Two new results of linear minimum variance estimation

In the linear minimum variance (LMV) estimation problems, we first consider the linear transformation of data which is needed to compress dimension of observation data without loss of performance. A necessary and sufficient condition is given. Furthermore, an explicit solution of a lossless linear minimal dimension compression in the sense of minimum variance is presented. Secondly, when there exists linear equality constraint for the linear combination coefficients of observation data in the LMV estimation, an optimal estimate of parameter under the aforementioned constraint is given in the sense of minimum variance. Both the developments of LUMV estimation described in this paper do not require any model for data and parameter.