共查询到20条相似文献,搜索用时 31 毫秒
1.
T. Royen 《Journal of multivariate analysis》1991,38(2)
Three classes of expansions for the distribution function of the χk2(d, R)-distribution are given, where k denotes the dimension, d the degree of freedom, and R the “accompanying correlation matrix.” The first class generalizes the orthogonal series with generalized Laguerre polynomials, originally given by Krishnamoorthy and Parthasarathy [12]. The second class contains always absolutely convergent representations of the distribution function by univariate chi-square distributions and the third class provides also the probabilities for any unbounded rectangular regions. In particular, simple formulas are given for the three-variate case including singular correlation matrices R, which simplify the computation of third order Bonferroni inequalities, e.g., for the tail probabilities of max{χi2|1 ≤ i ≤ k} (k > 3). 相似文献
2.
Haruhiko Ogasawara 《Annals of the Institute of Statistical Mathematics》2009,61(4):995-1017
Asymptotic cumulants of the distributions of the sample singular vectors and values of cross covariance and correlation matrices
are obtained under nonnormality. The asymptotic cumulants are used to have the approximations of the distributions of the
estimators by the Edgeworth expansions up to order O(1/n) and Hall’s method with variable transformation. The cases of Studentized estimators are also considered. As an application
of the method, the distributions of the parameter estimators in the model of inter-battery factor analysis are expanded. Interpreting
the singular vectors and values in the context of the factor model with distributional conditions, the asymptotic robustness
of some lower-order normal-theory cumulants of the distributions of the sample singular vectors and values under nonnormality
is shown. 相似文献
3.
Andrs Kro 《Journal of Approximation Theory》2002,118(2):235-245
Let K
d be a compact set with a smooth boundary and consider a polynomial p of total degree n such that pC(K)1. Then we show that DTp(x)=o(n2) for any x Bd K and T a tangential direction at x. Moreover, the o(n2) term is given in terms of the modulus of smoothness of Bd K. 相似文献
4.
Let the kp-variate random vector X be partitioned into k subvectors Xi of dimension p each, and let the covariance matrix Ψ of X be partitioned analogously into submatrices Ψij. The common principal component (CPC) model for dependent random vectors assumes the existence of an orthogonal p by p matrix β such that βtΨijβ is diagonal for all (i, j). After a formal definition of the model, normal theory maximum likelihood estimators are obtained. The asymptotic theory for the estimated orthogonal matrix is derived by a new technique of choosing proper subsets of functionally independent parameters. 相似文献
5.
Toshio Mikami 《Journal of multivariate analysis》2004,90(2):257-268
We modify and generalize the idea of covariance kernels for Borel probability measures on Rd, and study the relation between the central limit theorem in the total variation distance and the convergence of covariance kernels. 相似文献
6.
In R2 the integral of a regularly varying (RV) function f is regularly varying only if f is monotone. Generalization to R2 of the one-dimensional result on regular variation of the derivative of an RV-function however is straightforward. Applications are given to limit theory for partial sums of i.i.d. positive random vectors in R2+. 相似文献
7.
The parametric generalized linear model assumes that the conditional distribution of a response Y given a d-dimensional covariate X belongs to an exponential family and that a known transformation of the regression function is linear in X. In this paper we relax the latter assumption by considering a nonparametric function of the linear combination βTX, say η0(βTX). To estimate the coefficient vector β and the nonparametric component η0 we consider local polynomial fits based on kernel weighted conditional likelihoods. We then obtain an estimator of the regression function by simply replacing β and η0 in η0(βTX) by these estimators. We derive the asymptotic distributions of these estimators and give the results of some numerical experiments. 相似文献
8.
T.A. Suslina 《Functional Analysis and Its Applications》2010,44(4):318-322
Homogenization in the small period limit for the solution ue of the Cauchy problem for a parabolic equation in Rd is studied. The coefficients are assumed to be periodic in Rd with respect to the lattice ɛG. As ɛ → 0, the solution u ɛ converges in L2(Rd) to the solution u0 of the effective problem with constant coefficients. The solution u ɛis approximated in the norm of the
Sobolev space H
1(Rd) with error O( ɛ); this approximation is uniform with respect to the L2-norm of the initial data and contains a corrector
term of order ɛ. The dependence of the constant in the error estimate on time t is given. Also, an approximation in H
1(Rd) for the solution of the Cauchy problem for a nonhomogeneous parabolic equation is obtained. 相似文献
9.
Timur I. Nezhmetdinov 《代数通讯》2013,41(12):4669-4681
Let R be a finite commutative ring with identity and ? p d be the cyclic group of prime power order. Define R? p d to mean the group ring of ? p d over R. We determine the structure of the group of units of R? p d in the case when R is generated by an element whose order is not divisible by p. 相似文献
10.
Let R be a prime ring with involution * and d be a nonzero derivation on R such that d(x *) = -d(x)* for all x ∈ R. Suppose that n ≥ 1 is a fixed integer. Then (I) if d(s) n = 0 for all s = s *, then R is either a commutative domain or an order in a 4-dimensional central simple algebra; (II) if d(s) n ∈Z, the center of R for all s = s *, then R is either a commutative domain or an order in a simple algebra of dimension 4 or 16 over its center. 相似文献
11.
The direct and inverse theorems are established for the best approximation
in the weighted Lp space on the unit sphere of Rd+1, in
which the weight functions are invariant under finite reflection groups. The
theorems are stated using a modulus of smoothness of higher order, which is proved
to be equivalent to a K-functional defined using the power of the spherical
h-Laplacian. Furthermore, similar results are also established for weighted
approximation on the unit ball and on the simplex of Rd. 相似文献
12.
Xiuping Su 《Journal of Algebra》2004,280(2):501
We study the tame behaviour of the representations of wild quivers Q via tame roots. A positive root d of Q is called a tame root if d is sincere and for any positive sub-root d′ of d we have q(d′)0, where q(d′) is the Tits form of Q. We prove that a sincere root is a tame root if and only if for any decomposition of d into a sum of positive sub-roots d=d1++ds, there is at most one di with q(di)=0 and q(dj)=1. This is the essential property of a tame root and it is an alternative way to define tame roots. Then we give the canonical decomposition of a tame root. At the end we prove our main result that for any wild graph, there are only finitely many tame roots. 相似文献
13.
Changhua Chen Richard A. Davis Peter J. Brockwell 《Journal of multivariate analysis》1996,57(2):175-190
LetX1, …, Xnbe observations from a multivariate AR(p) model with unknown orderp. A resampling procedure is proposed for estimating the orderp. The classical criteria, such as AIC and BIC, estimate the orderpas the minimizer of the function[formula]wherenis the sample size,kis the order of the fitted model, Σ2kis an estimate of the white noise covariance matrix, andCnis a sequence of specified constants (for AIC,Cn=2m2/n, for Hannan and Quinn's modification of BIC,Cn=2m2(ln ln n)/n, wheremis the dimension of the data vector). A resampling scheme is proposed to estimate an improved penalty factorCn. Conditional on the data, this procedure produces a consistent estimate ofp. Simulation results support the effectiveness of this procedure when compared with some of the traditional order selection criteria. Comments are also made on the use of Yule–Walker as opposed to conditional least squares estimations for order selection. 相似文献
14.
We give a new upper bound onn
d(d+1)n
on the number of realizable order types of simple configurations ofn points inR
d
, and ofn2d
2
n on the number of realizable combinatorial types of simple configurations. It follows as a corollary of the first result that there are no more thann
d(d+1)n
combinatorially distinct labeled simplicial polytopes inR
d
withn vertices, which improves the best previous upper bound ofn
cn
d/2.Supported in part by NSF Grant DMS-8501492 and PSC-CUNY Grant 665258.Supported in part by NSF Grant DMS-8501947. 相似文献
15.
Annamaria Bianchi 《Statistical Inference for Stochastic Processes》2009,12(3):251-268
We consider the problem of the density and drift estimation by the observation of a trajectory of an
\mathbbRd{\mathbb{R}^{d}}-dimensional homogeneous diffusion process with a unique invariant density. We construct estimators of the kernel type based
on discretely sampled observations and study their asymptotic distribution. An estimate of the rate of normal approximation
is given. 相似文献
16.
Minoru Murata 《Journal of Differential Equations》2003,195(1):82-118
We give the asymptotics at infinity of a Green function for an elliptic equation with periodic coefficients on Rd. Basic ingredients in establishing the asymptotics are an integral representation of the Green function and the saddle point method. We also completely determine the Martin compactification of Rd with respect to an elliptic equation with periodic coefficients by using the exact asymptotics at infinity of the Green function. 相似文献
17.
The predictive ratio is considered as a measure of spread for the predictive distribution. It is shown that, in the exponential families, ordering according to the predictive ratio is equivalent to ordering according to the posterior covariance matrix of the parameters. This result generalizes an inequality due to Chaloner and Duncan who consider the predictive ratio for a beta-binomial distribution and compare it with a predictive ratio for the binomial distribution with a degenerate prior. The predictive ratio at x1 and x2 is defined to be pg(x1)pg(x2)/[pg(
)]2 = hg(x1, x2), where pg(x1) = ∫ ƒ(x1θ) g(θ) dθ is the predictive distribution of x1 with respect to the prior g. We prove that hg(x1, x2) ≥ hg*(x1, x2) for all x1 and x2 if ƒ(xθ) is in the natural exponential family and Covgx(θ) ≥ Covg*x(θ) in the Loewner sense, for all x on a straight line from x1 to x2. We then restrict the class of prior distributions to the conjugate class and ask whether the posterior covariance inequality obtains if g and g* differ in that the “sample size” 相似文献
18.
We consider systems of spatially distributed branching particles in R
d
. The particle lifelengths are of general form, hence the time propagation of the system is typically not Markov. A natural time-space-mass scaling is applied to a sequence of particle systems and we derive limit results for the corresponding sequence of measure-valued processes. The limit is identified as the projection on R
d of a superprocess in R
+×R
d
. The additive functional characterizing the superprocess is the scaling limit of certain point processes, which count generations along a line of descent for the branching particles. 相似文献
19.
It is shown that under certain conditions, attractive invariant measures for iterated function systems (indeed for Markov processes on locally compact spaces) depend continuously on parameters of the system. We discuss a special class of iterated function systems, the homogeneous affine ones, for which an inverse problem is easily solved in principle by Fourier transform methods. We show that a probability measureμ onR n can be approximated by invariant measures for finite iterated function systems of this class if \(\hat \mu (t)/\hat \mu (a^T t)\) is positive definite for some nonzero contractive linear mapa:R n →R n . Moments and cumulants are also discussed. 相似文献
20.
This paper concerns the problems of the average widths and the optimal recovery of the anisotropic Hölder classesW r H α (R d ) of smooth functions defined on the Euclidean spaceR d in the metricC k (R d ). The weak asymptotic behavior is established for the corresponding quantities. 相似文献