Abstract
In this paper, we derive characterization of admissible and linearly sufficient estimators of a vector of linear estimable functions of parameters in a partitioned linear model. Then, we compare this class of estimators with the class of admissible and linearly sufficient estimators of the same vector of linear parametric functions in a reduced linear model. We show that these classes are equal with probability one.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baksalary JK, Kala R (1981) Linear transformations preserving best linear unbiased estimators in a general Gauss–Markoff model. Ann Stat 9: 913–916
Baksalary JK, Kala R (1986) Linear sufficiency with respect to a given vector of parametric functions. J Stat Plan Inf 14: 331–338
Baksalary JK, Markiewicz A (1988) Admissible linear estimators in the general Gauss–Markov model. J Stat Plan Inf 19: 349–359
Baksalary JK, Markiewicz A (1990) Admissible linear estimators of an arbitrary vector of parametric functions in the general Gauss–Markov model. J Stat Plan Inf 26: 161–171
Chu KL, Isotalo J, Puntanen S, Styan GPH (2004) On decomposing the Watson efficiency of ordinary least squares in a partitioned weakly singular linear model. Sankhyā 66: 634–651
Chu KL, Isotalo J, Puntanen S, Styan GPH (2005) Some further results concerning the decomposition of the Watson efficiency in partitioned linear models. Sankhyā 67: 74–89
Drygas H (1983) Sufficiency and completeness in the general Gauss–Markov model. Sankhyā, Ser A 45: 88–98
Gross J, Puntanen S (2000) Estimation under a general partitioned linear model. Linear Algebra Appl 321: 131–144
Müller J (1987) Sufficiency and completeness in the linear model. J Multivar Anal 21: 312–323
Müller J, Rao CR, Sinha BK (1984) Inference on parameters in a linear model: a review of recent results. In: Hinkelmann K (eds) Experimental design, statistical models, and genetic statistics. Dekker, New York, pp 277–295
Rao CR (1976) Estimation of parameters in a linear model. Ann Stat 4: 1023–1037 [Corrigendum (1979), 7, p 696]
Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. Wiley, New York
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Markiewicz, A., Puntanen, S. Admissibility and linear sufficiency in linear model with nuisance parameters. Stat Papers 50, 847–854 (2009). https://doi.org/10.1007/s00362-009-0256-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00362-009-0256-2