Berman model on concentric objects with the presence of heteroscedasticity

This thesis aims to solve the problem of fitting two concentric circles and two concentric ellipses to noisy data. Statistical methodologies are deployed with additional information about the covariates. We assume that the angular differences between successively measured data points are known. This assumption was first introduced by Berman. We also assume that the covariates have heteroscedastic variances. Accordingly, several estimators are developed for each fitting problem, and their statistical properties are investigated theoretically. The problem of fitting concentric ellipses turns to be nonlinear, and as such, iterative algorithms are implemented using Gauss-Newton and Levenberg-Marquardt methods. Monte Carlo simulations were conducted to validate our results.