Minimum distance regression and autoregressive model fitting

This work proposes a class of tests for fitting a parametric regression model to a regression function when the underlying design variables are random and the model is possibly heteroscedastic. These tests are based on certain minimized L₂ distances between a nonparametric regression function estimator and the parametric model being fitted. The work obtains the asymptotic distribution of the proposed statistic under the null hypothesis. It also derives the asymptotic distribution of the corresponding minimum distance estimator. A class of tests based on a slightly different L₂ distance for fitting a parametric autoregressive model to a autoregressive function is also proposed in this thesis. The asymptotic properties of underlying parameter estimator and corresponding minimized distanced is derived.