The problem of adaptive estimation of constant parameters in the linear regressor model is studied without the hypothesis that regressor is Persistently Excited (PE). First, the initial vector estimation problem is transformed to a series of the scalar ones using the method of Dynamic Regressor Extension and Mixing (DREM). Second, several adaptive estimation algorithms are proposed for the scalar scenario. In such a case, if the regressor may be nullified asymptotically or in a finite time, then the problem of estimation is also posed on a finite interval of time. Robustness of the proposed algorithms with respect to measurement noise and exogenous disturbances is analyzed. The efficiency of the designed estimators is demonstrated in numeric experiments for an academic example.