ArticleOriginal scientific text
Title
Testing hypotheses in universal models
Authors 1
Affiliations
- Department of Mathematical Analysis and Applied Mathematics Faculty of Science, Palacký University Tomkova 40, 779 00 Olomouc, Czech Republic
Abstract
A linear regression model, when a design matrix has not full column rank and a covariance matrix is singular, is considered. The problem of testing hypotheses on mean value parameters is studied. Conditions when a hypothesis can be tested or when need not be tested are given. Explicit forms of test statistics based on residual sums of squares are presented.
Keywords
universal linear model, unbiased estimator, tests hypotheses
Bibliography
- L. Kubáček, L. Kubáčková and J. Volaufová, Statistical models with linear structures, Veda, Bratislava 1995.
- P.B. Pantnaik, The non-central χ² and F-distribution and their applications, Biometrika 36 (1949), 202-232.
- C.R. Rao, Linear statistical inference and its applications, J. Wiley and Sons, New York-London-Sydney 1965.
- C.R. Rao and S.K. Mitra, Generalized inverse of matrices and its applications, J. Wiley and Sons, New York-London-Sydney-Toronto 1971.
- J. Ryšavý, Higher geodesy, Česká matice technická, Praha 1947 (in Czech).
Pages:
127-149
Main language of publication
English
Received
2006-01-11
Published
2006
DOI: 10.7151/dmps.1078
Exact and natural sciences