Fiducial estimation of parameters in normal statistical models (Q1821456)

In this paper, confidence estimation of the parameters of linear models has been done under the assumptions that (i) the covariance of observations belongs to symmetrical matrix algebra \({\mathcal R}\), (ii) the vector of means belongs to a subspace \({\mathcal F}\) of the sample space \({\mathcal E}\) that is invariant with respect to all the matrices in \({\mathcal R}.\) A family of Gaussian n-dimensional distributions has been considered. Fiducial distribution of the parameters of the normal model is derived. Also, the fiducial estimates of parameters of the simplest regression model, the variance components for complete two factor design, three factor Latin square designs and incomplete balanced block designs are obtained. It is a highly mathematical paper.