共查询到20条相似文献,搜索用时 15 毫秒
1.
Error bounds for asymptotic expansions of the distribution of the MLE in a GMANOVA model 总被引:1,自引:0,他引:1
Yasunori Fujikoshi 《Annals of the Institute of Statistical Mathematics》1987,39(1):153-161
Summary In this paper we obtain asymptotic expansions for the distribution function and the density function of a linear combination
of the MLE in a GMANOVA model, and for the density function of the MLE itself. We also obtain certain error bounds for the
asymptotic expansions. 相似文献
2.
R Michel 《Journal of multivariate analysis》1975,5(1):67-82
It is shown that the probability that a suitably standardized asymptotic maximum likelihood estimator of a vector parameter (i.e., an estimator which approximates the solution of the likelihood equation in a reasonably good way) lies in a measurable convex set can be approximated by an integral involving a multidimensional normal density function and a series in with certain polynomials as coefficients. 相似文献
3.
Peter Hall 《Journal of multivariate analysis》1981,11(2):173-184
Let Y be an absolutely continuous random variable and W a nonnegative variable independent of Y. It is to be expected that when W is close to 1 in some sense, the distribution of the scale mixture YW will be close to Y. This notion has been investigated by a number of workers, who have provided bounds on the difference between the distribution functions of Y and YW. In this paper we examine the deeper problem of finding asymptotic expansions of the form P(YW ≤ x) = P(Y ≤ x) + Σn=1∞E(Wr ? 1)nGn(x), where r > 0 and the functions Gn do not depend on W. We approach the problem very generally, and then consider the normal and gamma distributions in greater detail. Our results are applied to obtain better uniform and nonuniform estimates of the difference between the distribution functions of Y and YW. 相似文献
4.
We consider Markovian queueing models with a finite number of states and a product form solution for its steady state probability distribution. Starting from the integral representation for the partition function in complex space we construct error bounds for its asymptotic expansion obtained by the saddle point method. The derivation of error bounds is based on an idea by Olver applicable to integral transforms with an exponentially decaying kernel. The bounds are expressed in terms of the supremum of a certain function and are asymptotic to the absolute value of the first neglected term in the expansion as the large parameter approaches infinity. The application of these error bounds is illustrated for two classes of queueing models: loss systems and single chain closed queueing networks. 相似文献
5.
黄辉 《高校应用数学学报(A辑)》2007,22(1):74-80
考虑了伪凸集值映射的误差界.证明了对于伪凸集值映射,局部误差界成立意味着整体误差界成立.通过相依导数,给出了伪凸集值映射存在误差界的一些等价叙述. 相似文献
6.
Kengo Kato 《Annals of the Institute of Statistical Mathematics》2009,61(3):531-542
The prediction problem for a multivariate normal distribution is considered where both mean and variance are unknown. When
the Kullback–Leibler loss is used, the Bayesian predictive density based on the right invariant prior, which turns out to
be a density of a multivariate t-distribution, is the best invariant and minimax predictive density. In this paper, we introduce an improper shrinkage prior
and show that the Bayesian predictive density against the shrinkage prior improves upon the best invariant predictive density
when the dimension is greater than or equal to three. 相似文献
7.
《Journal of Computational and Applied Mathematics》2002,147(1):215-231
We derive simple, explicit error bounds for the uniform asymptotic expansion of the incomplete gamma function Γ(a,z) valid for complex values of a and z as |a|→∞. Their evaluation depends on numerically pre-computed bounds for the coefficients ck(η) in the expansion of Γ(a,z) taken along rays in the complex η plane, where η is a variable related to z/a. The bounds are compared with numerical computations of the remainder in the truncated expansion. 相似文献
8.
Error bounds for set inclusions 总被引:1,自引:0,他引:1
郑喜印 《中国科学A辑(英文版)》2003,46(6):750-763
A variant of Robinson-Ursescu Theorem is given in normed spaces. Several error bound theorems for convex inclusions are proved and in particular a positive answer to Li and Singer's conjecture is given under weaker assumption than the assumption required in their conjecture. Perturbation error bounds are also studied. As applications, we study error bounds for convex inequality systems. 相似文献
9.
史薇 《数学物理学报(B辑英文版)》2008,28(4):834-842
In this article,the author extends the validity of a uniform asymptotic expansion of the Hermite polynomials Hn(√2n+1α)to include all positive values of α. His method makes use of the rational functions introduced by Olde Daalhuis and Temme (SIAM J.Math.Anal.,(1994),25:304-321).A new estimate for the remainder is given. 相似文献
10.
We present counterexamples to the asymptotic expansion of interpolation in finite element methods for solving differential
equations, which was expected to hold in the finite element community.
相似文献
11.
Let Λ=|Se|/|Se+Sh|, where Sh and Se are independently distributed as Wishart distributions Wp(q,Σ) and Wp(n,Σ), respectively. Then Λ has Wilks’ lambda distribution Λp,q,n which appears as the distributions of various multivariate likelihood ratio tests. This paper is concerned with theoretical accuracy for asymptotic expansions of the distribution of T=-nlogΛ. We derive error bounds for the approximations. It is necessary to underline that our error bounds are given in explicit and computable forms. 相似文献
12.
Benjamin A. Burton 《Journal of Combinatorial Theory, Series A》2011,118(4):1410-1435
The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significant improvements upon the best known asymptotic bounds on the number of admissible vertices, using polytopes in both the standard normal surface coordinate system and the streamlined quadrilateral coordinate system.To achieve these results we examine the layout of admissible points within these polytopes. We show that these points correspond to well-behaved substructures of the face lattice, and we study properties of the corresponding “admissible faces”. Key lemmata include upper bounds on the number of maximal admissible faces of each dimension, and a bijection between the maximal admissible faces in the two coordinate systems mentioned above. 相似文献
13.
R. Nair 《Proceedings Mathematical Sciences》1997,107(4):363-376
We show that the values of a polynomial with a-adic coefficients at integer and rational prime arguments are asymptotically
distributed on the a-adic integers and that the integer parts of certain sequences known to be uniformly distributed modulo
one, are uniformly distributed on the a-adic integers. 相似文献
14.
The paper is devoted to studying the Hoffman global error bound for convex quadratic/affine inequality/equality systems in the context of Banach spaces. We prove that the global error bound holds if the Hoffman local error bound is satisfied for each subsystem at some point of the solution set of the system under consideration. This result is applied to establishing the equivalence between the Hoffman error bound and the Abadie qualification condition, as well as a general version of Wang &; Pang's result [30], on error bound of Hölderian type. The results in the present paper generalize and unify recent works by Luo &; Luo in [17], Li in [16] and Wang &; Pang in [30]. 相似文献
15.
Chungou Zhang Quane Wang 《分析论及其应用》2007,23(1):76-82
In this paper, we derive the complete asymptotic expansion of classical Baskakov operators Vn (f;x) in the form of all coefficients of n^-k, k = 0, 1... being calculated explic- itly in terms of Stirling number of the first and second kind and another number G(i, p). As a corollary, we also get the Voronovskaja-type result for the operators. 相似文献
16.
Yu-Qiu Zhao 《Journal of Computational and Applied Mathematics》2003,150(2):329-355
In this paper, we investigate the uniform asymptotic behavior of the single variable Bell polynomials on the negative real axis, to which all zeros belong. It is found that there exists an ascending sequence {Zk}1∞(−e,0) such that the polynomials are represented by a finite sum of infinite asymptotic series, each in terms of the Airy function and its derivative, and the number of series under this sum is 1 in the interval (−∞,Z1) and k+1 in [Zk,Zk+1), k1. Furthermore, it is shown that an asymptotic expansion, also in terms of Airy function and its derivative, completed with error bounds, holds uniformly in (−∞,−δ] for positive δ. 相似文献
17.
Asymptotic expansion for distribution function of moment estimator for the extreme-value index 总被引:1,自引:0,他引:1
Asymptotic expansion for distribution function of the moment estimator
for the extreme-value index is obtained under reasonable conditions of second order regular variation. 相似文献
18.
Yuji Sakamoto Nakahiro Yoshida 《Annals of the Institute of Statistical Mathematics》2009,61(3):629-661
For an unknown parameter in the drift function of a diffusion process, we consider an M-estimator based on continuously observed data, and obtain its distributional asymptotic expansion up to the third order.
Our setting covers the misspecified cases. To represent the coefficients in the asymptotic expansion, we derive some formulas
for asymptotic cumulants of stochastic integrals, which are widely applicable to many other problems. Furthermore, asymptotic
properties of cumulants of mixing processes will be also studied in a general setting. 相似文献
19.
20.
Hong-xia Yin 《应用数学学报(英文版)》2009,25(4):685-696
In the paper we investigate smoothing method for solving semi-infinite minimax problems. Not like most of the literature in semi-infinite minimax problems which are concerned with the continuous time version(i.e., the one dimensional semi-infinite minimax problems), the primary focus of this paper is on multi- dimensional semi-infinite minimax problems. The global error bounds of two smoothing approximations for the objective function are given and compared. It is proved that the smoothing approximation given in this paper can provide a better error bound than the existing one in literature. 相似文献