Exact confidence regions for linear regression parameter under external arbitrary noise

The paper propose new method for identifying non-asymptotic confidence regions for linear regression parameter under external arbitrary noise. This method called Modified Sign-Perturbed Sums (MSPS) method and it is a modification of previously proposed one, called Sign-Perturbed Sums which is applicable only in case of symmetrical centred noise. MSPS algorithm correctness and obtained confidence region convergence are proved theoretically under some additional assumptions. SPS and MSPS methods are compared basing on simulated data. Few advantages of MSPS method in case of biased and asymmetric noise are illustrated.