Abstract
The paper provides a projector based approach to the best linear unbiased estimator (BLUE). By revisiting the so called generalized projection operator, introduced in Rao (J R Stat Soc Ser B Stat Methodol 36:442–448, 1974), a number of new formulae for BLUE is established. Furthermore, some attention is paid to the coincidence of the BLUE and the ordinary least squares estimator.
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References
Afriat SN (1957) Orthogonal and oblique projectors and the characteristics of pairs of vector spaces. Proc Camb Phil Soc 53: 800–816
Baksalary OM, Trenkler G (2009) Functions of orthogonal projectors involving the Moore–Penrose inverse. Comput Math Appl (in press)
Ben-Israel A, Greville TNE (2003) Generalized inverses: theory and applications, 2nd edn. Springer, New York
Greville TNE (1974) Solutions of the matrix equation XAX = X, and relations between oblique and orthogonal projectors. SIAM J Appl Math 26: 828–832
Groß J (2004) The general Gauss–Markov model with possibly singular dispersion matrix. Stat Pap 45: 311–336
Kala R (1981) Projectors and linear estimation in general linear model. Comm Stat Theory Methods A 10: 849–873
Piziak R, Odell PL, Hahn R (1999) Constructing projections on sums and intersections. Comput Math Appl 37: 67–74
Pollock DSG (1979) The algebra of econometrics. Wiley, Chichester
Puntanen S, Styan GPH (1989) The equality of the ordinary least squares estimator and the best linear unbiased estimator. Am Stat 43: 153–164
Rao CR (1973) Linear statistical inference and its applications, 2nd edn. Wiley, New York
Rao CR (1974) Projectors, generalized inverses and the BLUE’s. J R Stat Soc Ser B Stat Methodol 36: 442–448
Rao CR (1978) Choice of best linear estimators in the Gauss–Markoff model with a singular dispersion matrix. Comm Stat Theory Methods A 7: 1199–1208
Rao CR (1983) A unified approach to inference from linear models. In: Pukkila T, Puntanen S (eds) Proceedings of the first international tampere seminar on linear statistical models and their applications. University of Tampere, Tampere, pp 9–36
Rao CR, Yanai H (1979) General definition and decomposition of projectors and some applications to statistical problems. J Stat Plann Infer 3: 1–17
Tian Y, Styan GPH (2001) Rank equalities for idempotent and involutory matrices. Linear Algebra Appl 335: 101–117
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Baksalary, O.M., Trenkler, G. A projector oriented approach to the best linear unbiased estimator. Stat Papers 50, 721–733 (2009). https://doi.org/10.1007/s00362-009-0252-6
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DOI: https://doi.org/10.1007/s00362-009-0252-6
Keywords
- General Gauss–Markov model
- Ordinary least squares estimator
- Oblique projector
- Generalized projection operator