On a generalization of the orthogonal regression

summary:The parameters of the linear conform transformation between two twodimensional coordinate systems should be estimated from the results of the measurement performed in both systems. The aim of the measurement is to determine the coordinates of $N$ points which are called identical. The maximum-likehood solution of this problem is given

Multivariate models with constraints confidence regions

summary:In multivariate linear statistical models with normally distributed observation matrix a structure of a covariance matrix plays an important role when confidence regions must be determined. In the paper it is assumed that the covariance matrix is a linear combination of known symmetric and positive semidefinite matrices and unknown parameters (variance components) which are unbiasedly estimable. Then insensitivity regions are found for them which enables us to decide whether plug-in approach can be used for confidence regions

Locally and uniformly best estimators in replicated regression model

summary:The aim of the paper is to estimate a function $\gamma=tr(D\beta\beta')+tr(C\sum)$ (with $d, C$ known matrices) in a regression model $(Y, X\beta,\sum)$ with an unknown parameter $\beta$ and covariance matrix $\sum$. Stochastically independent replications $Y_1,\ldots, Y_m$ of the stochastic vector $Y$ are considered, where the estimators of $X\beta$ and $\sum$ are $\bar{Y}=\frac 1 m \sum ^m _{i=1} Y_i$ and $\hat{\sum}=(m-1)^{-1} \sum^m_{i=1}(Y_i-\bar{Y})(Y_i-\bar{Y})'$, respectively. Locally and uniformly best inbiased estimators of the function $\gamma$, based on $\bar{Y}$ and $\hat{\sum}$, are given