Dear Waed,

Not very much to complicate a task, the linear is needed. Normality of noise is needed for verification of hypotheses about the points of switching. If the points of switching are known, the task of evaluation decides simply enough. In this case estimations of parameters will be optimum at standard assumptions of regression analysis. If the points of switching are unknown, a task becomes difficult. In this case it is necessary to know regression is continuous in points switching or not. The method of decision depends on an answer for this question.

Best regards,

Arnold Korkhin

 Mr. Arnold S. Korkhin, 

Thank you a lot. Yes, the switching point is known. 

Let regression is linear. Then it is necessary to know, there are the breaks of regression in switching points or not. If they are, an initial regression divides into n +1 regressions, where n is number of switching points. Parameters of n regressions are estimated independent of each other. If noise in a regression is correlated and its covariance matrix is known, it is possible to make an effort decrease variances estimations of parameters estimations. Then it is needed to find Aitken’s parameters estimations of initial regression.

It is desirable to verify the validity of the assumption that each switching point is true.

Best regards,

Arnold Korkhin