Improved estimation and inference for regression models with functional components

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Regression models with unknown functional components, like generalized additive models (see, e.g., Hastie and Tibshirani, 1986, DOI: 10.1214/ss/1177013604 and Wood, 2017, DOI: 10.1201/9781315370279) and functional regression models (see, e.g. Ramsay and Silverman, 2005, DOI: 10.1007/b98888) are finding numerous applications in diverse areas of statistical practice. This PhD project will develop methods that aim to reduce the bias of estimators of functional components present due to finite sample sizes and the need to introduce a roughness penalty for controlling the smoothness of the functional estimators. We will also consider developing and assessing methods for inference about the functional components.We will begin with methods for estimating generalized additive models, initially attempting to extend the reduced-bias M-estimation framework of Kosmidis and Lunardon (2021, arXiv:2001.03786) to cases where an adaptive, smoothness penalty is added to the estimation objectives. That extended framework or any alternative we produce to reduce bias and improve inference in generalized additive models will then be adapted and applied to functional regression settings.The project will look at developing new methods, assessed theoretically and through comprehensive simulation studies, and applying the methodology to real-world data-analytic settings.