South African Statistical Journal

Testing for no effect in the spatial functional linear regression model

Stéphane Bouka — 2024-03-23

We consider a functional linear regression model with a real-valued response and a functional random variable with its derivative as covariates. We are interested in testing the null hypothesis of no covariates effect using a spatially dependent sample. We propose two test statistics which take into account the proximity between sites and we establish the asymptotic normality of cross covariance operator between both interest variables. From this result, we derive asymptotic distributions of these both statistics. Then, we illustrate our test procedure by means of a simulation study.

Construction of Archimedean copulas using total time on test transforms

N. Unnikrishnan Nair — 2024-03-23

In the present work, we propose a method of constructing Archimedean copulas using the total time on test transform, extensively used in reliability modelling. It is observed that the copula can be specified in terms of a univariate life distribution with a finite mean and monotone hazard rate. We discuss some new properties of the Kendall distribution arising from the proposed new generator and the associated measures of dependence.

Strong uniform convergence rates of the linear wavelet estimator of a multivariate copula density

Cheikh Tidiane Seck — 2024-03-23

In this paper, we investigate the almost sure convergence, in supremum norm, of the rank-based linear wavelet estimator for the multivariate copula density over Besov classes. Using empirical process tools, we establish a uniform limit law for the deviation of an oracle estimator (which assumes known margins) from its expectation. This enables us to derive strong convergence rates for the rank-based linear estimator.

Multiscale decomposition of spatial lattice data for hotspot detection

René Stander — 2024-03-23

Hotspot detection in spatial analysis identifies geographic areas with elevated event rates, facilitating more effective policy interventions aimed at reducing such incidents. In the current literature, several methods have been used to detect hotspots such as measures for local spatial association and spatial scan methods. However, the performance of these methods is limited for small-scale hotspots as well as spatial domains where the number of areas is small. In this work, we propose a new approach, making use of the Discrete Pulse Transform (DPT) to decompose spatial lattice data along with the multiscale Ht-index and the spatial scan statistic as a measure of saliency on the extracted pulses to detect significant hotspots. The proposed method outperforms the well-used local Getis-Ord statistic in a simulation study, especially on small-scale hotspots. The method is also illustrated on South African COVID-19 cases and South African crime data.