# A characterization of admissible linear estimators of fixed by Synowka-Bejenka E., Zontek S.

By Synowka-Bejenka E., Zontek S.

Within the paper the matter of simultaneous linear estimation of fastened and random results within the combined linear version is taken into account. an important and adequate stipulations for a linear estimator of a linear functionality of mounted and random results in balanced nested and crossed type versions to be admissible are given.

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Additional info for A characterization of admissible linear estimators of fixed and random effects in linear models

Example text

Let BZ9, a,,(x3) = t l b E Ku(x3) = ub E Kv(X3) PZ,(XJ) where ub and ub are given vectors. 1, n*(C)belongs to the game surface through x ' ; hence it follows from the definitions of a game surface and of an optimal path that the game surface through x z is C ( C ) . 4. Paths IIg(C') and nim(C"). 2 that ( I ) no point of I [\$(C’)is a B-point relative to C(C); and ( 1 1 ) no point of I I ~ ~ z ( C is”an ) A-point relative to C(C). 26) 11 ;

5 JOINING OF PATHS Let ni3be a path emanating from xi,generated by ( r p , rE), and ending at x3; and let xis be a path emanating from xi,generated by (Ep, i E ) and , ending at xs. 16) We shall call this assumption an additivity property of the cost. 1. No point of a path rIp(C') which emanates from x i is an A-point relative to the game surface through x i . iOf course, superscript f means that the terminal point of the path belongs to 0. (C), and IIFL (C). 18 11 SOME GEOMETRIC ASPECTS OF QUANTITATIVE GAMES \ \ Frci.

Transfer time T. 2) For given strategies p and e , Eq. 3) x = x ( T ) , T E [0, T ~ ) is , a solution of Eq. 4) 10, T s ) There may be more than one solution of Eq. 3) that satisfies x(0) = x*. 3) satisfying x(0) = xi on an interval AT containing T = 0. 3) that emanates from xi. Furthermore, a solution that is unique in a neighborhood of the initial time may bifurcate at some later time, if the trajectory reaches a point of discontinuity of p or e , or of both. Also, there may be no solution of Eq.