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UBC Theses and Dissertations

Local linear regression versus backcalculation in forecasting Li, Xiaochun


The local linear forecasting estimator is proposed in this thesis as an alternative technique to either parametric regression or the backcalculation approach in the context of forecasting for independent data. The asymptotic bias and variance of the local linear forecasting estimator are derived and used to develop procedures for the estimation of the optimal bandwidth for forecasting. Both the theoretical and the computational aspects of these procedures are explored. Simulation study shows that a cross-validation procedure has the best performance in forecasting among four bandwidth estimation procedures under study. Simulations and statistical analyses show that the backcalculation approach is very vulnerable to violations of the assumptions underlying this approach and that its application to AIDS data fails to achieve its two primary goals, to forecast the numbers of new AIDS cases and to estimate the historical HIV infection curve. To test the proposed forecasting estimator over parametric regression, both techniques are applied to the Canadian AIDS data and the UK AIDS data. The results of the two examples expose the weakness of parametric regression and show that the proposed technique does better than parametric regression in forecasting.

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