IDENTITY TEST FOR REGRESSION-MODELS

It is considered in this paper the adjustment of H regression equation s in the case of juxtaposition of r polynomial submodels of k degree. The points of intersection of the submodels are supposed to be known. Appropriate restrictions are imposed in such a way that the polynomial submodels are concordant in the points of intersection. The linear mo del for the h(th) equation is (Y) under bar(h) = X(h)<(beta)under bar> (h)+<(epsilon)under bar>(h), h = 1,2,...,H, where (Y) under bar(h) is an n(h) x 1 vector of observations, X(h) is an n(h) x p matrix of know n constants, <(beta)under bar>(h) is an p x 1 vector of unknown parame ters and <(epsilon)under bar>(h) is an n(h) x 1 vector of errors that is distributed MD (<(beta)under bar>(h): phi, sigma(2)I). In the param eters estimation, the Least Square Method was used. A statistic test w as derived for the hypothesis that H regression models in the case of juxtapositon of r polynomial submodels of k degree were identical, The : hypothesis in consideration is: H-0: <(beta)under bar>(1) = <(beta)u nder bar>(2) =...= <(beta)under bar>(H) (H models are identical) vs. H a: <(beta)under bar>(i) not equal <(beta)under bar>(j) for at least on e i not equal j (the H models are not all identical). This method is a pplied to a set of H = two regression equations in the case of juxtapo sition of r = two polynomial submodels of first degree.