Imputation of numerical data under linear edit restrictions

• Autores: Wieger Coutinho, Ton de Waal, Marco Remmerswaal
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 35, Nº. 1, 2011, págs. 39-64
• Idioma: inglés
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• Resumen

  • A common problem faced by statistical offices is that data may be missing from collected data sets. The typical way to overcome this problem is to impute the missing data. The problem of imputing missing data is complicated by the fact that statistical data often have to satisfy certain edit rules, which for numerical data usually take the form of linear restrictions. Standard imputation methods generally do not take such edit restrictions into account. In the present article we describe two general approaches for imputation of missing numerical data that do take the edit restrictions into account. The first approach imputes the missing values by means of an imputation method and afterwards adjusts the imputed values so they satisfy the edit restrictions. The second approach sequentially imputes the missing data. It uses Fourier-Motzkin elimination to determine appropriate intervals for each variable to be imputed. Both approaches are not based on a specific imputation model, but allow one to specify an imputation model. To illustrate the two approaches we assume that the data are approximately multivariately normally distributed. To assess the performance of the imputation approaches an evaluation study is carried out.

• Referencias bibliográficas
  • Banff Support Team (2008).Functional Description of the Banff System for Edit and Imputation. Technical Report, Statistics Canada.
  • Chambers, R. (2003). Evaluation Criteria for Statistical Editing and Imputation. In:Methods and Experimental Results from the EUREDIT Project(ed....
  • Chvátal, V. (1983).Linear Programming. W.H. Freeman and Company, New York. De Waal, T. (2001). SLICE: Generalised software for statistical...
  • De Waal, T. (2005). Automatic error localisation for categorical, continuous and integer data,Statistics and Operations Research Transactions,...
  • De Waal, T. and W. Coutinho (2005). Automatic editing for business surveys: an assessment of selected algorithms.International Statistical...
  • Duffin, R.J. (1974). On Fourier’s analysis of linear inequality systems.Mathematical Programming Studies, 1, 71–95.
  • Fylstra, D. L. Lasdon, J. Watson and A. Warren (1998). Designand use of the Microsoft Excel Solver, Interface, 28, 29–55.
  • Geweke, J. (1991).Efficient Simulation from the Multivariate Normal and Student-t Distributions Subject to Linear Constraints and the Evaluation...
  • Kalton, G. en D. Kasprzyk (1986). The treatment of missing survey data.Survey Methodology, 12, 1–16.
  • Kovar, J. and P. Whitridge (1990). Generalized edit and imputation system; overview and applications. Revista Brasileira de Estadistica, 51,...
  • Kovar, J. en P. Whitridge (1995). Imputation of business survey data. In:Business Survey Methods(ed. B.G. Cox, D. A. Binder, B.N. Chinnappa,...
  • Lasdon, L.S. and S. Smith (1992). Solving large sparse non-linear programs using GRG,ORSA Journal on Computing, 4, 2–15.
  • Little, R.J.A. and D.B. Rubin (2002).Statistical Analysis with Missing Data (second edition).John Wiley & Sons, New York.
  • Longford, N.T. (2005).Missing Data and Small-Area Estimation. Springer, New York.
  • Nemhauser, G.L. and L.A. Wolsey (1988).Integer and Combinatorial Optimisation.Wiley, New York.
  • Pannekoek, J. and T. De Waal (2005). Automatic edit and imputation for business surveys: the Dutch contribution to the EUREDIT project.Journal...
  • Pannekoek, J., N. Shlomo and T. De Waal (2008).Calibrated Imputation of Numerical Data under Linear Edit Restriction. UN/ECE Work Session...
  • Raghunathan, T.E., J.M. Lepkowski, J. Van Hoewyk and P. Solenberger (2001). A multivariate technique for multiply imputing missing values...
  • Rubin, D.B. (1987).Multiple Imputation for Nonresponse in Surveys. John Wiley & Sons, New York.
  • Rubin, D.B. (2003). Nested multiple imputation of NMES via partially incompatible MCMC.Statistica Neerlandica, 57, 3–18.
  • Särndal, C.-E. and S. Lundström (2005).Estimation in Surveys with Nonresponse, John Wiley & Sons,
  • Chichester. Schafer, J.L. (1997).Analysis of Incomplete Multivariate Data. Chapman & Hall, London.
  • Tempelman, C. (2007).Imputation of Restricted Data. Doctoral thesis, University of Groningen.
  • Van Buuren, S. and C.G.M., Oudshoorn (1999).Flexible Multivariate Imputation by MICE. TNO Preventie en Gezondheid, TNO/PG 99.054, Leiden.
  • Van Buuren, S. and C.G.M. Oudshoorn C.G.M. (2000).Multivariate Imputation by Chained Equations: MICE V1.0 User’s Manual. Report PG/VGZ/00.038,...
  • Winkler, W.E. and L.A. Draper (1997). The SPEER edit system.Statistical Data Editing (Volume 2); Methods and Techniques, United Nations, Geneva.