A. Econometric and .. Censored-dependent-variable, The Generalized Box-Cox (GBC) idea and time-series explanations of total cost

.. Multi-cost, 6 3.3. Overcoming barriers to optimal form GBC estimation

U. Traffic, 19 5.1. Maximal detailed contents: a Four-Quality, Four-Traffic 19 5.2. Form, aggregation and the key role of zero handling rules 19 A. Embarras de richesse : a tridimensional table 19 B. A statistically preferred 4-traffic U-GBC model: the rows and the last column of Table 8 20 C. The preferred 4-traffic U-GBC model and the specificity of damages by train category, Full Trans-Log, p.26

P. Abrantes, P. E. Wheat, S. Iwnicki, C. Nash, and A. Smith, CATRIN (Cost Allocation of TRansport INfrastructure cost), Review of rail track cost allocation studies for Deliverable 1 of CATRIN. Funded by Sixth Framework Programme, 2007.

D. J. Aigner, Basic Econometrics, 1971.

T. Amemiya and J. L. Powell, A comparison of the Box-Cox maximum likelihood estimator and the nonlinear two stage least squares estimator, 1980.

M. Andersson, Marginal railway infrastructure cost estimates in the presence of unobserved effects, 2006.

M. Andersson, CATRIN (Cost Allocation of TRansport INfrastructure cost) Deliverable 8, Rail Cost Allocation for Europe ? Annex 1A? Marginal Costs of Railway Infrastructure Wear and Tear for Freight and Passenger Trains in Sweden. Funded by Sixth Framework Programme, 2009.

M. Andersson, Marginal cost of railway infrastructure wear and tear for freight and passenger trains in Sweden. Department of transport economics, Presented at the Fourth International Transport Economics Conference, p.31, 2009.

J. P. Baumgartner, The Production Function of a Railway, International Journal of Transport Economics, vol.5, issue.2, pp.145-159, 1978.

E. R. Berndt, B. H. Hall, R. E. Hall, and J. A. Hausman, Estimation and Inference in Nonlinear Models, Annals of Economic and Social Measurement, vol.3, pp.653-665, 1974.

E. R. Berndt and M. S. Khaled, Parametric Productivity Measurement and Choice Among Flexible Functional Forms, Journal of Political Economy, vol.87, issue.6, pp.1220-1245, 1979.
DOI : 10.1086/260833

C. G. Bereskin, Estimating Maintenance-of-Way Costs for U.S. Railroads After Deregulation, Transportation Research Record: Journal of the Transportation Research Board, vol.1707, pp.13-21, 2000.
DOI : 10.3141/1707-02

P. J. Bickel and K. A. Doksum, An Analysis of Transformations Revisited, Journal of the American Statistical Association, vol.10, issue.374, pp.296-311, 1981.
DOI : 10.1080/01621459.1981.10477649

M. Bierlaire, BIOGEME: a free package for the estimation of discrete choice models, Proceedings of the 3rd Swiss Transportation Research Conference, 2003.

M. Bierlaire, An introduction to BIOGEME Version 1, 2008.

C. Blackorby, D. Primont, and R. R. Russell, On testing separability restrictions with flexible functional forms, Journal of Econometrics, vol.5, issue.2, pp.195-209, 1977.
DOI : 10.1016/0304-4076(77)90024-0

B. Borger and . De, Hedonic versus homogeneous output specifications of railroad technology: Belgian railroads 1950???1986, Transportation Research Part A: General, vol.25, issue.4, pp.227-238, 1991.
DOI : 10.1016/0191-2607(91)90009-F

B. Borger and . De, Estimating a multiple-output generalized Box-Cox cost function, European Economic Review, vol.36, issue.7, pp.1379-1398, 1992.
DOI : 10.1016/0014-2921(92)90073-6

G. H. Borts, The Estimation of Rail Cost Functions, Econometrica, vol.28, issue.1, pp.108-131, 1960.
DOI : 10.2307/1905297

G. E. Box and D. R. Cox, An Analysis of Transformations, Journal of the Royal Statistical Society, Series B, vol.26, pp.211-243, 1964.

G. E. Box and P. W. Tidwell, Transformation of the Independent Variables, Technometrics, vol.222, issue.4, pp.531-550, 1962.
DOI : 10.2307/3001938

R. S. Brown, D. W. Caves, and L. R. Christensen, Modelling the Structure of Cost and Production for Multiproduct Firms, Southern Economic Journal, vol.46, issue.1, pp.256-273, 1979.
DOI : 10.2307/1057018

D. F. Burgess, A Cost Minimization Approach to Import Demand Equations, The Review of Economics and Statistics, vol.56, issue.2, pp.225-234, 1974.
DOI : 10.2307/1924443

D. W. Caves, L. R. Christensen, and J. A. Swanson, Productivity in U.S. Railroads, 1951-1974, The Bell Journal of Economics, vol.11, issue.1, pp.168-181, 1980.
DOI : 10.2307/3003406

D. W. Caves, L. R. Christensen, and M. W. Tretheway, Flexible Cost Functions for Multiproduct Firms, The Review of Economics and Statistics, vol.62, issue.3, pp.477-481, 1980.
DOI : 10.2307/1927120

D. W. Caves, L. R. Christensen, M. W. Tretheway, and J. Windle, Network effects and the measurement of returns to scale and density for U.S. railroads. Ch. 4 in, Analytical Studies in Transport Economics, pp.97-120, 1985.

L. R. Christensen, D. W. Jorgenson, and L. J. Lau, Conjugate Duality and the Transcendental Logarithmic Function, Econometrica, vol.39, issue.4, pp.255-256, 1971.

M. Dagenais, M. Gaudry, and T. C. Liem, Urban travel demand: The impact of Box-Cox transformations with nonspherical residual errors, Transportation Research Part B: Methodological, vol.21, issue.6, pp.443-477, 1987.
DOI : 10.1016/0191-2615(87)90041-5

R. Davidson and J. G. Mackinnon, Testing Linear and Loglinear Regressions against Box-Cox Alternatives, The Canadian Journal of Economics, vol.18, issue.3, pp.499-517, 1985.
DOI : 10.2307/135016

M. Denny and M. Fuss, The Use of Approximation Analysis to Test for Separability and the Existence of Consistent Aggregates, America Economic Review, vol.67, issue.3, pp.404-418, 1977.

M. Denny and C. Pinto, An Aggregate Model with Multi-Product Technologies, Production Economics: A Dual Approach to Theory and Applications, pp.249-267, 1978.
DOI : 10.1016/B978-0-444-85013-3.50016-4

W. E. Diewert, An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function, Journal of Political Economy, vol.79, issue.3, pp.481-507, 1971.
DOI : 10.1086/259764

W. E. Diewert, Separability and a Generalization of the Cobb-Douglas Cost, Production and Indirect Utility Functions, Research Branch, Department of Manpower and Immigration, 1973.

W. E. Diewert, Functional Forms for Revenue and Factor Requirements Functions, International Economic Review, vol.15, issue.1, pp.199-130, 1974.
DOI : 10.2307/2526093

N. R. Draper and D. R. Cox, On distributions and their transformations to normality, Journal of the Royal Statistical Society B31, pp.472-476, 1969.

E. Fekpe, Bridge Cost Allocation Issues. Canadian Transportation Research Forum, Proceedings, vol.2, pp.883-892, 1996.

M. Fuss, D. Mcfadden, Y. , and M. , A Survey of Functional Forms in the Economic Analysis of Production Production Economics: a Dual Approach to Theory and Applications, Ch. II, vol.1, pp.219-268, 1978.

M. Gaudry, TRIO, Version 2.0, Agora Jules Dupuit, 2002.

M. Gaudry, U. Blum, and T. Liem, Turning Box-Cox, including Quadratic Forms in Regression Structural Road Accident Models: The International DRAG Family, Ch, pp.335-346, 2000.

M. Gaudry and R. Laferrière, The box-cox transformation, Economics Letters, vol.30, issue.1, pp.27-29, 1989.
DOI : 10.1016/0165-1765(89)90151-1

M. Gaudry and M. J. Wills, Estimating the functional form of travel demand models, Transportation Research, vol.12, issue.4, pp.257-289, 1978.
DOI : 10.1016/0041-1647(78)90068-0

M. Gaudry and E. Quinet, Rail track wear-and-tear costs by traffic class in France. Publication AJD-66, Recherche en Analyse Socio-économique, École nationale des Ponts et Chaussées (ENPC-CERAS), 2003.

M. Gaudry and E. Quinet, CATRIN (Cost Allocation of TRansport INfrastructure cost), Deliverable 8, Rail Cost Allocation for Europe ? Annex 1Di? Track Maintenance Costs in France. Funded by Sixth Framework Programme, 2009.

W. S. Gosset, The probable error of a mean, Biometrica, vol.6, issue.1, pp.1-25, 1908.

R. C. Griffin, J. M. Montgomery, and M. E. Rister, Selecting Functional Form in Production Function Analysis, Western Journal of Agricultural Economics, vol.12, issue.2, pp.216-227, 1987.

G. Hariton, Railway Costing: A Review, Canadian Transport Commission, vol.112, pp.60-64, 1984.

I. Heggie, User Charging and Accountability for Roads: An Agenda for Reform. The World Bank, 1991.

I. Heggie, Improving Management and Charging Policies for Roads: An Agenda for Reform, p.81, 1991.

R. Highway and . Board, The AASHO Road Test, Report, vol.5, 1962.

B. G. Hutchinson, Some Technical Issues in Implementing Road User Pavement Damage Charges, Infrastructure Pricing, Investment Decisions and Financing, pp.26-27, 1991.

J. O. Jansson, An Analysis of the Rail Transport System, Classics in Transport Analysis: Railways, pp.135-181, 2002.

S. Jara-díaz, The estimation of transport cost functions: a methodological review, Transport Reviews, vol.69, issue.3, pp.257-278, 1982.
DOI : 10.1080/01441648208716498

P. Johansson and J. Nilsson, An economic analysis of track maintenance costs, Transport Policy, vol.11, issue.3, pp.277-286, 2004.
DOI : 10.1016/j.tranpol.2003.12.002

F. W. Jung, R. Kher, and W. A. Phang, Ontario Pavement Analysis of Costs: A Performance Prediction System, Research Report, vol.200, 1975.

M. S. Khaled, Productivity Analysis and Functional Specification. A Parametric Approach, 1978.

R. Laferrière, L'usage du coefficient de Pearson comme mesure du R 2 dans les modèles non linéaires. Publication AJD-57, Agora Jules Dupuit, issue.2, 1999.

S. Lcpc, Conception et Dimensionnement des Structures de Chaussée: Guide Technique. Laboratoire Central des Ponts et Chaussées et Service d'Études Techniques des Routes et Autoroutes, 1994.

. T. Liem, M. Dagenais, and M. Gaudry, The L-1.4 program for BC-GAUHESEQ (Box-Cox Generalized AUtoregressive HEteroskedastic Single EQuation) models. Publication CRT-510, Centre de recherche sur les transports, 1987.

T. C. Liem, M. Gaudry, M. Dagenais, and U. Blum, LEVEL: The L-1.5 program for BC- GAUHESEQ (Box-Cox Generalized AUtoregressive HEteroskedastic Single EQuation) regression and multimoment analysis Structural Road Accident Models: The International DRAG Family, pp.263-324, 2000.

H. Link, CATRIN (Cost Allocation of TRansport INfrastructure cost) Deliverable 8, Rail Cost Allocation for Europe ? Annex 1C -Marginal costs of rail maintenance in Austria. Funded by Sixth Framework Programme, 2009.

H. Link, A. Stuhlemmer, M. Haraldsson, P. Abrantes, P. Wheat et al., CATRIN (Cost Allocation of TRansport INfrastructure cost, Deliverable D 1, Cost allocation Practices in the European Transport Sector. Funded by Sixth Framework Programme. VTI, p.93, 2008.

W. Lloyd and R. Addis, Current Road-Vehicle Interaction Research in the UK. Paper presented at the International Seminar on Heavy Vehicle Weights and Dimensions, p.12, 2000.

M. Marti, R. Neuenschwander, and P. Walker, CATRIN (Cost Allocation of TRansport INfrastructure cost) Deliverable 8, Rail Cost Allocation for Europe ? Annex 1B?. Track maintenance and renewal costs in Switzerland. Funded by Sixth Framework Programme, 2009.

C. D. Martland, Allocating the Costs of Railroad Infrastructure to Specific Traffic Classes. Publication AJD-36, 2001.

W. Nördling and . Von, Prix de revient des transports par chemin de fer, Annales des Ponts et Chaussées, vol.11, issue.10, pp.292-303, 1886.

R. J. Olsen, The method of Box and Cox, a pitfall. Institution for Social and Policy Studies, 1978.

T. H. Oum, W. G. Waters, and I. , A Survey of Recent Developments in Transportation Cost Function Research, Logistics and Transportation Review, vol.32, issue.4, pp.423-463, 1996.

T. H. Oum, W. G. Waters, and I. , Recent developments in cost function research in transportation, Recent developments in transport economics, pp.33-73, 1997.

D. J. Poirier, The Use of the Box-Cox Transformation in Limited Dependent Variable Models, Journal of the American Statistical Association, vol.26, issue.362, pp.284-287, 1978.
DOI : 10.1080/01621459.1978.10481570

E. Quinet, Détermination des coûts marginaux sociaux du rail. Manuscrit, 38 pages, mars, 2002.

R. Rivier, Y. Et, and . Putallaz, Audit sur l'état du réseau ferré national français. Laboratoire d'Intermodalité des Transports et de Planification, p.30, 2005.

W. E. Robert, J. D. Chapman, and C. D. Martland, Effects of Axle Loads and Train Capacity on Heavy Haul Network Performance, Proceedings of the 39 th Meeting of the Transportation Research Forum, 1997.

R. N. Rosett and F. D. Nelson, Estimation of the Two-Limit Probit Regression Model, Econometrica, vol.43, issue.1, pp.141-146, 1975.
DOI : 10.2307/1913419

P. C. Sánchez, Vertical Relationships between Railway Operations and the Infrastructure for the European Case, Helsinki Workshop on Infrastructure Charging on Railways, VATT Discussion Papers 245, Government Institute for Economic Research, pp.71-94, 2000.

J. Schlesselman, Power families: a note on the Box and Cox transformation, Journal of the Royal Statistical Society Series B, vol.33, pp.307-338, 1971.

R. W. Shephard, Cost and Production Functions, 1953.
DOI : 10.1007/978-3-642-51578-1

K. A. Small, Highway Infrastructure: Crisis in finance or Crisis in Management?, ITS Review, vol.13, issue.2, pp.4-8, 1990.

K. A. Small, C. Winston, and C. A. Evans, Road Works. The Brookings Institution, 1989.

K. A. Small and F. Zhang, A Reanalysis of the AASHO Road Test Data: Rigid Pavements. Department of Economics and Institute of Transportation Studies, p.34, 1988.

J. J. Spitzer, The Demand for Money, the Liquidity Trap, and Functional Forms, International Economic Review, vol.17, issue.1, pp.220-227, 1976.
DOI : 10.2307/2526077

J. J. Spitzer, Variance Estimates in Models with the Box-Cox Transformation: Implications for Estimation and Hypothesis Testing, The Review of Economics and Statistics, vol.66, issue.4, pp.645-652, 1984.
DOI : 10.2307/1935988

J. Thomas, EU Task Force on Rail Infrastructure charging: summary findings on best practice in marginal cost pricing, 2001.

J. Tobin, Estimation of Relationships for Limited Dependent Variables, Econometrica, vol.26, issue.1, pp.24-36, 1958.
DOI : 10.2307/1907382

B. Tovar, S. Jara-díaz, and L. Trujillo, Production and cost functions and their application to the port sector: a literature survey, 2003.

P. Wheat and S. J. Smith, Assessing the Marginal Infrastructure Maintenance Wear and Tear Costs for Britains's Railway Network, Journal of Transport Economics and Policy, vol.42, issue.2, pp.189-224, 2008.

P. Wheat, C. Smith, and . Nash, CATRIN (Cost Allocation of TRansport INfrastructure cost), Deliverable 8 -Rail Cost Allocation for Europe. Funded by Sixth Framework Programme, 2009.

G. W. Wilson, Economic Analysis of Intercity Freight Transportation, 1980.

C. Winston, Conceptual Developments in the Economics of Transportation: An Interpretative Survey, Journal of Economic Litterature, vol.23, pp.57-94, 1985.

F. Zhang, A Reanalysis of the AASHO Road Test Data: Flexible Pavements. Manuscript, Department of Economics and Institute of Transportation Studies, pp.36-37, 1989.