Necessary Condition For Admissibility Research Articles

Prior Consistent Statement Witness Rehabilitation, Fed.R.Evid. 801(d)(1)(B), and Prior Identification Statements, Fed.R.Evid. 801(d)(1)(C)

Prior Consistent Statement Witness Rehabilitation, Fed.R.Evid. 801(d)(1)(B), and Prior Identification Statements, Fed.R.Evid. 801(d)(1)(C)

Admissibility of groups over function fields of p-adic curves

Let K be a field and G a finite group. The question of ‘admissibility’ of G over K was originally posed by Schacher, who gave partial results in the case K=Q. In this paper, we give necessary conditions for admissibility of a finite group G over function fields of curves over complete discretely valued fields. Using this criterion, we give an example of a finite group which is not admissible over Qp(t). We also prove a certain Hasse principle for division algebras over such fields.

Necessary conditions for admissibility of matrix linear estimators in a multivariate linear model

This article provides necessary conditions for the admissibility of matrix linear estimators of an estimable parameter matrix linear function under two kinds of quadratic matrix loss functions in a multivariate linear model following a family of matrix normal distributions, where the covariance matrix associated is completely unknown. Further it is demonstrated that if a more concrete condition supplied for one of the subdivided conditions is satisfied, then the special condition concerning the Stein problem is necessary for the admissibility of the kind of estimators under each of the loss functions.

Admissible Linear Estimators with Respect to Inequality Constraints

Admissibility of linear estimators is characterized in linear models E(Y)=Xβ, D(Y)=V, with an unknown multidimensional parameter (β, V) varying in the Cartesian product C × ν, where C is a subset of space and ν is a given set of non negative definite symmetric matrices. The relation between admissibility of inhomogeneous and homogeneous linear estimators is discussed, and some sufficient and necessary conditions for admissibility of an inhomogeneous linear estimator are given.

A smooth version of the step-up procedure for multiple tests of hypotheses

Cohen and Sackrowitz [2005. Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure. Ann. Statist. 33, 145–158; 2007. More on the inadmissibility of step-up. J. Multivariate Anal. 97, 481–492] have demonstrated that the popular step-up (SU) multiple testing procedure is inadmissible under a wide variety of conditions. All conditions, however, did assume a permutation invariant (symmetric) model. In this paper we find a necessary condition for admissibility of multiple testing procedures in the asymmetric case. Once again SU does not satisfy the condition and is inadmissible. Since SU has a somewhat less favorable practical property and a less favorable theoretical property, we offer a smooth version of SU which retains the favorable practical properties and avoids some of the less favorable ones. In terms of performance the smooth version and nonsmooth version seem to be comparable at least in low dimensions.

Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure

The problem of multiple endpoint testing for k endpoints is treated as a 2 k finite action problem. The loss function chosen is a vector loss function consisting of two components. The two components lead to a vector risk. One component of the vector risk is the false rejection rate (FRR), that is, the expected number of false rejections. The other component is the false acceptance rate (FAR), that is, the expected number of acceptances for which the corresponding null hypothesis is false. This loss function is more stringent than the positive linear combination loss function of Lehmann [Ann. Math. Statist. 28 (1957) 1-25] and Cohen and Sackrowitz [Ann. Statist. (2005) 33 126-144] in the sense that the class of admissible rules is larger for this vector risk formulation than for the linear combination risk function. In other words, fewer procedures are inadmissible for the vector risk formulation. The statistical model assumed is that the vector of variables Z is multivariate normal with mean vector μ and known intraclass covariance matrix E. The endpoint hypotheses are H i : μ i = 0 vs K i : μ i > 0, ι = 1,..., k. A characterization of all symmetric Bayes procedures and their limits is obtained. The characterization leads to a complete class theorem. The complete class theorem is used to provide a useful necessary condition for admissibility of a procedure. The main result is that the step-up multiple endpoint procedure is shown to be inadmissible.

Admissible linear estimators in linear models with respect to inequality constraints

Admissibility of linear estimators is characterized in linear models E( Y)= Xβ,D( Y)= V, with an unknown multidimensional parameter ( β, V) varying in the Cartesian product C× V , where C is a halfspace and V is a given set of nonnegative definite symmetric matrices. The relation between admissibility of inhomogeneous and homogeneous linear estimators is discussed, and some sufficient and necessary conditions for admissibility of an inhomogeneous linear estimator are given. Some results were extended to the case where C is a given polyhedral convex cone.

Wavelets on the 2-Sphere: A Group-Theoretical Approach

We present a purely group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of general coherent states associated to square integrable group representations. The parameter space X of our CWT is the product of SO(3) for motions and R+* for dilations on S2, which are embedded into the Lorentz group SO0(3, 1) via the Iwasawa decomposition, so that X ≃ SO0(3, 1) M Y S O L N, where N ≃ C. We select an appropriate unitary representation of SO0(3, 1) acting in the space L2(S2, d μ) of finite energy signals on S2. This representation is square integrable over X; thus it yields immediately the wavelets on S2 and the associated CWT. We find a necessary condition for the admissibility of a wavelet, in the form of a zero mean condition. Finally, the Euclidean limit of this CWT on S2 is obtained by redoing the construction on a sphere of radius R and performing a group contraction for R → ∞. Then the parameter space goes into the similitude group of R2 and one recovers exactly the CWT on the plane, including the usual zero mean necessary condition for admissibility.

Admissibility of inhomogeneous linear estimaiors in linear models with respect to incomplete ellipsoidal restrictions

The admissibility of an inhomogeneous linear estimator is characterized in the linear models may be singular, (θ.o2) varies in , such restrictions are called incomplete ellipsoidal restrictions The relation between admissible inhomogeneous linear estimators and homogeneous linear estimators is discussed, and a sufficient and necessary condition for admissibility of an inhomogeneous linear estimator is given.

Admissibility of experimental designs in linear regression with constant term

Karlin and Studden (1966a) proved that each support point of an admissible approximate experimental design in a linear regression setup maximizes a nonnegative quadratic form in the vector of regression functions. As noted by them, this result becomes trivial whenever the regression function contains a constant term. The main purpose of the present paper is to establish nontrivial necessary conditions for admissibility in these situations. By a characterization of comparability of two information matrices at a time it is proved that the information matrix of an admissible design maximizes a linear function under certain linear restrictions. This implies that it solves an unconstrained nonconstant linear optimization problem, too, yielding nontrivial conditions on the support points similar to those of the Karlin and Studden result. Exemplary, we consider multiple polynomial regression. For the linear setup we give all ‘invariant’ and admissible designs. In the quadratic case (under the additional assumption of convexity of the experimental region K ) the support points of an ‘invariant’ and admissible design are found to be either zero or special boundary points of K .

Admissibility of a test procedure in a conditionally specified random model

Admissibility of a test procedure is a desirable property though not a compelling one; while lack of it often results in discarding a given test procedure. In this paper we have proved necessary conditions for admissibility for a test procedure.

A Sharp Necessary Condition for Admissibility of Sequential Tests-- Necessary and Sufficient Conditions for Admissibility of SPRT'S

Consider the problem of sequentially testing the hypothesis that the mean of a normal distribution of known variance is less than or equal to a given value versus the alternative that it is greater than the given value. Impose the linear combination loss function under which the risk becomes a constant $c$, times the expected sample size, plus the probability of error. It is known that all admissible tests must be monotone--that is, they stop and accept if $S_n$, the sample sum at stage $n$, satisfies $S_n \leq a_n$; stop and reject if $S_n \geq b_n$. In this paper we show that any admissible test must in addition satisfy $b_n - a_n \leq 2\bar{b}(c)$. The bound $2\bar{b}(c)$ is sharp in the sense that the test with stopping bounds $a_n \equiv -\bar{b}(c), b_n \equiv \bar{b}(c)$ is admissible. As a consequence of the above necessary condition for admissibility of a sequential test, it is possible to characterize all sequential probability ratio tests (SPRT's) regarding admissibility. In other words necessary and sufficient conditions for the admissibility of an SPRT are given. Furthermore, an explicit numerical upper bound for $\bar{b}(c)$ is provided.

A Necessary Condition for Admissibility

The main theorem of this note is required in a paper of Brown. Briefly, the theorem shows that procedures which can be improved on in a neighborhood of infinity are either inadmissible or are generalized Bayes for a (possibly improper) prior whose rate of growth at infinity is of an appropriate order. This theorem is applied here to show that the risk of the usual estimator of a two dimensional normal mean, $\theta$, cannot be improved on near $\infty$ at order $\|\theta\|^{-2}$.