This thesis is concerned with the analysis of spatio-temporal data sets in which it is required to estimate the effects of (potentially several) covariates upon the distribution of a response variable. Regression analysis is particularly useful in the modelling of such data; we consider generalized additive models, and quantile regression models. Our contributions concern two aspects: estimation and inference. Accurate estimation and inference in the presence of dependence remains challenging. Here we consider a penalized spline framework. This provides a class of smoothers that are easy to fit, and allows for flexibility via the combination of different spline bases and penalties. Inference procedures may be misleading when failing to account for the dependence in the data; we develop inference tools to ensure valid statistical inference. The first part of the thesis extends generalized additive models by fitting smooth functions to the data incorporating all relevant covariates of space and time. The spatial dependence is accounted for by assuming independence during fitting and then adjusting the standard errors of parameter estimates to ensure valid inferences. The second part of the thesis concerns quantile regression; we introduce a simple modification and parameterization of the standard nonparametric quantile regression problem which can be exploited to determine a set of procedures which approximate the computationally demanding nonlinear optimization problem for quantile estimation. We also address the issue of smoothing parameter selection and inference of quantile regression estimates in the presence of dependence. This work is motivated by, and illustrated using, the southwest Western Australia rainfall data set as a case study. The developments in this thesis will be useful to practitioners who require a practical and computationally convenient way to compute nonparametric mean and quantile regression curves for spatio-temporal applications. Importantly, they are also readily implementable using existing statistical software.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:626593 |
| Date | January 2014 |
| Creators | Liang, X. M. |
| Publisher | University College London (University of London) |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://discovery.ucl.ac.uk/1428444/ |
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