Abstract
This thesis presents new methods for multivariate, survival and time series analysis with network.We begin by describing a new method for computing the projection median, its influence curve and techniques for the production of projected quantile plots. A theoretical result on the form of the influence curve and numerical simulations are displayed. A comparison of the computational performance between the projection median and other existing multivariate medians is conducted as well. We also produce animated multidimensional projection quantile plots, and all results are generated using our R software package Yamm.
The second section introduces Bayesian wavelet approaches to estimate the density function and the hazard rate for right-censored data. To estimate the hazard rate, a Bayesian wavelet threshold approach and a Dirichlet process model are used, which shows good performance in our simulation examples. To improve the density estimates, we use the detailed covariance structure of the empirical wavelet coefficients, which enables a non-dyadic grid for the evaluation points.
A method to estimate survival functions using recurrent lifetimes is motivated in the third section, which allows the use of covariate information of individuals to construct a network structure of separate clusters. Our method shows an improvement on estimation performance when the number of data points is not large enough for good performance using standard methods.
The last section provides a model for analysing multivariate time series based on the structure of a network and exogenous regressors. Our model allows the target series to be regressed by previous time lags of itself and its neighbours, as well as another multivariate time series, which is related to the target one on the same network. It is shown numerically that our model has a good prediction performance with few parameters.
Date of Award | 12 May 2022 |
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Original language | English |
Awarding Institution |
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Supervisor | Haeran Cho (Supervisor) & Guy Nason (Supervisor) |