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1.
In this article, mixture distributions and weighted likelihoods are derived within an information-theoretic framework and shown to be closely related. This surprising relationship obtains in spite of the arithmetic form of the former and the geometric form of the latter. Mixture distributions are shown to be optima that minimize the entropy loss under certain constraints. The same framework implies the weighted likelihood when the distributions in the mixture are unknown and information from independent samples generated by them have to be used instead. Thus the likelihood weights trade bias for precision and yield inferential procedures such as estimates that can be more reliable than their classical counterparts.  相似文献   

2.
Copositive approximation of periodic functions   总被引:1,自引:0,他引:1  
Let f be a real continuous 2π-periodic function changing its sign in the fixed distinct points y i Y:= {y i } i∈ℤ such that for x ∈ [y i , y i−1], f(x) ≧ 0 if i is odd and f(x) ≦ 0 if i is even. Then for each nN(Y) we construct a trigonometric polynomial P n of order ≦ n, changing its sign at the same points y i Y as f, and
where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s, ω 3(f, t) is the third modulus of smoothness of f and ∥ · ∥ is the max-norm. This work was done while the first author was visiting CPT-CNRS, Luminy, France, in June 2006.  相似文献   

3.
In this paper we consider the problem of a deflected mode of a shallow shell. The stress function and the normal component of the displacement of the median surface of the shell are unknown functions. We propose a mixed variational statement of the problem, where the second derivatives of the stress function and the normal component of the displacement of the median surface are additional unknowns. This enables us to construct the finite element approximation of the initial problem. We prove the existence of a unique solution of the approximating problem and estimate the rate of convergence of the discrete solution.  相似文献   

4.
Some remarks on trigonometric sums   总被引:1,自引:1,他引:0  
Let
where m 1 < m 2 < … < m t ≦ , δ x → 0, p runs over the primes p ≧ ≦ 1, |X p | ≦ 1. It is assumed that m v , , X p may depend on x. Assume that . It is proved that
for almost all irrational α, π(x) = number of primes up to x. Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA T46993.  相似文献   

5.
There is very little literature concerning modeling the correlation between paired angular observations. We propose a bivariate model with von Mises marginal distributions. An algorithm for generating bivariate angles from this von Mises distribution is given. Maximum likelihood estimation is then addressed. We also develop a likelihood ratio test for independence in paired circular data. Application of the procedures to paired wind directions is illustrated. Employing simulation, using the proposed model, we compare the power of the likelihood ratio test with six existing tests of independence.  相似文献   

6.
This note is devoted to study the preservation of connectedness under the basic operators in generalized topological spaces. Some characterizations of generalized connectedness are given. As an application, we generalize some results in topological spaces. Supported in part by the NSFC (No. 10571151, 10671173).  相似文献   

7.
We study the operad of finite labeled tournaments. We describe the structure of suboperads of this operad generated by simple tournaments. We prove that a suboperad generated by a tournament with two vertices (i.e., the operad of finite linearly ordered sets) is isomorphic to the operad of symmetric groups, and a suboperad generated by a simple tournament with more that two vertices is isomorphic to the quotient operad of the free operad with respect to a certain congruence. We obtain this congruence explicitly.  相似文献   

8.
Suppose a convex body wants to pass through a circular hole in a wall. Does its ability to do so depend on the thickness of the wall? In fact in most cases it does, and in this paper we present a sufficient criterion for a polytope to allow an affirmative answer to the question.  相似文献   

9.
In this paper we determine all collapsing transformation monoids that contain at least one unary constant operation and whose nonconstant operations are permutations. Furthermore, we find an infinite family of transformation monoids that consist of at least three unary constant operations and some permutations for which the corresponding monoidal intervals are 2-element chains. This research is supported by Hungarian National Foundation for Scientific Research grant nos. T 37877 and K 60148.  相似文献   

10.
We prove the existence of non-smooth solutions to fully non-linear elliptic equations. Received: June 2006, Accepted: January 2007  相似文献   

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