asymptotic theory of simultaneous estimation of poisson means abstract the poisson distribution is often a good approximation to the underlying sampling distribution and is central to the study of categorical data in this paper we propose a new unified approach to an investigation of point properties of simultaneous estimations of poisson population parameters with general quadratic loss functions the main accent is made on the shrinkage estimation we build a series of estimators that could be represented as a convex combination of linear statistics such as maximum likelihood estimator benchmark estimator restricted estimator composite estimator preliminary test estimator shrinkage estimator positive rule shrinkage estimator james stein type estimator all these estimators are represented in a general integrated estimation approach which allows us to unify our investigation and order them with respect to the risk a simulation study with numerical and graphical results is conducted to illustrate the properties of the investigated estimators

a convergent series expansion for hyperbolic systems of conservation laws the discontinuities piecewise analytic initial value problem for a wide class of conservation laws is considered which includes the full three dimensional euler equations the initial interaction at an arbitrary curved surface is resolved in time by a convergent series among other features the solution exhibits shock contact and expansion waves as well as sound waves propagating on characteristic surfaces the expansion waves correspond to he one dimensional rarefactions but have a more complicated structure the sound waves are generated in place of zero strength shocks and they are caused by mismatches in derivatives

optimal critical values of pre tests when estimating the regression error variance analytical findings under a general loss structure this paper re visits the problem of estimating the regression error variance in a linear multiple regression model after preliminary hypothesis tests for either linear restrictions on the coefficients or homogeneity of variances there is an extensive literature that discusses these problems particularly in terms of the sampling properties of the pre test estimators using various loss functions as the basis for risk analysis in this paper a unified framework for analysing the risk properties of these estimators is developed under a general class of loss structures that incorporates virtually all first order differentiable losses particular consideration is given to the choice of critical values for the pre tests analytical results indicate that an level substantially higher than those normally used may be appropriate for optimal risk properties under a wide range of loss functions the paper also generalizes some known analytical results in the pre test literature and proves other results only previously shown numerically

analytic regularity of uniformly stable shock fronts with analytic data on considere un systeme hyperbolique de lois de conservation u t j 1 f j u x j o ou x x 1 x n appartient a un sous ensemble ouvert de r n t o et u t u 1 u m f u f 1 u f n u est une application c d un sous ensemble ouvert g de r m dans r m n

improving upon standard estimators in discrete exponential families with applications to poisson and negative binomial cases assume that xi xp are independent random observations having discrete exponential densities p1 0 ti x rj 1 i 1 p respectively a general technique of improving upon the uniform minimum variance unbiased estimator umvue of o1 op is developed under possibly weighted squared error loss functions it is shown that improved estimators can be constructed by solving a difference inequality typical difference inequalities of a fairly general type are presented and solved when specialized to poisson and negative binomial cases broad classes of estimators are given that dominate the umvue these results unify many known results in this rapidly diverging field and some of them are new especially those related to negative binomial distributions improved estimators are also obtained for the problems in which some of the observations are from poisson families and some from negative binomial families for sum of squared errors loss estimators which dominate the umvue in the discrete exponential families are also given explicitly

sufficient conditions for local existence via glimm s scheme for large bv data abstract using glimm s scheme sufficient conditions are derived for the global existence of a weak solution to a strictly hyperbolic genuinely nonlinear system of partial differential equations in one space dimension when the initial data is a small bv perturbation of a solvable riemann problem by using the finite propagation speed of the system this yields a local existence theorem for arbitrary bv initial data that satisfies the above mentioned conditions at all large jumps the case of linearly degenerate fields is also treated and the results are applied to the p system and to the 1 d nonisentropic gas law euler equations

simultaneous prediction of independent poisson observables simultaneous predictive distributions for independent poisson observables are investigated a class of improper prior distributions for poisson means is introduced the bayesian predictive distributions based on priors from the introduced class are shown to be admissible under the kullback leibler loss a bayesian predictive distribution based on a prior in this class dominates the bayesian predictive distribution based on the jeffreys prior

a complete class theorem for statistical problems with finite sample spaces this paper contains a complete class theorem theorem 3 2 which applies to most statistical estimation problems having a finite sample space this theorem also applies to many other statistical problems with finite sample spaces the description of this complete class involves a stepwise algorithm at each step of the process it is necessary to construct the bayes procedures in a suitably modified version of the original problem the complete class is a minimal complete class if the loss function is strictly convex some examples are given to illustrate the application of this complete class theorem among these is a new result concerning the estimation of the parameters of a multinomial distribution under a normalized quadratic loss function see example 4 5

x robustness of interval circulant matrices in fuzzy algebra abstract fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by and where a b max a b a b min a b a matrix is x robust if its eigenspace is achieved starting at each vector from a given interval vector x the possible and universal x robustness of interval matrices over fuzzy algebra are defined polynomial algorithms for checking the possible and universal x robustness of interval circulant matrices are described

orbits in max min algebra abstract properties of orbits in max min algebra are described mainly the properties of periodic orbits an o n 3 algorithm computing the period of a periodic orbit is presented as a consequence an o n 3 log n algorithm computing the period of arbitrary orbit is obtained as the pre periodic part of the orbit has length at most n 1 2 1

systems of linear interval equations this paper presents theory and methods for computing the exact bounds on the solution of a system of n linear equations in n variables whose coefficients and right hand sides vary in some real intervals finite and iterative methods are given based on results from linear complementarity theory also regularity conditions regularity testing and computing the exact inverse of an interval matrix are dealt with

robustness of fuzzy interval circulant hankel matrices abstract fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by and where a b max a b a b min a b a square matrix is circulant hankel if the input values in every row are the same as the values in the previous row but they are cyclically shifted by one position to the left the robustness and the x robustness of fuzzy circulant hankel matrices are studied we define the possible and universal robustness and x robustness of interval matrices the necessary and sufficient conditions for the possible and universal robustness and x robustness of interval circulant hankel matrices are given

double shock fronts for hyperbolic systems of conservation laws in multidimensional space the existence of a unique double shock front for hyperbolic systems of conservation laws in several space variables is established extending an earlier result of metivier an example of a double shock wave arising from physical applications is given the purpose of this paper is to show the existence of a unique double shock front for hyperbolic systems of conservation laws in several space variables describing physical phenomena unlike the one dimensional case it is only recently that majda 7 using microlocal analysis established the existence of a unique stable shock front for hyperbolic systems for double shock fronts the only known result is due to metivier 8 9 where 2 x 2 systems of conservation laws in two dimensional space are considered in this paper the existence of a double shock front for hyperbolic systems of conservation laws in several space variables is established when restricted to 2 x 2 systems in two dimensional space our result is similar to that of metivier but our approach is somewhat different and perhaps simpler the notation and the basic assumptions are given in 1 the free boundary problem is transformed in 2 into one with fixed boundaries the linearized problem is considered in 3 and the nonlinear one is studied in 4 using the iteration method finally in 5 an application to isentropic gas in two dimensional space is given let g be an open subset of rn with a smooth boundary ag and let x xi xn be the generic point of g for each n tuple a a n of nonnegative integers we write n n d f dj dj 0 x la zaj j l j l received by the editors january 17 1987 and in revised form april 15 1988 1980 mathematics subject classification 1985 revision primary 35l65 35l50 secondary 76l05 work supported by nserc canada 1989 american mathematical society 0002 9947 89 1 00 25 per page

eigenvectors in bottleneck algebra abstract let b be a nonempty linearly ordered set without maximum and minimum and max min a vector x is said to be an eigenvector of a square matrix a if a x x the aim of the present paper is to characterize the eigenvectors by means of the associated graph of the matrix and to give bounds for the set of all eigenvectors we define the lower and the upper basic eigenvectors and derive efficient methods for computing them

simultaneous estimation of poisson means under entropy loss on caracterise des estimateurs lineaires admissibles de parametres de poisson multiples sous une perte d entropie on donne les estimateurs dominant certains des estimateurs standards

the robustness of interval fuzzy matrices abstract robust interval matrices over max min algebra fuzzy matrices are studied and equivalent conditions for interval fuzzy matrices to be robust are presented polynomial algorithms for checking the necessary and sufficient conditions for robustness of interval fuzzy matrices are introduced in addition more efficient algorithms for verifying the robustness of interval circulant matrices are described

estimation of a covariance matrix under stein s loss on decrit la technique generale de stein pour ameliorer l estimateur sans biais invariant le meilleur et l estimateur minimax de la matrice de covariance normale

on the powers of matrices in bottleneck fuzzy algebra abstract powers of square matrices under the operations max and min are studied we show that the powers of a given matrix stabilize if and only if its orbits stabilize for each starting vector and prove a necessary and sufficient condition for this property using the associated graphs of the matrix applications of the obtained results to several special classes of matrices including circulants are given

propagation of singularities hamilton jacobi equations and numerical applications we consider applications of hamilton jacobi equations for which the initial data is only assumed to be in l such problems arise for example when one attempts to describe several characteristic singularities of the compressible euler equations such as contact and acoustic surfaces propagating from the same discontinuous initial front these surfaces represent the level sets of solutions to a hamilton jacobi equation which belongs to a special class for such hamilton jacobi equations we prove the existence and regularity of solutions for any positive time and convergence to initial data along rays of geometrical optics at any point where the gradient of the initial data exists