Local polynomial Lₚ norm regression

The local least-squares estimator for a regression curve cannot provide optimal results when non-Gaussian noise is present. Theoretically and empirically, there is evidence that residuals often exhibit distributional properties different from that of a normal distribution, so it is worth considering estimation based on other norms. It is suggested to use Lₚ-norm estimators to minimize the residuals when residuals have non-normal kurtosis. This thesis proposes local polynomial Lₚ-norm regression, which replaces weighted least-square estimation with weighted Lₚ norm estimation for fitting the polynomial locally. We investigate the performance of our proposed method when data depart from the normal distribution. Our technique shows good improvement on both simulated and real-life data compared to locally weighted least squares. Our study shows that our method can be a practical alternative to ordinary weighted least-squares when fitting local polynomials and can generalize well to regression data following different error distributions, including normal.Science, Irving K. Barber Faculty of (Okanagan)Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)Graduat