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The class of $LR$ translation grammars is introduced. This class is characterized by a possibility to implement a formal translation as an algorithm directed by $LR$ parsing. To perform a translation, the conventional $LR$ parser is extended by a facility to perform output operations within the parsing actions shift and reduce. The definitions of Kernel$\left(R\right)$- and $LR$-translation grammars are presented. The transformations shaking-down and postponing that enable to transform some translation grammars into Kernel...

The regression model X(t),Y(t);t=1,...,n with random explanatory variable X is transformed by prescribing a partition $S_1,...,S_k$ of the given domain S of X-values and specifying$X\left(1\right),...,X\left(n\right)\cap S_i=X_{i1},...,X_{i\alpha \left(i\right)},i=1,...,k.$Through the conditioning$\alpha \left(i\right)=a\left(i\right),i=1,...,k,X_{i1},...,X_{i\alpha \left(i\right)};i=1,...,k=x_{11},...,x_{ka\left(k\right)}$the initial model with i.i.d. pairs (X(t),Y(t)),t=1,...,n, becomes a conditional fixed-design $(x_{11},...,x_{ka\left(k\right)})$ model$Y_{ij},i=1,...,k;j=1,...,a\left(i\right)$where the response variables $Y_{ij}$ are independent and distributed according to the mixed conditional distribution $Q(·,x_{ij})$ of Y given X at the observed value $x_{ij}$.Afterwards, we investigate the case$\left(Q\right)E\left(Y^{\text{'}}\right|x)={\sum }_{i=1}^k{b}_i\left(x\right){\theta }_i{I}_{S_i}\left(x\right),\left(Q\right)D\left(Y\right|x)={\sum }_{i=1}^k{d}_i\left(x\right){\Sigma }_i{I}_{S_i}\left(x\right)$which arises when...

We consider a system of linear response models with random explanatory variables in which the global matrix parameter is subject to arbitrary constraints. A generalized least squares estimate (GLSE) of the global parameter is defined by its property of minimizing some norm of the global residual over an affine manifold, called the support, containing the global parameter range. The crucial relation is the one between the true global parameter value and the so-called global mean square (msq) regression...