CONSIDERATIONS ON THE VALIDITY AND APPLICABILITY OF THE UEK METHOD
Abstract
In Popławski and Kaczmarczyk (2013) a method referred to as UEK was presented and used as a tool in the analysis of sustainable rural development. The purpose of this paper is to demonstrate the methodological inappropriateness of that method. In the linear regression model, the matrix of explanatory variables can have either less than full or full column rank. While all regression parameters are non-estimable in the first case, the well-known and widely used ordinary least squares method can be applied in the second one.
Keywords
linear regression; Moore–Penrose pseudoinverse; UEK method
References
Geweke, J. (2005). Contemporary Bayesian Econometrics and Statistics. New York: John Wiley & Sons, Inc.
Goldberger, A. S. (1964). Econometric Theory. New York: J. Wiley.
Harville, D. A. (2008). Matrix Algebra From a Statistician’s Perspective. New York: Springer Science+Business Media, LLC.
Kawa, B., Kaczmarczyk, B. (2012). Wskaźnikowy i modelowy sposób oceny sytuacji finansowej Gminy Kraków na koniec 2011 roku [An Assessment of the Financial
Standing of the Gmina of Krakow at the End of 2011 with the Use of the Ratio and Model-based Analysis]. Zesz. Nauk. PTE,13, 199–213 [in Polish].
Kaczmarczyk, B. (2012). Wycena wartości rynkowych spółek z wykorzystaniem macierzy MP-odwrotnych [An evaluation of market values of companies using the MP-pseudoinverse matrix]. In: T. Grabiński, L. Woszczek, S. Sorys, A. Tabor (red.), W poszukiwaniu skutecznych narzędzi i modeli analizy zjawisk społeczno-gospodarczych (pp. 145–160). Chrzanów: Wyższa Szkoła Przedsiębiorczości i Marketingu [in Polish].
Pajor A. (2017). A Note on the UEK Method. Barom. Reg. Anal. Progn., 15(3), 7–10.
Popławski, Ł., Kaczmarczyk, B. (2013). Możliwości zastosowania metody UEK dla gmin województwa świętokrzyskiego – na przykładzie danych za 2006 rok [Possibilities of Adapting Authorized Method of the Cracow University of Economics for Świętokrzyskie Voivodeship Communities, According to the 2006 Data]. J. Agribus. Rural Dev., 4(30), 207–218 [in Polish].
Searle, S. (1966). Estimable functions and testable hypotheses in linear models. Tech. Rep. BU-213-M. Cornell University, Biometrics Unit.
Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. New York: John Wiley and Sons, INC.
Department of Mathematics, Cracow University of Economics, Rakowicka 27 St., 31-510 Kraków Poland
https://orcid.org/0000-0001-5643-0649
Cracow University of Economics Poland
This journal permits and encourages authors to post items submitted to the journal on personal websites or institutional repositories both prior to and after publication, while providing bibliographic details that credit, if applicable, its publication in this journal.
