical performance for both stationary and nonstationary functional time series. We define the generalized dynamic functional principal components (GDFPCs) as static factor time series in a functional dynamic factor model and obtain their multivariate representation from a truncation of the functional dynamic factor model. Estimation is based on a least-squares reconstruction criterion and implemented via a two-step procedure for the coefficient vectors of the loading curves under a basis expansion. We establish mean-square consistency of the reconstructed functional time series under weak stationarity. Simulation studies show that GDFPCA performs comparably to dynamic functional principal component analysis (DFPCA) for stationary data, while providing improved reconstruction accuracy in nonstationary settings, where both DFPCA and functional principal component analysis (FPCA) deteriorate. Applications to real datasets support the empirical advantages observed in the simulations.

stat.ME↗

arXiv2024

Forecasting mortality rates with functional signatures

This study introduces an innovative methodology for mortality forecasting, which integrates signature-based methods within the functional data framework of the Hyndman-Ullah (HU) model. This new approach, termed the Hyndman-Ullah with truncated signatures (HUts) model, aims to enhance the accuracy and robustness of mortality predictions. By utilizing signature regression, the HUts model is able to capture complex, nonlinear dependencies in mortality data which enhances forecasting accuracy across various demographic conditions. The model is applied to mortality data from 12 countries, comparing its forecasting performance against variants of the HU models across multiple forecast horizons. Our findings indicate that overall the HUts model not only provides more precise point forecasts but also shows robustness against data irregularities, such as those observed in countries with historical outliers. The integration of signature-based methods enables the HUts model to capture complex patterns in mortality data, making it a powerful tool for actuaries and demographers. Prediction intervals are also constructed with bootstrapping methods

stat.ME↗

arXiv2023

A Markov-switching spatio-temporal ARCH model

Stock market indices are volatile by nature, and sudden shocks are known to affect volatility patterns. The autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) models neglect structural breaks triggered by sudden shocks that may lead to an overestimation of persistence, causing an upward bias in the estimates. Different regime-switching models that have abrupt regime-switching governed by a Markov chain were developed to model volatility in financial time series data. Volatility modelling was also extended to spatially interconnected time series, resulting in spatial variants of ARCH models. This inspired us to propose a Markov switching framework of the spatio-temporal log-ARCH model. In this article, we discuss the Markov-switching extension of the model, the estimation procedure and the smooth inferences of the regimes. The Monte-Carlo simulation studies show that the maximum likelihood estimation method for our proposed model has good finite sample properties. The proposed model was applied to 28 stock indices data that were presumably affected by the 2015-2016 Chinese stock market crash. The results showed that our model is a better fit compared to that of the one-regime counterpart. Furthermore, the smoothed inference of the data indicated the approximate periods where structural breaks occurred. This model can capture structural breaks that simultaneously occur in nearby locations.

stat.ME↗

arXiv2023

A unified approach for morphometrics and functional data analysis with machine learning for craniodental shape quantification in shrew species

This work proposes a functional data analysis approach for morphometrics with applications in classifying three shrew species (S. murinus, C. monticola and C. malayana) based on the images. The discrete landmark data of craniodental views (dorsal, jaw and lateral) are converted into continuous curves where the curves are represented as linear combinations of basis functions. A comparative study based on four machine learning algorithms such as naive Bayes, support vector machine, random forest, and generalized linear models was conducted on the predicted principal component scores obtained from the FDA approach and classical approach (combination of all three craniodental views and individual views). The FDA approach produced better results in separating the three clusters of shrew species compared to the classical method and the dorsal view gave the best representation in classifying the three shrew species. Overall, based on the FDA approach, GLM of the predicted PCA scores was the most accurate (95.4% accuracy) among the four classification models.

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