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A combinatorial optimization approach to the selection of statistical units
1. | Università di Roma "Sapienza", Dip. di Ing. Informatica, Automatica e Gestionale (DIAG), Via Ariosto 25, Roma, 00185, Italy |
2. | Italian National Statistic Office “Istat", Dip. per i Censimenti e gli Archivi Amm. e Statistici (DICA), Viale Oceano Pacifico 171, Roma, 00144, Italy |
3. | Italian National Statistic Office “Istat”, Dip. per i Censimenti e gli Archivi Amm. e Statistici (DICA), Viale Oceano Pacifico 171, Roma, 00144, Italy |
References:
[1] |
E. Balas, Facets of the knapsack polytope,, Mathematical Programming, 8 (1975), 146.
doi: 10.1007/BF01580440. |
[2] |
R. M. Bell and M. L. Cohen, Coverage Measurement in the 2010 Census - Panel on Correlation Bias and Coverage Measurement in the 2010 Decennial Census,, The National Academic Press, (2008). Google Scholar |
[3] |
G. Bianchi, R. Bruni and A. Reale, Information reconstruction via discrete optimization for agricultural census data,, Applied Mathematical Sciences, 6 (2012), 6241. Google Scholar |
[4] |
G. Bianchi, R. Bruni and A. Reale, Balancing of agricultural census data by using discrete optimization,, Optimization Letters, 8 (2014), 1553.
doi: 10.1007/s11590-013-0652-3. |
[5] |
G. Bianchi, R. Bruni and A. Reale, Open source integer linear programming solvers for error localization in numerical data,, In Advances in Theoretical and Applied Statistics (eds. N. Torelli, (2012).
doi: 10.1007/978-3-642-35588-2_28. |
[6] |
E. Boros, A. Scozzari, F. Tardella and P. Veneziani, Polynomially computable bounds for the probability of the union of events,, Mathematics of Operations Research, 39 (2014), 1311.
doi: 10.1287/moor.2014.0657. |
[7] |
R. Bruni, Discrete models for data imputation,, Discrete Applied Mathematics, 144 (2004), 59.
doi: 10.1016/j.dam.2004.04.004. |
[8] |
R. Bruni, Error correction for massive data sets,, Optimization Methods and Software, 20 (2005), 295.
doi: 10.1080/10556780512331318281. |
[9] |
European Parliament, Regulation of the European Parliament,, N. 1166/2008, (1166). Google Scholar |
[10] |
Food and Agriculture Organization of the United Nations (FAO), A System of Integrated Agricultural Censuses and Surveys,, Vol.1 - World Programme for the Census of Agriculture 2010. FAO Statistical Development Series (2005)., (2005). Google Scholar |
[11] |
M. Ferri and M. Piccioni, Optimal selection of statistical units: An approach via simulated annealing,, Computational Statistics & Data Analysis, 13 (1992), 47.
doi: 10.1016/0167-9473(92)90153-7. |
[12] |
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness,, W.H. Freeman, (1979).
|
[13] |
R. M. Groves, F. J. Jr. Fowler, M. P. Couper, J. M. Lepkowski, E. Singer and R. Tourangeau, Survey Methodology,, Wiley Series in Survey Methodology, (2009).
|
[14] |
T. Hailperin, Best possible inequalities for the probability of a logical function of events,, The American Mathematical Monthly, 72 (1965), 343.
doi: 10.2307/2313491. |
[15] |
P. L. Hammer, E. L. Johnson and U. N. Peled, Facets of regular 0-1 polytopes,, Mathematical Programming, 8 (1975), 179.
doi: 10.1007/BF01580442. |
[16] |
W. K. Kremers, Completeness and unbiased estimation for sum-quota sampling,, Journal of the American Statistical Association, 81 (1986), 1070.
|
[17] |
H. Marchand, A. Martin, R. Weismantel and L. Wolsey, Cutting planes in integer and mixed integer programming,, Discrete Applied Mathematics, 123 (2002), 397.
doi: 10.1016/S0166-218X(01)00348-1. |
[18] |
C. A. Moser, Quota sampling,, Journal of the Royal Statistical Society, 115 (1952), 411.
doi: 10.2307/2980740. |
[19] |
A. Mucherino, P. Papajorgji and P. M. Pardalos, Data Mining in Agriculture,, Springer, (2009).
doi: 10.1007/978-0-387-88615-2. |
[20] |
K. G. Murty, Linear Programming,, John Wiley & Sons Inc., (1983).
|
[21] |
G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization,, John Wiley, (1988).
doi: 10.1002/9781118627372. |
[22] |
T. M. F. Smith, Populations and selection: Limitations of statistics,, Journal of the Royal Statistical Society Series A (Statistics in Society), 156 (1993), 144.
doi: 10.2307/2982726. |
[23] |
S. Sudman, Probability sampling with quotas,, Journal of the American Statistical Association, 61 (1966), 749.
doi: 10.1080/01621459.1966.10480903. |
[24] |
L. A. Wolsey, Faces for a linear inequality in 0-1 variables,, Mathematical Programming, 8 (1975), 165.
doi: 10.1007/BF01580441. |
[25] |
Y. Zhang, F. Zhang and M. Cai, Some new results on multi-dimension Knapsack problem,, Journal of Industrial and Management Optimization, 1 (2005), 315.
doi: 10.3934/jimo.2005.1.315. |
show all references
References:
[1] |
E. Balas, Facets of the knapsack polytope,, Mathematical Programming, 8 (1975), 146.
doi: 10.1007/BF01580440. |
[2] |
R. M. Bell and M. L. Cohen, Coverage Measurement in the 2010 Census - Panel on Correlation Bias and Coverage Measurement in the 2010 Decennial Census,, The National Academic Press, (2008). Google Scholar |
[3] |
G. Bianchi, R. Bruni and A. Reale, Information reconstruction via discrete optimization for agricultural census data,, Applied Mathematical Sciences, 6 (2012), 6241. Google Scholar |
[4] |
G. Bianchi, R. Bruni and A. Reale, Balancing of agricultural census data by using discrete optimization,, Optimization Letters, 8 (2014), 1553.
doi: 10.1007/s11590-013-0652-3. |
[5] |
G. Bianchi, R. Bruni and A. Reale, Open source integer linear programming solvers for error localization in numerical data,, In Advances in Theoretical and Applied Statistics (eds. N. Torelli, (2012).
doi: 10.1007/978-3-642-35588-2_28. |
[6] |
E. Boros, A. Scozzari, F. Tardella and P. Veneziani, Polynomially computable bounds for the probability of the union of events,, Mathematics of Operations Research, 39 (2014), 1311.
doi: 10.1287/moor.2014.0657. |
[7] |
R. Bruni, Discrete models for data imputation,, Discrete Applied Mathematics, 144 (2004), 59.
doi: 10.1016/j.dam.2004.04.004. |
[8] |
R. Bruni, Error correction for massive data sets,, Optimization Methods and Software, 20 (2005), 295.
doi: 10.1080/10556780512331318281. |
[9] |
European Parliament, Regulation of the European Parliament,, N. 1166/2008, (1166). Google Scholar |
[10] |
Food and Agriculture Organization of the United Nations (FAO), A System of Integrated Agricultural Censuses and Surveys,, Vol.1 - World Programme for the Census of Agriculture 2010. FAO Statistical Development Series (2005)., (2005). Google Scholar |
[11] |
M. Ferri and M. Piccioni, Optimal selection of statistical units: An approach via simulated annealing,, Computational Statistics & Data Analysis, 13 (1992), 47.
doi: 10.1016/0167-9473(92)90153-7. |
[12] |
M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness,, W.H. Freeman, (1979).
|
[13] |
R. M. Groves, F. J. Jr. Fowler, M. P. Couper, J. M. Lepkowski, E. Singer and R. Tourangeau, Survey Methodology,, Wiley Series in Survey Methodology, (2009).
|
[14] |
T. Hailperin, Best possible inequalities for the probability of a logical function of events,, The American Mathematical Monthly, 72 (1965), 343.
doi: 10.2307/2313491. |
[15] |
P. L. Hammer, E. L. Johnson and U. N. Peled, Facets of regular 0-1 polytopes,, Mathematical Programming, 8 (1975), 179.
doi: 10.1007/BF01580442. |
[16] |
W. K. Kremers, Completeness and unbiased estimation for sum-quota sampling,, Journal of the American Statistical Association, 81 (1986), 1070.
|
[17] |
H. Marchand, A. Martin, R. Weismantel and L. Wolsey, Cutting planes in integer and mixed integer programming,, Discrete Applied Mathematics, 123 (2002), 397.
doi: 10.1016/S0166-218X(01)00348-1. |
[18] |
C. A. Moser, Quota sampling,, Journal of the Royal Statistical Society, 115 (1952), 411.
doi: 10.2307/2980740. |
[19] |
A. Mucherino, P. Papajorgji and P. M. Pardalos, Data Mining in Agriculture,, Springer, (2009).
doi: 10.1007/978-0-387-88615-2. |
[20] |
K. G. Murty, Linear Programming,, John Wiley & Sons Inc., (1983).
|
[21] |
G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization,, John Wiley, (1988).
doi: 10.1002/9781118627372. |
[22] |
T. M. F. Smith, Populations and selection: Limitations of statistics,, Journal of the Royal Statistical Society Series A (Statistics in Society), 156 (1993), 144.
doi: 10.2307/2982726. |
[23] |
S. Sudman, Probability sampling with quotas,, Journal of the American Statistical Association, 61 (1966), 749.
doi: 10.1080/01621459.1966.10480903. |
[24] |
L. A. Wolsey, Faces for a linear inequality in 0-1 variables,, Mathematical Programming, 8 (1975), 165.
doi: 10.1007/BF01580441. |
[25] |
Y. Zhang, F. Zhang and M. Cai, Some new results on multi-dimension Knapsack problem,, Journal of Industrial and Management Optimization, 1 (2005), 315.
doi: 10.3934/jimo.2005.1.315. |
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