A bstvxt
Several theorems on estimation and verification of linear hypotheses in some iiiodels are given. The assumptions are as follows. Let y=Xp + e or (y, Xp, uZV) be a fixed model whei~e y is a vector of n observations, X is a known matrix n x p with rank r ( X ) = r s p < n , where 1' is H. number of coordinates of the unknown parameter vector p. e is a random vector of errom wit.11 covariance matrix a'V, where u2 is unknown scalar parameter, V is a known non-negative definite matrix such that R ( X ) c R( V). Symbol R(A) denotes a vector epace generated by columns of iiiatrix A. The expected value of y is Xp. In this paper four following Zyskind-Martin (ZM) inodels are considered: ZMd, ZMa, ZMc and ZMqd (definitions in sec. 1) when vector y = involves a vector yi of m missing values and a vector yz with (n -m ) observed values.
-4 special transformation of ZM model gives again ZM model (cf. theorem 2.1). Ten properties of actual (ZMa) and complete (ZMc) Zyskind-Martin models with missing values (cf. theorem 2.2) teat fiiiictions F are given in (2.11)) are presented.
The third propriety constitutes a generalization of R. A. Fisher's rule from standard model (y, SP, &I) t o ZM model. Estimation of vector yI (cf. 3.3) of vector fi (cf. th. 3.2) and of scalar 62 (cf. th. 3.4) in actual Znin model and in diagonal quasi-ZM model (ZMqd) are presented. Relation between 91 and fi is given in theorem 3.1. The results of section 2 are illustrated by numerical example in section 4.