Supervisor: Dr Eftychia Solea
Project description:Quantile regression models are very useful in statistical modelling to detect the dependence on the covariates in different parts, like the center and the lower and upper tails of the response distribution. Most classical quantile regression models treat the covariates or the response as vectors. High-throughput technologies applications produce large and highly structured data of more complex form such as functional data. Traditional statistical and computational methods are proving insufficient for the analysis of these high-throughput data due to their complexity and size. Despite the recent developments in functional data analysis, little has been done for functional data characterised by extreme events or skewness. The project addresses this gap by developing a new family of statistical quantile regression models that are better able to analyse sample of functions characterised by extreme events or skewness using quantiles. This new framework effectively exploits the complex structure in the data, and substantially reduces dimensionality, which in turn increases statistical power.
The research is divided into two areas: (1) functional quantile regression to analyse samples of functions, treating the response or the covariates as functions, and (2) functional quantile causal mediation analysis to estimate causal effects for functional data that occur on other parts of the distribution, such as median and lower/upper tails. Current mediation analyses are focuses on mean regression models which may not capture the effects in susceptible subgroups.
The work will study asymptotic properties of these new estimators, statistical inference procedures, and efficient algorithms to implement these methods. This research is timely as it responds to the growing demands and needs for adequate statistical analysis of samples of complex data and aligns with the themes of Al & Data Modelling. The methods to be developed will have applications in the social, behavioural, medical research, epidemiology, and environmental sciences.
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