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We consider the two-line fitting problem. True points lie on two straightlines and are observed with Gaussian perturbations. For each observed point, itis not known on which line the corresponding true point lies. The parameters ofthe lines are estimated. This model is a restriction of the conic sectionfitting model because a couple of two lines is a degenerate conic section. Thefollowing estimators are constructed: two projections of the adjusted leastsquares estimator in the conic section fitting model, orthogonal regressionestimator, parametric maximum likelihood estimator in the Gaussian model, andregular best asymptotically normal moment estimator. The conditions for theconsistency and asymptotic normality of the projections of the adjusted leastsquares estimator are provided. All the estimators constructed in the paper areequivariant. The estimators are compared numerically.

Equivariant adjusted least squares estimator in two-line fitting model