Variance component estimation in linear inverse ill-posed models

Journal of Geodesy

Volumn 80, Issue 2, 2006, Pages 69-81

  Xu, Peiliang ^a   Shen, Yunzhong ^b   Fukuda, Yoichi ^a   Liu, Yumei ^c  

^a KYOTO UNIVERSITY   (Japan)

^b TONGJI UNIVERSITY   (China)

^c SHENYANG JIANZHU UNIVERSITY   (China)

Author keywords

Bias corrected estimation; Inverse problem; Regularization; Variance component

Indexed keywords

EID: 34548273513     PISSN: 09497714     EISSN: 14321394     Source Type: Journal    
DOI: 10.1007/s00190-006-0032-1     Document Type: Article

References (29)

1. Grafarend EW (1985) Variance-covariance component estimation: theoretical results and geodetic applications. Stat Decis 4: 407-441
2. Graybill FA, Wortha AW (1956) A note on uniformly best unbiased estimators for variance components. J Am Stat Assoc 51: 266-268
3. Graybill FA, Hultquist RA, (1961) Theorems concerning Eisenhart's model II, Ann Math Stat 32: 261-269
4. Hartley HO, Rao JNK (1967) Maximum-likelihood estimation for the mixed analysis of variance model. Biometrika 54: 93-108
5. Helmert FR (1907) Die Ausgleichungsrechnung nach der Methode der kleinsten Quadrate, Zweite Auflage, Teubner, Leipzig
6. Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems, Technometrics, 12: 55-67
7. Horn SD, Horn RA, Duncan DB, (1975) Estimating heteroscedastic variances in linear models, J Am Stat. Ass 70: 380-385
8. Hwang C (2001) Gravity recovery using COSMIC GPS data: application of orbital perturbation theory. J Geod 75: 117-136
9. Koch K-R (1986) Maximum likelihood estimate of variance components. Bull Géod 60: 329-338
10. Koch K-R (1999) Parameter estimation and hypothesis testing in linear models, 2nd edn. Springer, Berlin Heidelberg New York
11. Koch K-R, Kusche J (2002) Regularization of geopotential determination from satellite data by variance components. J Geod 76: 259-268
12. Kubik K (1970) The estimation of the weights of measured quantities within the method of least squares, Bull Géod 44: 21-40
13. Kusche J (2002) Inverse Probleme bei der Gravitationsfeldbestimmung mittels SST-und SGG-Satellitenmissionen, Deutsche Geodätische Kommission, C548, Munich
14. LaMotte LR (1973) On non-negative quadratic unbiased estimation of variance components, J Am Stat. Assoc. 68: 728-730
15. Patterson HD, Thompson R (1971) Recoveryofinter-blockinformation when block sizes are unequal. Biometrika, 58: 545-554
16. Patterson HD, Thompson R (1975) Maximum likelihood estimation of components of variance. In: Proceedings of the 8th Int biometric Conference, pp.197-207
17. Rao CR (1970) Estimation of heteroscedastic variances in linear models. J Am Stat Assoc, 65: 161-171
18. Rao CR (1971a) Estimation of variance and covariance components -MINQUE theory. J Multivariate Anal 1: 257-275
19. Rao CR (1971b) Minimum variance quadratic unbiased estimation of variance components, J Multivariate Anal 1: 445-456
20. Rao CR, Kleffe J (1988) Estimation of variance components and applications. North-Holland, Amsterdam
21. Schwintzer P (1990) Sensitivity analysis in least squares gravity modelling by means of redundancy decomposition of stochastic prior information. Internal Report, Deutsches Geodätisches Forschungsin-stitut
22. Searle SR (1971) Linear models. Wiley, New York
23. Shen YZ, Liu DJ (2002) An unbiased estimate of the variance of unit weight after regularization,(in Chinese with English abstract) Geomatics Inf Sci Wuhan Univ 27:604-606
24. Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems. Wiley, New York
25. Xu PL (1992) Determination of surface gravity anomalies using gradiometric observables, Geophys J Int 110: 321-332
26. Xu PL (1998) Truncated SVD methods for linear discrete ill-posed problems. Geophys. J. Int, 135: 505-514
27. Xu PL, Fukuda Y, Liu YM (2006) Multiple parameter regularization: numerical solutions and applications to the determination of geopotential from precise satellite orbits. J. Geod, DOI 10.1007/s00190-006-0025-0
28. Xu PL, Shimada S (2000) Least squares parameter estimation in multiplicative noise models, Commun Stat B29:83-96
29. Yu ZC (1996) A universal formula of maximum likelihood estimation of variance-covariance components. J Geod 70: 233-240