共查询到20条相似文献,搜索用时 31 毫秒
1.
Muni S. Srivastava 《Journal of multivariate analysis》2011,102(6):1090-1103
This article analyzes whether some existing tests for the p×p covariance matrix Σ of the N independent identically distributed observation vectors work under non-normality. We focus on three hypotheses testing problems: (1) testing for sphericity, that is, the covariance matrix Σ is proportional to an identity matrix Ip; (2) the covariance matrix Σ is an identity matrix Ip; and (3) the covariance matrix is a diagonal matrix. It is shown that the tests proposed by Srivastava (2005) for the above three problems are robust under the non-normality assumption made in this article irrespective of whether N≤p or N≥p, but (N,p)→∞, and N/p may go to zero or infinity. Results are asymptotic and it may be noted that they may not hold for finite (N,p). 相似文献
2.
Sang-Gu Lee 《Linear algebra and its applications》2011,435(9):2097-2109
We investigate simultaneous solutions of the matrix Sylvester equations AiX-XBi=Ci,i=1,2,…,k, where {A1,…,Ak} and {B1,…,Bk} are k-tuples of commuting matrices of order m×m and p×p, respectively. We show that the matrix Sylvester equations have a unique solution X for every compatible k-tuple of m×p matrices {C1,…,Ck} if and only if the joint spectra σ(A1,…,Ak) and σ(B1,…,Bk) are disjoint. We discuss the connection between the simultaneous solutions of Sylvester equations and related questions about idempotent matrices separating disjoint subsets of the joint spectrum, spectral mapping for the differences of commuting k-tuples, and a characterization of the joint spectrum via simultaneous solutions of systems of linear equations. 相似文献
3.
This paper considers the generalized growth curve model subject to R(Xm)⊆R(Xm-1)⊆?⊆R(X1), where Bi are the matrices of unknown regression coefficients, Xi,Zi and U are known covariate matrices, i=1,2,…,m, and E splits into a number of independently and identically distributed subvectors with mean zero and unknown covariance matrix Σ. An unbiased invariant minimum norm quadratic estimator (MINQE(U,I)) of tr(CΣ) is derived and the conditions for its optimality under the minimum variance criterion are investigated. The necessary and sufficient conditions for MINQE(U,I) of tr(CΣ) to be a uniformly minimum variance invariant quadratic unbiased estimator (UMVIQUE) are obtained. An unbiased invariant minimum norm quadratic plus linear estimator (MINQLE(U,I)) of is also given. To compare with the existing maximum likelihood estimator (MLE) of tr(CΣ), we conduct some simulation studies which show that our proposed estimator performs very well. 相似文献
4.
Suppose that random factor models with k factors are assumed to hold for m, p-variate populations. A model for factorial invariance has been proposed wherein the covariance or correlation matrices can be written as Σi = LCiL′ + σi2I, where Ci is the covariance matrix of factor variables and L is a common factor loading matrix, i = 1,…, m. Also a goodness of fit statistic has been proposed for this model. The asymptotic distribution of this statistic is shown to be that of a quadratic form in normal variables. An approximation to this distribution is given and thus a test for goodness of fit is derived. The problem of dimension is considered and a numerical example is given to illustrate the results. 相似文献
5.
Empirical likelihood (EL) ratio tests are developed for testing for or against the hypothesis that k-population means μ1,μ2,…,μk are isotonic with respect to some quasi-order ? on {1,2,…,k}. The null asymptotic distributions are derived and are shown to be of chi-bar squared type. The asymptotic power of the proposed test for testing for equality of these means against the order restriction is derived under contiguous alternatives and a simulation study is carried out to investigate the finite sample behaviors of this test. In addition, an adjusted EL test is used to improve the small size performance of our test and an example is also discussed to illustrate the theoretical results. 相似文献
6.
Dalibor Froncek 《Discrete Mathematics》2009,309(2):501-389
We completely solve certain case of a “two delegation negotiation” version of the Oberwolfach problem, which can be stated as follows. Let H(k,3) be a bipartite graph with bipartition X={x1,x2,…,xk},Y={y1,y2,…,yk} and edges x1y1,x1y2,xkyk−1,xkyk, and xiyi−1,xiyi,xiyi+1 for i=2,3,…,k−1. We completely characterize all complete bipartite graphs Kn,n that can be factorized into factors isomorphic to G=mH(k,3), where k is odd and mH(k,3) is the graph consisting of m disjoint copies of H(k,3). 相似文献
7.
Hiro Ito 《Discrete Applied Mathematics》2006,154(16):2330-2334
Let H=(N,E,w) be a hypergraph with a node set N={0,1,…,n-1}, a hyperedge set E⊆2N, and real edge-weights w(e) for e∈E. Given a convex n-gon P in the plane with vertices x0,x1,…,xn-1 which are arranged in this order clockwisely, let each node i∈N correspond to the vertex xi and define the area AP(H) of H on P by the sum of the weighted areas of convex hulls for all hyperedges in H. For 0?i<j<k?n-1, a convex three-cut C(i,j,k) of N is {{i,…,j-1}, {j,…,k-1}, {k,…,n-1,0,…,i-1}} and its size cH(i,j,k) in H is defined as the sum of weights of edges e∈E such that e contains at least one node from each of {i,…,j-1}, {j,…,k-1} and {k,…,n-1,0,…,i-1}. We show that the following two conditions are equivalent:
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- AP(H)?AP(H′) for all convex n-gons P.
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- cH(i,j,k)?cH′(i,j,k) for all convex three-cuts C(i,j,k).
8.
Joe Masaro 《Linear algebra and its applications》2010,432(6):1578-1594
For a real, Hermitian, or quaternion normal random matrix Y with mean zero, necessary and sufficient conditions for a quadratic form Q(Y) to have a Wishart-Laplace distribution (the distribution of the difference of two independent central Wishart Wp(mi,Σ) random matrices) are given in terms of a certain Jordan algebra homomorphism ρ. Further, it is shown that {Qk(Y)} is independent Laplace-Wishart if and only if in addition to the aforementioned conditions, the images ρk(Σ+) of the Moore-Penrose inverse Σ+ of Σ are mutually orthogonal: ρk(Σ+)ρ?(Σ+)=0 for k≠?. 相似文献
9.
Y. Chikuse 《Journal of multivariate analysis》2004,88(1):163-176
A test of uniformity on the shape space Σmk is presented, together with modifications of the test statistic which bring its null distribution close to the large-sample asymptotic distribution. The asymptotic distribution under suitable local alternatives to uniformity is given. A family of distributions on Σmk is proposed, which is suitable for modelling shapes given by landmarks which are almost collinear. 相似文献
10.
V.V. Bavula 《Journal of Pure and Applied Algebra》2008,212(10):2320-2337
Let K be an arbitrary field of characteristic p>0. We find an explicit formula for the inverse of any algebra automorphism of any of the following algebras: the polynomial algebra Pn?K[x1,…,xn], the ring of differential operators D(Pn) on Pn, D(Pn)⊗Pm, the n’th Weyl algebra An or An⊗Pm, the power series algebra K[[x1,…,xn]], the subalgebra Tk1,…,kn of D(Pn) generated by Pn and the higher derivations , 0≤j<pki, i=1,…,n (where k1,…,kn∈N), Tk1,…,kn⊗Pm or an arbitrary central simple (countably generated) algebra over an arbitrary field. 相似文献
11.
For positive integers s and k1,k2,…,ks, the van der Waerden number w(k1,k2,…,ks;s) is the minimum integer n such that for every s-coloring of set {1,2,…,n}, with colors 1,2,…,s, there is a ki-term arithmetic progression of color i for some i. We give an asymptotic lower bound for w(k,m;2) for fixed m. We include a table of values of w(k,3;2) that are very close to this lower bound for m=3. We also give a lower bound for w(k,k,…,k;s) that slightly improves previously-known bounds. Upper bounds for w(k,4;2) and w(4,4,…,4;s) are also provided. 相似文献
12.
Shinya Fujita 《Discrete Mathematics》2009,309(11):3534-3540
Let k,n be integers with 2≤k≤n, and let G be a graph of order n. We prove that if max{dG(x),dG(y)}≥(n−k+1)/2 for any x,y∈V(G) with x≠y and xy∉E(G), then G has k vertex-disjoint subgraphs H1,…,Hk such that V(H1)∪?∪V(Hk)=V(G) and Hi is a cycle or K1 or K2 for each 1≤i≤k, unless k=2 and G=C5, or k=3 and G=K1∪C5. 相似文献
13.
Dominique Fourdrinier 《Journal of multivariate analysis》2010,101(6):1390-1399
For independently distributed observables: Xi∼N(θi,σ2),i=1,…,p, we consider estimating the vector θ=(θ1,…,θp)′ with loss ‖d−θ‖2 under the constraint , with known τ1,…,τp,σ2,m. In comparing the risk performance of Bayesian estimators δα associated with uniform priors on spheres of radius α centered at (τ1,…,τp) with that of the maximum likelihood estimator , we make use of Stein’s unbiased estimate of risk technique, Karlin’s sign change arguments, and a conditional risk analysis to obtain for a fixed (m,p) necessary and sufficient conditions on α for δα to dominate . Large sample determinations of these conditions are provided. Both cases where all such δα’s and cases where no such δα’s dominate are elicited. We establish, as a particular case, that the boundary uniform Bayes estimator δm dominates if and only if m≤k(p) with , improving on the previously known sufficient condition of Marchand and Perron (2001) [3] for which . Finally, we improve upon a universal dominance condition due to Marchand and Perron, by establishing that all Bayesian estimators δπ with π spherically symmetric and supported on the parameter space dominate whenever m≤c1(p) with . 相似文献
14.
It is known, for example, that the eigenvalues of the N×N matrix A, arising in the discretization of the wave equation, whose only nonzero entries are Akk+1=Ak+1k=-1,k=1,…,N-1, and Akk=2,k=1,…,N, are 2{1-cos[pπ/(N+1)]} with corresponding eigenvectors v(p) given by . We show by considering a simple finite difference approximation to the second derivative and using the summation formulae for sines and cosines that these and other similar formulae arise in a simple and unified way. 相似文献
15.
Let f1,…,fd be an orthogonal basis for the space of cusp forms of even weight 2k on Γ0(N). Let L(fi,s) and L(fi,χ,s) denote the L-function of fi and its twist by a Dirichlet character χ, respectively. In this note, we obtain a “trace formula” for the values at integers m and n with 0<m,n<2k and proper parity. In the case N=1 or N=2, the formula gives us a convenient way to evaluate precisely the value of the ratio L(f,χ,m)/L(f,n) for a Hecke eigenform f. 相似文献
16.
Anna Lladó Jordi Moragas 《European Journal of Combinatorics》2012,33(4):427-434
A sequence m1≥m2≥?≥mk of k positive integers isn-realizable if there is a partition X1,X2,…,Xk of the integer interval [1,n] such that the sum of the elements in Xi is mi for each i=1,2,…,k. We consider the modular version of the problem and, by using the polynomial method by Alon (1999) [2], we prove that all sequences in Z/pZ of length k≤(p−1)/2 are realizable for any prime p≥3. The bound on k is best possible. An extension of this result is applied to give two results of p-realizable sequences in the integers. The first one is an extension, for n a prime, of the best known sufficient condition for n-realizability. The second one shows that, for n≥(4k)3, an n-feasible sequence of length k isn-realizable if and only if it does not contain forbidden subsequences of elements smaller than n, a natural obstruction forn-realizability. 相似文献
17.
Jigao Yan 《Journal of Mathematical Analysis and Applications》2008,343(2):644-653
Let X(i,n,m,k), i=1,…,n, be generalized order statistics based on F. For fixed r∈N, and a suitable counting process N(t), t>0, we mainly discuss the precise asymptotic of the generalized stochastic order statistics X(N(n)−r+1,N(n),m,k). It not only makes the results of Yan, Wang and Cheng [J.G. Yan, Y.B. Wang, F.Y. Cheng, Precise asymptotics for order statistics of a non-random sample and a random sample, J. Systems Sci. Math. Sci. 26 (2) (2006) 237-244] as the special case of our result, and presents many groups of weighted functions and boundary functions, but also permits a unified approach to several models of ordered random variables. 相似文献
18.
19.
Darryn Bryant 《Journal of Combinatorial Theory, Series A》2010,117(8):1258-1284
Let m1,m2,…,mt be a list of integers. It is shown that there exists an integer N such that for all n?N, the complete graph of order n can be decomposed into edge-disjoint cycles of lengths m1,m2,…,mt if and only if n is odd, 3?mi?n for i=1,2,…,t, and . In 1981, Alspach conjectured that this result holds for all n, and that a corresponding result also holds for decompositions of complete graphs of even order into cycles and a perfect matching. 相似文献
20.
Weiwei Zhuang 《Journal of multivariate analysis》2010,101(3):640-644
For any positive integers m and n, let X1,X2,…,Xm∨n be independent random variables with possibly nonidentical distributions. Let X1:n≤X2:n≤?≤Xn:n be order statistics of random variables X1,X2,…,Xn, and let X1:m≤X2:m≤?≤Xm:m be order statistics of random variables X1,X2,…,Xm. It is shown that (Xj:n,Xj+1:n,…,Xn:n) given Xi:m>y for j−i≥max{n−m,0}, and (X1:n,X2:n,…,Xj:n) given Xi:m≤y for j−i≤min{n−m,0} are all increasing in y with respect to the usual multivariate stochastic order. We thus extend the main results in Dubhashi and Häggström (2008) [1] and Hu and Chen (2008) [2]. 相似文献