Let Xn,1 = Xn,2 = ... = Xn,n be the ordered variables corresponding to a random sample of size n with respect to a family of probability measures {P[theta]:[theta] [set membership, variant] [Theta]} where [Theta] is an open subset of the real line. In many practical situations the Xn,i are the...

A new proof of admissibility of tests in MANOVA is given using Stein's theorem [7]. The convexity condition of Stein's theorem is proved directly by means of majorization rather than by the supporting hyperplane approach. This makes the geometrical meaning of the admissibility result clearer.

In this paper, the authors derived asymptotic expressions for the null distributions of the likelihood ratio test statistics for multiple independence and multiple homogeneity of the covariance matrices when the underlying distributions are complex multivariate normal. Also, asymptotic...

Let X [reverse not equivalent] (X1, ..., Xt) have a multinomial distribution based on N trials with unknown vector of cell probabilities p [reverse not equivalent] (p1, ..., pt). This paper derives admissibility and complete class results for the problem of simultaneously estimating p under...

Let be the Schwartz space of rapidly decreasing real functions. The dual space * consists of the tempered distributions and the relation [subset of] L2() [subset of] * holds. Let [gamma] be the Gaussian white noise on * with the characteristic functional , [xi] [set membership, variant] , where...

Let {X(t): t [set membership, variant] [a, b]} be a Gaussian process with mean [mu] [set membership, variant] L2[a, b] and continuous covariance K(s, t). When estimating [mu] under the loss [integral operator]ab ([mu](t)-[mu](t))2 dt the natural estimator X is admissible if K is unknown. If K is...

We establish contiguity of families of probability measures indexed by T, as T -- [infinity], for classes of continuous time stochastic processes which are either stationary diffusions or Gaussian processes with known covariance. In most cases, and in all the examples we consider in Section 4,...

Let X1,...,Xn be i.i.d. random vectors in Rm, let [theta][epsilon]Rm be an unknown location parameter, and assume that the restriction of the distribution of X1-[theta] to a sphere of radius d belongs to a specified neighborhood 1 of distributions spherically symmetric about 0. Under regularity...

In this paper a diffusion approximation to the two-type Galton-Watson branching processes with mean matrix close to the identity is given in the form of Berstein stochastic differentials. An associated diffusion equation is found using an extension of the one-dimensional Bernstein technique....

Certain results on large deviation probabilities for linear and m-dependent processes are considered here.