ABSTRACT. Let R be a commutative noetherian ring, I and J are two ideals of R. Inthis paper we introduce the concept of (I;J)- minimax R- module, and it is shown thatif M is an (I;J)- minimax R- module and t a non-negative integer such that HiI;J(M) is(I;J)- minimax for all i

 Minimax estimation problems with restricted parameter space reached increasing interest within the last two decades Some authors derived minimax and admissible estimators of bounded parameters under squared error loss and scale invariant squared error loss In some truncated estimation problems the most natural estimator to be considered is the truncated version of a classic...

a classical result of neumann characterizes the groups in which each subgroup has finitely many conjugates only as central-by-finite groups. if x is a class of groups, a group g is said to have x-conjugate classes of subgroups if g/coreg(ng(h)) 2 x for each subgroup h of g. here we study groups which have soluble minimax conjugate classes of subgroups, giving a description in terms of g/z(g). w...

We consider the problem of estimating the scale parameter &beta of a rescaled F-distribution when &beta has a lower bounded constraint of the form &beta&gea, under the entropy loss function. An admissible minimax estimator of the scale parameter &beta, which is the pointwise limit of a sequence of Bayes estimators, is given. Also in the class of truncated linear estimators, the admissible estim...

The bounded normal mean problem has important applications in nonparametric function estimation. It is to estimate the mean of a normal distribution whose mean is restricted to a bounded interval. The minimax risk for such a problem is generally unknown. It is shown in Donoho, Liu and MacGibbon(1990) that the linear minimax risk provides a good approximation to the minimax risk. We show in this...

a result of dixon‎, ‎evans and smith shows that if $g$ is a locally (soluble-by-finite) group whose proper subgroups are (finite rank)-by-abelian‎, ‎then $g$ itself has this property‎, ‎i.e‎. ‎the commutator subgroup of $g$ has finite rank‎. ‎it is proved here that if $g$ is a locally (soluble-by-finite) group whose proper subgroups have minimax commutator subgroup‎, ‎then also the commutator s...

let $r=oplus_{nin bbb n_0}r_n$ be a noetherian homogeneous ring with local base ring $(r_0,frak{m}_0)$, $m$ and $n$ two finitely generated graded $r$-modules. let $t$ be the least integer such that $h^t_{r_+}(m,n)$ is not minimax. we prove that $h^j_{frak{m}_0r}(h^t_{r_+}(m,n))$ is artinian for $j=0,1$. also, we show that if ${rm cd}(r_{+},m,n)=2$ and $tin bbb n_0$, then $h^t_{frak{m}_0r}(h^2_{...

The problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including Binomial Negative Binomial discrete Weibull and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function....