Modern Stochastics: Theory and Applications

This model is a restriction of the conic section fitting model because a couple of two lines is a degenerate conic section. The following estimators are constructed: two projections of the adjusted least squares estimator in the conic section fitting model, orthogonal regression estimator, parametric maximum likelihood estimator in the Gaussian model, and regular best asymptotically normal moment estimator.

The conditions for the consistency and asymptotic normality of the projections of the adjusted least squares estimator are provided. All the estimators constructed in the paper are equivariant. The estimators are compared numerically.