Skip to main content

Entropy Optimizing Methods for the Estimation of Tables

  • Conference paper
Classification, Data Analysis, and Data Highways

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • BACHARACH, M. (1970): Biproportional Matrices and Input-Output-Change, Cambridge

    Google Scholar 

  • BACHEM, A. and KORTE, B. (1979): On the RAS-Algorithm. In: Computing Vol. 23, 189 ff

    Google Scholar 

  • Batey, P.W.J. and Madden, M. (1986) (eds): Integrated analysis of regional systems. London: Pion

    Google Scholar 

  • BATTEN, D.F. (1983): Spatial Analysis of Interacting Economics. Boston etc.: Kluwer-Nijhoff

    Google Scholar 

  • BATTEN, D. and BOYCE, D. (1986): Spatial interaction, transportation, and interregional commodity flow models. In: Nijkamp (1986)

    Google Scholar 

  • BISHOP, Y., FIENBERG, S. and HOLLAND, P. (1975): Discrete Multivariate Analysis: Theory and practice. Cambridge, London

    Google Scholar 

  • BLIEN, U. and GRAEF, F. (1991): Entropieoptimierungsverfahren in der empirischen Wirtschaftsforschung. In: Jahrbücher für Nationalökonomie und Statistik 208 /4, 399–413

    Google Scholar 

  • 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

    Google Scholar 

  • BLIEN, U. and TESSARING, M. (1988): Die Bildungsgesamtrechnung des IAB. In: Mertens, D. (ed): Konzepte der Arbeitsmarkt-und Berufsforschung, 3rd ed..BeitrAB 70, Nürnberg

    Google Scholar 

  • 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.

    Google Scholar 

  • 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

    Google Scholar 

  • CENSOR, Y. (1981): Row-actions methods for huge and sparse systems and their applications. In: SIAM Review, Vol. 23

    Google Scholar 

  • 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

    Google Scholar 

  • CHIANG, A. (1974): Fundamental methods of mathematical economics. ( 2nd ed. ), Tokyo etc.: Mcgraw-Hill Kogakusha

    Google Scholar 

  • 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

    Google Scholar 

  • DRENICK, R. and KOZIN, F. (1982) (eds): System Modeling and Optimization. Lecture Notes in Control and Information Science 38, Heidelberg etc.: Springer

    Google Scholar 

  • GOLAN, A., JUDGE, G., and MILLER, D. (1996): Maximum Entropy Econometrics: Robust Estimation With Limited Data. Chichester etc.: Wiley

    Google Scholar 

  • GORMAN, W. (1963): Estimating Trends in Leontief Matrices. A Note on Mr. Bacharach’s Paper. Discussion paper, NuffieldCollege, Oxford

    Google Scholar 

  • HABERMAN, S.J. (1984): Adjustment by minimum discriminant information. The Annals of Statistics, 12/3, 971ff

    Google Scholar 

  • HARRIGAN, F. and MCGREGOR, P.G. (1988) (eds): Recent advances in regional economic modelling. London: Pion

    Google Scholar 

  • 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

    Google Scholar 

  • IRELAND, C. and KULLBACK, S. (1968): Contingency tables with given marginals. Biometrika 55, 179 ff

    Google Scholar 

  • JUSTER, F.T. and LAND, K.C. (1981) (eds): Social Accounting Systems. Essays on the State of the Art. New York etc.: Academic Press

    Google Scholar 

  • 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

    Google Scholar 

  • KOSKO, B. (1992): Neural networks and fuzzy systems. Englewood Cliffs: Prentice Hall

    Google Scholar 

  • KULLBACK, S. (1968): Information Theory and Statistics, 2nd ed., New York: Dover

    Google Scholar 

  • LAND, K.C. and McMillen, M.M. (1981): Demographic Accounts and the Study of Social Change, In: Juster, Land (1981)

    Google Scholar 

  • LAND, K.J. and JUSTER, F.T. (1981): Social Accounting Systems: An Overview. In: Juster, Land (1981)

    Google Scholar 

  • LEVINE, R.D. and TRIBUS, M. (1979) (eds): The maximum entropy formalism. Cambridge (Mass.), London: MIT-Press

    Google Scholar 

  • NIJKAMP, P. (1986) (ed): Handbook of regional and urban economics, Vol. I: Regional economics. Amsterdam etc.: North-Holland

    Google Scholar 

  • PAASS, G. (1988): Stochastic Generation of a Synthetic Sample from Marginal Information. Gesellschaft für Mathematik und Datenverarbeitung, Arbeitspapiere der GMD Nr. 308. St. Augustin

    Google Scholar 

  • SHANNON, C.E. and WEAVER, W. (1949): The Mathematical Theory of Communication. Urbana: University of Illinois Press

    Google Scholar 

  • SLATER, P.B. (1992): Equilibrium and nonequilibrium statistical thermodynamical approaches to modeling spatial interaction dynamics. Environment and Planning A, vol. 24: 441–446

    Article  Google Scholar 

  • SNICKARS, F. and WEIBULL, J. (1976): A minimum information principle. Regional Science and Urban Economics Vol. 7, 137ff

    Google Scholar 

  • STONE, R.N. (1962): Multiple classifications in social accounting. Bulletin de l’Institut International de Statistique, Vol. 39, No. 3, 215 ff

    Google Scholar 

  • STONE, R.N. (1981): The Relationship of Demographic Accounts to National Income and Product Accounts. In: Juster, Land (1981)

    Google Scholar 

  • STONE, R.N. and WEALE, M. (1986): Two populations and their economies. In: Batey, Madden (1986)

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    Article  Google Scholar 

  • TESSARING, M., BLIEN, U., FISCHER, G., HOFMANN, I. and REINBERG, A. (1990): Bildung und Beschäftigung im Wandel. Die Bildungsgesamtrechnung des IAB. BeitrAB 126. Nürnberg

    Google Scholar 

  • TESSARING, M., REINBERG, A., FISCHER, G. and SCHWEITZER, C. (1992): Übergänge zwischen Bildung, Ausbildung und Beschäftigung und die Entwicklung der Qualifikationsstruktur. Forthcoming paper. Nürnberg

    Google Scholar 

  • THEIL, H. (1967): Economics and Information Theory. Amsterdam

    Google Scholar 

  • WAUSCHKUHN, U. (1982): Anpassung von Stichproben und n-dimensionalen Tabellen an Randbedingungen. München, Wien: R. Oldenbourg

    Google Scholar 

  • WILSON, A. (1970): Entropy in urban and regional modelling. London: Pion Ltd.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-72087-1_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63909-1

  • Online ISBN: 978-3-642-72087-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics