It is shown that commutativity of two oblique projectors is equivalent with their product idempotency if both projectors are not necessarily Hermitian but orthogonal with respect to the same inner product.
In the paper two approaches to the problem of estimation of transition probabilities are considered. The approach by McCullagh and Nelder [5], based on the independent model and the quasi-likelihood function, is compared with the approach based on the marginal model and the standard likelihood function. The estimates following from these two approaches are illustrated on a simple example which was used by McCullagh and Nelder.
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One of the main problems in plant breeding is the selection of the best genotypes. Most often the selection is made using yield as a main trait of continuous type, and ignoring the other traits of discrete type. Here, a simple procedure is proposed for dealing with the selection problem using not only the yield, but also an auxiliary discrete trait. The method is based on transforming the continuous variable into a discrete one and testing the dependence of variables with the use of contingency tables. The procedure is illustrated by a real unreplicated experiment with winter wheat.
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