Abstract
A new procedure for the problem of recovering tabular data in case of incomplete or inconsistent information is presented. It generalizes the well kown RAS (or IPF) algorithm by allowing a wider class of constraints concerning the table entries such as equalities and inequalities over arbitrary cross sections. The theoretical background of the procedure is outlined and some examples of applications are reported.
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References
BACHARACH, M. (1970): Biproportional Matrices and Input-Output-Change, Cambridge
BACHEM, A. and KORTE, B. (1979): On the RAS-Algorithm. In: Computing Vol. 23, 189 ff
Batey, P.W.J. and Madden, M. (1986) (eds): Integrated analysis of regional systems. London: Pion
BATTEN, D.F. (1983): Spatial Analysis of Interacting Economics. Boston etc.: Kluwer-Nijhoff
BATTEN, D. and BOYCE, D. (1986): Spatial interaction, transportation, and interregional commodity flow models. In: Nijkamp (1986)
BISHOP, Y., FIENBERG, S. and HOLLAND, P. (1975): Discrete Multivariate Analysis: Theory and practice. Cambridge, London
BLIEN, U. and GRAEF, F. (1991): Entropieoptimierungsverfahren in der empirischen Wirtschaftsforschung. In: Jahrbücher für Nationalökonomie und Statistik 208 /4, 399–413
BLIEN, U. and GRAEF, F. (1992): Entrop: A General Purpose Entropy Optimizing Method for the Estimation of Tables, the Weighting of Samples, the Disaggregation of Data, and the Development of Forecasts. In: Faulbaum, F. (1992) (ed): Softstat ‘81. Advances in Statistical Software 3. Stuttgart: Gustav Fischer
BLIEN, U. and TESSARING, M. (1988): Die Bildungsgesamtrechnung des IAB. In: Mertens, D. (ed): Konzepte der Arbeitsmarkt-und Berufsforschung, 3rd ed..BeitrAB 70, Nürnberg
BLIEN, U. and TESSARING, M. (1992): Transitions between education and the labour market in Germany. The application of the ENTROP procedure in the Educational Accounting System. Unpublished paper prepared for presentation at the EALE Conference at the University of Warwick.
BREGMAN, L. (1967): The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comp. Math. and Math. Phys. Vol. 7/3, 200ff
CENSOR, Y. (1981): Row-actions methods for huge and sparse systems and their applications. In: SIAM Review, Vol. 23
CENSOR, Y. and LENT, A. (1981): An iterative row-action method for interval convex programming Journal of Optimization Theory and Applications, Vol. 31, 321 ff
CHIANG, A. (1974): Fundamental methods of mathematical economics. ( 2nd ed. ), Tokyo etc.: Mcgraw-Hill Kogakusha
DEMING, W.E. and STEPHAN, F.F. (1940): On a least squares adjustment of a sampled frequency table when the expected marginal totals are known. The Annals of Mathematical Statistics 11/1, March, 427ff
DRENICK, R. and KOZIN, F. (1982) (eds): System Modeling and Optimization. Lecture Notes in Control and Information Science 38, Heidelberg etc.: Springer
GOLAN, A., JUDGE, G., and MILLER, D. (1996): Maximum Entropy Econometrics: Robust Estimation With Limited Data. Chichester etc.: Wiley
GORMAN, W. (1963): Estimating Trends in Leontief Matrices. A Note on Mr. Bacharach’s Paper. Discussion paper, NuffieldCollege, Oxford
HABERMAN, S.J. (1984): Adjustment by minimum discriminant information. The Annals of Statistics, 12/3, 971ff
HARRIGAN, F. and MCGREGOR, P.G. (1988) (eds): Recent advances in regional economic modelling. London: Pion
HINTON, G.E. and SEJNOWSKI, T.J. (1986): Learning and Relearning in Boltzmann Machines. In: Rumelhart, D.E., McClelland, J.L. et al. ( 1986 ) (eds): Parallel distributed processing. Vol. 1: Foundations, Cambridge (Mass.), London: MIT Press
IRELAND, C. and KULLBACK, S. (1968): Contingency tables with given marginals. Biometrika 55, 179 ff
JUSTER, F.T. and LAND, K.C. (1981) (eds): Social Accounting Systems. Essays on the State of the Art. New York etc.: Academic Press
KADAS, S.A. and KLAFSKY, E. (1976): Estimation of the Parameters in the Gravity Model for Trip Distribution: a New Model and Solution Algorithm, Regional Science and Urban Economics Vol. 6, 439 if
KOSKO, B. (1992): Neural networks and fuzzy systems. Englewood Cliffs: Prentice Hall
KULLBACK, S. (1968): Information Theory and Statistics, 2nd ed., New York: Dover
LAND, K.C. and McMillen, M.M. (1981): Demographic Accounts and the Study of Social Change, In: Juster, Land (1981)
LAND, K.J. and JUSTER, F.T. (1981): Social Accounting Systems: An Overview. In: Juster, Land (1981)
LEVINE, R.D. and TRIBUS, M. (1979) (eds): The maximum entropy formalism. Cambridge (Mass.), London: MIT-Press
NIJKAMP, P. (1986) (ed): Handbook of regional and urban economics, Vol. I: Regional economics. Amsterdam etc.: North-Holland
PAASS, G. (1988): Stochastic Generation of a Synthetic Sample from Marginal Information. Gesellschaft für Mathematik und Datenverarbeitung, Arbeitspapiere der GMD Nr. 308. St. Augustin
SHANNON, C.E. and WEAVER, W. (1949): The Mathematical Theory of Communication. Urbana: University of Illinois Press
SLATER, P.B. (1992): Equilibrium and nonequilibrium statistical thermodynamical approaches to modeling spatial interaction dynamics. Environment and Planning A, vol. 24: 441–446
SNICKARS, F. and WEIBULL, J. (1976): A minimum information principle. Regional Science and Urban Economics Vol. 7, 137ff
STONE, R.N. (1962): Multiple classifications in social accounting. Bulletin de l’Institut International de Statistique, Vol. 39, No. 3, 215 ff
STONE, R.N. (1981): The Relationship of Demographic Accounts to National Income and Product Accounts. In: Juster, Land (1981)
STONE, R.N. and WEALE, M. (1986): Two populations and their economies. In: Batey, Madden (1986)
TESSARING, M. (1986): Educational accounting in the Federal Republic of Germany. In: Parkes, D.L., Sellin, B. and Tessaring, M.: Education/ training and labour market policy. Gravenhage: SVO
TESSARING, M. (1987): Demographic aspects of educational expansion and labour-force development in the Federal Republic of Germany. European Journal of Population Vol 3: 327–358
TESSARING, M., BLIEN, U., FISCHER, G., HOFMANN, I. and REINBERG, A. (1990): Bildung und Beschäftigung im Wandel. Die Bildungsgesamtrechnung des IAB. BeitrAB 126. Nürnberg
TESSARING, M., REINBERG, A., FISCHER, G. and SCHWEITZER, C. (1992): Übergänge zwischen Bildung, Ausbildung und Beschäftigung und die Entwicklung der Qualifikationsstruktur. Forthcoming paper. Nürnberg
THEIL, H. (1967): Economics and Information Theory. Amsterdam
WAUSCHKUHN, U. (1982): Anpassung von Stichproben und n-dimensionalen Tabellen an Randbedingungen. München, Wien: R. Oldenbourg
WILSON, A. (1970): Entropy in urban and regional modelling. London: Pion Ltd.
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Blien, U., Graef, F. (1998). Entropy Optimizing Methods for the Estimation of Tables. In: Balderjahn, I., Mathar, R., Schader, M. (eds) Classification, Data Analysis, and Data Highways. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72087-1_1
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DOI: https://doi.org/10.1007/978-3-642-72087-1_1
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