Previous |  Up |  Next

Article

Summary:
The parameters of the linear conform transformation between two twodimensional coordinate systems should be estimated from the results of the measurement performed in both systems. The aim of the measurement is to determine the coordinates of $N$ points which are called identical. The maximum-likehood solution of this problem is given.
References:
[1] Anderson T. W.: An introduction to multivariate statistical analysis. J. Wiley, New York (1958). MR 0091588 | Zbl 0083.14601
[2] Bartlett M. S.: Fitting a straight line when both variables are subject to error. Biometrics, 5(1949), 207-212. DOI 10.2307/3001936 | MR 0031687
[3] Bourbaki N.: Elements de Mathématique. Livre II, Algebre. Ch. 3, Hermann, Paris (1958).
[4] Creasy M. A.: Confidence limits for the gradient in the linear functional relationship. J. Roy. Statist. Soc. B 18, (1956), 65-69. MR 0081600 | Zbl 0070.37801
[5] Dorff M., Gurland J.: Estimation of the parameters of a linear functional relation. J. Roy. Statist. Soc. B 23, (1961), 160-170. MR 0124110 | Zbl 0115.14101
[6] Geary R. C.: Determination of linear relations between systematic parts of variables with errors observations the variances of which are unknown. Econometrica 17, (1949), 30-59. DOI 10.2307/1912132 | MR 0028560
[7] Halperin M.: Fitting of straight lines and prediction when both variables are subject to error. J. Amer. Statist. Assoc. 56, (1961), 657-669. DOI 10.1080/01621459.1961.10480651 | MR 0124953 | Zbl 0108.16004
[8] Kubáček L.: Some statistical aspects of the estimation of parameters of a linear conform transformation. Aplikace matematiky 15, (1970), 190-206. MR 0261753
[9] Madansky A.: The fitting of straight lines when both variables are subject to error. Amer. Statist. Ass. Journ, 54, (1959), 173-206. DOI 10.1080/01621459.1959.10501505 | MR 0102875 | Zbl 0088.35804
[10] Rao C. R.: Linear statistical inference and its applications. J. Wiley, New York (1965). MR 0221616 | Zbl 0137.36203
[11] Villegas C.: Maximum likelihood estimation of a linear functional relationship. Ann. Math. Statist. 32, (1961), 1048-1062. DOI 10.1214/aoms/1177704845 | MR 0131920 | Zbl 0104.12902
[12] Villegas C.: On the least squares estimation of a linear relation. Bol. Fac. Ingen. Agrimens. 8, (1963), 47-63; Fac. Ingen. Montevideo. Publ. Inst. Mat. Estadist. 3, (1963), 189-203. MR 0159390 | Zbl 0115.14302
[13] Villegas C.: Confidence region for a linear relation. Ann. Math. Statist. 35, (1964), 780- 788. DOI 10.1214/aoms/1177703577 | MR 0163394 | Zbl 0133.11901
[14] Villegas C.: On the asymptotic efficiency of least squares estimators. Ann. Math. Statist. 37, (1966), 1676-1683. DOI 10.1214/aoms/1177699156 | MR 0203859 | Zbl 0158.18101
[15] Wald A.: The fitting of straight lines if both variables are subject to error. Ann. Math. Statist. 11, (1940), 284-300. DOI 10.1214/aoms/1177731868 | MR 0002739 | Zbl 0023.34402
[16] Wilks S. S.: Mathematical Statistics. J. Wiley, New York (1963). MR 0144404
Partner of
EuDML logo