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1.
We introduce and study the concept of similarity between soft sets, which is an extension of the equality for soft set theory. We also introduce the concepts of conjunction parameter (αβ) and disjunction parameter (αβ) of ordered pair parameter 〈α,β〉 for soft set theory, and we investigate modified operations of soft set theory in terms of ordered parameters.  相似文献   

2.
当研究目标的实际测量具有不可修复的破坏性或耗资巨大时,有效的抽样设计将是一项重要的研究课题.在统计推断方面,排序集抽样(RSS)被视为一种比简单随机抽样(SRS)更为有效的收集数据的方式.动态极值RSS (MERSS)是一种修正的RSS.文章在SRS和MERSS下研究了Logistic分布中参数的极大似然估计(MLEs).在这两种抽样下证明了该分布中位置参数和刻度参数的MLEs的存在性和唯一性,并计算了所含参数的Fisher信息量和Fisher信息矩阵.比较了这两种抽样下对应估计的渐近效率.数值结果表明MERSS下的MLEs一致优于SRS下的MLEs.  相似文献   

3.
In this paper, we present new results relating the numerical range of a matrix A with the generalized Levinger transformation L(A,α,β)=αHA+βSA, where HA and SA, are, respectively the Hermitian and skew-Hermitian parts of A. Using these results, we then derive expressions for eigenvalues and eigenvectors of the perturbed matrix A+L(E,α,β), for a fixed matrix E and α, β are real parameters.  相似文献   

4.
Let G be the abelian group generated by α and β. We write Σ(G; α, β) for the set of groupoid identities that are satisfied in the group ring ${\mathbb{Z}[G]}$ when the binary operation is α xβ y. When the constant e, representing the zero of ${\mathbb{Z}}$ , is added to the type, we write Σ e (G; α, β) for the corresponding set of identities. In this paper, we assume that G is an infinite cyclic group with generator δ. We write Σ a,b for Σ(G; δ a , δ b ) and ${\Sigma^{e}_{a,b}}$ for Σ e (G; δ a , δ b ). For each pair of relatively prime integers a and b, we determine whether Σ a,b is finitely based and whether ${\Sigma^{e}_ {a,b}}$ is finitely based. One of our results implies that Σ e (G; α, β) is finitely based whenever G is finite.  相似文献   

5.
On the geometry of generalized Gaussian distributions   总被引:1,自引:0,他引:1  
In this paper we consider the space of those probability distributions which maximize the q-Rényi entropy. These distributions have the same parameter space for every q, and in the q=1 case these are the normal distributions. Some methods to endow this parameter space with a Riemannian metric is presented: the second derivative of the q-Rényi entropy, the Tsallis entropy, and the relative entropy give rise to a Riemannian metric, the Fisher information matrix is a natural Riemannian metric, and there are some geometrically motivated metrics which were studied by Siegel, Calvo and Oller, Lovri?, Min-Oo and Ruh. These metrics are different; therefore, our differential geometrical calculations are based on a new metric with parameters, which covers all the above-mentioned metrics for special values of the parameters, among others. We also compute the geometrical properties of this metric, the equation of the geodesic line with some special solutions, the Riemann and Ricci curvature tensors, and the scalar curvature. Using the correspondence between the volume of the geodesic ball and the scalar curvature we show how the parameter q modulates the statistical distinguishability of close points. We show that some frequently used metrics in quantum information geometry can be easily recovered from classical metrics.  相似文献   

6.
The restricted EM algorithm under inequality restrictions on the parameters   总被引:1,自引:0,他引:1  
One of the most powerful algorithms for maximum likelihood estimation for many incomplete-data problems is the EM algorithm. The restricted EM algorithm for maximum likelihood estimation under linear restrictions on the parameters has been handled by Kim and Taylor (J. Amer. Statist. Assoc. 430 (1995) 708-716). This paper proposes an EM algorithm for maximum likelihood estimation under inequality restrictions A0β?0, where β is the parameter vector in a linear model W=+ε and ε is an error variable distributed normally with mean zero and a known or unknown variance matrix Σ>0. Some convergence properties of the EM sequence are discussed. Furthermore, we consider the consistency of the restricted EM estimator and a related testing problem.  相似文献   

7.
This paper considers the Maximum Likelihood (ML) estimation of the five parameters of a linear structural relationship y = α + βx when α is known. The parameters are β, the two variances of observation errors on x and y, the mean and variance of x. When the ML estimates of the parameters cannot be obtained by solving a simple simultaneous system of five equations, they are found by maximizing the likelihood function directly. Some asymptotic properties of the estimates are also obtained.  相似文献   

8.
For a stable autoregressive process of order p with unknown vector parameter θ, it is shown that under a sequential sampling scheme with the stopping time defined by the trace of the observed Fisher information matrix, the least-squares estimator of θ is asymptotically normally distributed uniformly in θ belonging to any compact set in the parameter region.  相似文献   

9.
We describe a family {Ψ α,β } of polygon exchange transformations parameterized by points (α,β) in the square $[0, {\frac{1}{2}}]\times[0, {\frac{1}{2}}]$ . Whenever α and β are irrational, Ψ α,β has periodic orbits of arbitrarily large period. We show that for almost all parameters, the polygon exchange map has the property that almost every point is periodic. However, there is a dense set of irrational parameters for which this fails. By choosing parameters carefully, the measure of non-periodic points can be made arbitrarily close to full measure. These results are powered by a notion of renormalization which holds in a more general setting. Namely, we consider a renormalization of tilings arising from the Corner Percolation Model.  相似文献   

10.
Let α and β be automorphisms on a ring R and δ:RR an (α,β)-derivation. It is shown that if F is a right Gabriel filter on R then F is δ-invariant if it is both α and β-invariant. A consequence of this result is that every hereditary torsion theory on the category of right R-modules is differential in the sense of Bland (2006). This answers in the affirmative a question posed by Vaš (2007) and strengthens a result due to Golan (1981) on the extendability of a derivation map from a module to its module of quotients at a hereditary torsion theory.  相似文献   

11.
The permanent of a matrix is a linear combination of determinants of block diagonal matrices which are simple functions of the original matrix. To prove this, we first show a more general identity involving α-permanents: for arbitrary complex numbers α and β, we show that the α-permanent of any matrix can be expressed as a linear combination of β-permanents of related matrices. Some other identities for the α-permanent of sums and products of matrices are shown, as well as a relationship between the α-permanent and general immanants. We conclude with some discussion and a conjecture for the computational complexity of the α-permanent, and provide some numerical illustrations.  相似文献   

12.
《Journal of Complexity》2003,19(3):301-320
It is known from the analysis by Sloan and Woźniakowski that under appropriate conditions on the weights, the optimal rate of convergence for multivariate integration in weighted Korobov spaces is O(nα/2+δ) where α>1 is some parameter of the spaces, δ is an arbitrary positive number, and the implied constant in the big O notation depends only on δ, and is independent on the number of variables. Similarly, the optimal rate for weighted Sobolev spaces is O(n−1+δ). However, their work did not show how to construct rules achieving these rates of convergence. The existing theory of the component-by-component constructions developed by Sloan, Kuo and Joe for the Sobolev case yields the rules achieving O(n−1/2) error bounds. Here we present theorems which show that those lattice rules constructed by the component-by-component algorithms in fact achieve the optimal rate of convergence under appropriate conditions on the weights.  相似文献   

13.
In this paper, we are dealing with q analogue of Durrmeyer type modified the Baskakov operators with two parameter α and β, which introduces a new sequence of positive linear q-integral operators. We show that this sequence is an approximation process in the polynomial weighted space of continuous function defined on the interval [0, ∞). We study moments, weighted approximation properties, the rate of convergence using a weighted modulus of smoothness, asymptotic formula and better error estimation for these operators.  相似文献   

14.
For every value of the parameters α,β>−1 we find a matrix valued weight whose orthogonal polynomials satisfy an explicit differential equation of Jacobi type.  相似文献   

15.
Let α and β be polygons with the same area. A Dudeney dissection of α to β is a partition of α into parts which can be reassembled to produce β as follows: Hinge the parts of α like a string along the perimeter of α, then fix one of the parts to from β with the perimeter of α going into its interior and with its perimeter consisting of the dissection lines in the interior of α, without turning the surfaces over. In this paper we discuss a special case of Dudeney dissection where α is congruent to β, in particular, when all hinge points are on the vertices of the polygon α. We determine necessary and sufficient conditions under which such dissections exist.  相似文献   

16.
We propose a parametric model for a bivariate stable Lévy process based on a Lévy copula as a dependence model. We estimate the parameters of the full bivariate model by maximum likelihood estimation. As an observation scheme we assume that we observe all jumps larger than some ε>0 and base our statistical analysis on the resulting compound Poisson process. We derive the Fisher information matrix and prove asymptotic normality of all estimates when the truncation point ε→0. A simulation study investigates the loss of efficiency because of the truncation.  相似文献   

17.
In this work, we obtain good upper bounds for the diameter of any graph in terms of its minimum degree and its order, improving a classical theorem due to Erd¨os, Pach, Pollack and Tuza.We use these bounds in order to study hyperbolic graphs(in the Gromov sense). To compute the hyperbolicity constant is an almost intractable problem, thus it is natural to try to bound it in terms of some parameters of the graph. Let H(n, δ_0) be the set of graphs G with n vertices and minimum degree δ_0, and J(n, Δ) be the set of graphs G with n vertices and maximum degree Δ. We study the four following extremal problems on graphs: a(n, δ_0) = min{δ(G) | G ∈ H(n, δ_0)}, b(n, δ_0) = max{δ(G) |G ∈ H(n, δ_0)}, α(n, Δ) = min{δ(G) | G ∈ J(n, Δ)} and β(n, Δ) = max{δ(G) | G ∈ J(n, Δ)}. In particular, we obtain bounds for b(n, δ_0) and we compute the precise value of a(n, δ_0), α(n, Δ) andβ(n, Δ) for all values of n, δ_0 and Δ, respectively.  相似文献   

18.
We consider regression models involving multilayer perceptrons (MLP) with one hidden layer and Gaussian noise. The estimation of the parameters of the MLP can be made by maximizing the likelihood of the model. In this framework, it is difficult to determine the true number of hidden units because the information matrix of Fisher is not invertible if this number is overestimated. However, if the parameters of the MLP are in a compact set, we prove that the minimization of a suitable information criteria leads to consistent estimation of the true number of hidden units. To cite this article: J. Rynkiewicz, C. R. Acad. Sci. Paris, Ser. I 342 (2006).  相似文献   

19.
We show that a graph with minimum degree δ, independence number αδ and without isolated vertices, possesses a partition by vertex-disjoint cycles and at most αδ+1 edges or vertices.  相似文献   

20.
Given complex numbers α1,...,αn, β1,...,βn, what can we say about the determinant of A+B, where A (B) is an n×n normal matrix with eigenvalues α1,...,αn1,...,βn)? Some partial answers are offered to this question.  相似文献   

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