An overview of linear structural models in errors in variables regression

REVSTAT-Statistical Journal

Volumn 8, Issue 1, 2010, Pages 57-80

  Gillard, Jonathan ^a  

^a CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Errors in variables; Linear structural model; Measurement error; Regression

Indexed keywords

EID: 80055050378     PISSN: 16456726     EISSN: 21830371     Source Type: Journal    
DOI: None     Document Type: Article

References (63)

1. Adcock, R.J. (1877). Note on the method of least squares, The Analyst, 4(6), 183-184.
2. Adcock, R.J. (1878). A problem in least squares, The Analyst, 5(2), 53-54.
3. Anderson, T.W. (1984). Estimating linear statistical relationships, Ann. Statist., 12, 1-45.
4. Barker, F.; Soh, Y.C. and Evans, R.J. (1988). Properties of the geometric mean functional relationship, Biometrics, 44(1), 279-281.
5. Barnett, V.D. (1970). Fitting straight lines-The linear functional relationship with replicated observations, J. Roy. Statist. Soc. Ser. C Appl. Statist., 19, 135-144.
6. Bartlett, M.S. (1949). Fitting a straight line when both variables are subject to error, Biometrics, 5, 207-212.
7. Birch, M.W. (1964). A note on the maximum likelihood estimation of a linear structural relationship, J. Amer. Statist. Assoc., 59, 1175-1178.
8. Carroll, R.J., Ruppert, D. and Stefanski, L.A. (1995). Measurement Error in Nonlinear Models, Chapman & Hall, London.
9. Casella, G. and Berger, R.L. (1990). Statistical Inference, Wadsworth & Brooks, Pacific Grove, CA.
10. Cheng, C.-L. and Van Ness, J.W. (1999). Statistical Regression with Measure-ment Error, Kendall's Library of Statistics, 6, Arnold, London.
11. Copas, J.B. (1972). The likelihood surface in the linear functional relationship problem, J. Roy. Statist. Soc. Ser. B, 34, 274-278.
12. Cragg, J.G. (1997). Using higher moments to estimate the simple errors-invariables model, The RAND Journal of Economics, 28(0), S71-S91.
13. Creasy, M.A. (1956). Confidence limits for the gradient in the linear functional relationship, J. Roy. Statist. Soc. Ser. B, 18, 65-69.
14. Dagenais, M.G. and Dagenais, D.L. (1997). Higher moment estimators for linear regression models with errors in the variables, J. Econometrics, 76(1-2), 193-221.
15. Deming, W.E. (1931). The application of least squares, Philos. Mag. Ser., 7(11), 146-158.
16. Draper, N.R. and Smith, H. (1998). Applied Regression Analysis, Third Ed., Wiley-Interscience, Canada.
17. Drion, E.F. (1951). Estimation of the parameters of a straight line and of the variances of the variables, if they are both subject to error, Indagationes Math., 13, 256-260.
18. Dunn, G. (2004). Statistical Evaluation of Measurement Errors, Second Ed., Arnold, London.
19. Durbin, J. (1954). Errors in variables, Rev. Inst. Internat. Statist., 22, 23-32.
20. Fuller, W.A. (1987). Measurement error models, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons Inc., New York.
21. Geary,R.C. (1942). Inherent relations between random variables, Proc.R. Irish. Acad. Sect. A, 47, 1541-1546.
22. Geary, R.C. (1943). Relations between statistics: the general and the sampling problem when the samples are large, Proc. R. Irish. Acad. Sect. A, 22, 177-196.
23. Geary, R.C. (1949). Determination of linear relations between systematic parts of variables with errors of observation the variances of which are unknown, Econo-metrica, 17, 30-58.
24. Geary, R.C. (1949). Sampling aspects of the problem from the error-in-variable approach, Econometrica, 17, 26-28.
25. Gibson, W.M. and Jowett, G.H. (1957). Three-group regression analysis-Part 1: Simple regression analysis, Appplied Statistics, 6, 114-122.
26. Gillard, J.W. (2007). Errors in Variables Regression: What is the appropriate model? Cardiff University PhD Thesis.
27. Gillard, J.W. and Iles, T.C. (2005). Method of moments estimation in linear regression with errors in both variables, Cardiff School of Mathematics Technical Report.
28. Golub, G.H. and Van Loan, C.F. (1980). An analysis of the total least squares problem, SIAM J. Numer. Anal., 17(6), 883-893.
29. Gupta, Y.P. and Amanullah. (1970). A note on the moments of the Wald's estimator, Statistica Neerlandica, 24, 109-123.
30. Hood, K.; Nix, A.B.J. and Iles, T.C. (1999). Asymptotic information and variance-covariance matrices for the linear structural model, The Statistician, 48(4), 477-493.
31. Johnson, R.A. and Wichern, D.W. (1992). Applied Multivariate Statistical Analysis, Prentice-Hall, Inc.
32. Jolicouer, P. (1975). Linear regressions in fishery research: some comments, J. Fish. Res. Board Can., 32(8), 1491-1494.
33. Joreskog, K.G. and Sorbom, D. (1984). LISREL VI-Analysis of linear structural relations by maximum likelihood, instrumental variables and least squares methods, User's Guide, Department of Statistics, University of Uppsala, Uppsala, Sweden.
34. Judge, G.G.; Griffiths, W.E.; Carter Hill, R. and Lee, T.-C. (1980). The Theory and Practise of Econometrics, Wiley, New York.
35. Kendall, M.G. (1951). Regression, structure and functional relationship-I, Biometrika, 38, 11-25.
36. Kendall, M.G. (1952). Regression, structure and functional relationship-II, Biometrika, 39, 96-108.
37. Kendall, M.G. and Stuart, A. (1973). The Advanced Theory of Statistics, Volume Two, Third Ed., Charles Griffin and Co. Ltd., London.
38. Kummel, C.H. (1879). Reduction of observed equations which contain more than one observed quantity, The Analyst, 6, 97-105.
39. Lindley, D.V. (1947). Regression lines and the linear functional relationship, Suppl. J. Roy. Statist. Soc., 9, 218-244.
40. Madansky, A. (1959). The fitting of straight lines when both variables are subject to error, J. Amer. Statist. Assoc., 54, 173-205.
41. Maddala, G.S. (1988). Introduction to Econometrics, Second Ed., Prentice Hall International, Inc.
42. Markovsky, I. and Van Huffel, S. (2006). On weighted structured total least squares. In "Large-Scale Scientific Computing", Lecture Notes in Comput. Sci., 3743, Springer, Berlin, pp. 695-702.
43. Moran, P.A.P. (1971). Estimating structural and functional relationships, Multivariate Analysis, 1, 232-255.
44. Nair, K.R. and Banerjee, K.S. (1942). A note on fitting of straight lines if both variables are subject to error, Sankhya, 6, 331.
45. Neyman, J. and Scott, E.L. (1948). Consistent estimates based on partial consistent observations, Econometrica, 16, 1-32.
46. Neyman, J. and Scott, E.L. (1951). On certain methods of estimating the linear structural relation, Ann. Math. Statist., 22, 352-361.
47. Pakes, A. (1982). On the asymptotic bias of the Wald-type estimators of a straight line when both variables are subject to error, Int. Econ. Rev., 23, 491-497.
48. Pal, M. (1980). Consistent moment estimators of regression coefficients in the presence of errors in variables, J. Econometrics, 14, 349-364.
49. Pearson, K. (1901). On lines and planes of closest fit to systems of points in space, Philos. Mag., 2, 559-572.
50. Ricker, W.E. (1973). Linear regressions in fishery research, J. Fish. Res. Board Can., 30, 409-434.
51. Riggs, D.S.; Guarnieri, J.A. and Addleman, S. (1978). Fitting straight lines when both variables are subject to error, Life Sciences, 22, 1305-1360.
52. Scott, E.L. (1950). Note on consistent estimates of the linear structural relation between two variables, Anal. Math. Stat., 21(2), 284-288.
53. Seber, G.A.F. and Wild, C.J. (1989). Nonlinear Regression, Wiley, New York.
54. Solari, M.E. (1969). The 'maximum likelihood solution' to the problem of estimating a linear functional relationship, J. Roy. Statist. Soc. Ser. B, 31, 372-375.
55. Sprent, P. (1969). Models in Regression and Related Topics, Methuen's Statistical Monographs, Matheun & Co Ltd, London.
56. Sprent, P. (1970). The saddlepoint of the likelihood surface for a linear functional relationship, J. Roy. Statist. Soc. Ser. B, 32, 432-434.
57. Sprent, P. and Dolby, G.R. (1980). Query: the geometric mean functional relationship, Biometrics, 36(3), 547-550.
58. Teissier, G. (1948). La relation d'allometrie sa signification statistique et biologique, Biometrics, 4(1), 14-53.
59. Van Huffel, S. and Vanderwalle, J. (1991). The Total Least Squares Prob-lem: Computational Aspects and Analysis, SIAM, Philadelphia.
60. Van Montfort, K. (1989). Estimating in Structural Models with Non-Normal Distributed Variables: Some Alternative Approaches, DSWO Press, Leiden.
61. Van Montfort, K.; Mooijaart, A. and de Leeuw, J. (1987). Regression with errors in variables: estimators based on third order moments, Statist. Neer-landica, 41(4), 223-237.
62. Wald, A. (1940). The fitting of straight lines if both variables are subject to error, Ann. Math. Statistics, 11, 285-300.
63. Wong, M.Y. (1989). Likelihood estimation of a simple linear regression model when both variables have error, Biometrika, 76(1), 141-148.