共查询到20条相似文献，搜索用时 47 毫秒

1.

Yongge Tian 《Central European Journal of Mathematics》2010,8(5):855-870

A complex square matrix

*A*is called an orthogonal projector if*A*^{2}=*A*=*A**, where*A** denotes the conjugate transpose of*A*. In this paper, we give a comprehensive investigation to matrix expressions consisting of orthogonal projectors and their properties through ranks of matrices. We first collect some well-known rank formulas for orthogonal projectors and their operations, and then establish various new rank formulas for matrix expressions composed by orthogonal projectors. As applications, we derive necessary and sufficient conditions for various equalities for orthogonal projectors and their operations to hold. 相似文献2.

In their paper [Y. Tian, G.P.H. Styan, Rank equalities for idempotent and involutory matrices. Linear Algebra Appl. 335 (2001) 101-117], Tian and Styan established several rank equalities involving a pair of idempotent matrices

**P**and**Q**. Subsequently, these results are reinvestigated from the point of view of the following question: provided that idempotent**P**,**Q**are Hermitian, which relationships given in the aforementioned paper remain valid when ranks are replaced with column spaces? Simultaneously, some related results are established, which shed additional light on the links between subspaces attributed to various functions of a pair of orthogonal projectors. 相似文献3.

Haruhiko Ogasawara 《Journal of multivariate analysis》2010,101(9):2149-2167

Asymptotic expansions of the distributions of the pivotal statistics involving log-likelihood derivatives under possible model misspecification are derived using the asymptotic cumulants up to the fourth-order and the higher-order asymptotic variance. The pivots dealt with are the studentized ones by the estimated expected information, the negative Hessian matrix, the sum of products of gradient vectors, and the so-called sandwich estimator. It is shown that the first three asymptotic cumulants are the same over the pivots under correct model specification with a general condition of the equalities. An application is given in item response theory, where the observed information is usually used rather than the estimated expected one. 相似文献

4.

Wolfgang Bischoff 《Journal of multivariate analysis》2000,73(2):1017

Consider a general linear model

*Y*=*Xβ*+*Z*where Cov*Z*may be known only partially. We investigate carefully the notions of sufficiency, ancillarity, invariance, and equivariance and related notions for projectors in a general linear model. In this way we can prove a Basu type theorem. This result can be used to give the relation between the sufficiency of the generalized least-squares estimator and the assumption that*Z*is normally distributed. So we can generalize the well-known result that the generalized least-squares estimator is sufficient for*β*if*Z*is normally distributed. Further we can solve the converse problem as well. 相似文献5.

Hiroshi Kurata 《Journal of multivariate analysis》1998,67(2):297-305

This paper presents a generalization of Rao's covariance structure. In a general linear regression model, we classify the error covariance structure into several categories and investigate the efficiency of the ordinary least squares estimator (OLSE) relative to the Gauss–Markov estimator (GME). The classification criterion considered here is the rank of the covariance matrix of the difference between the OLSE and the GME. Hence our classification includes Rao's covariance structure. The results are applied to models with special structures: a general multivariate analysis of variance model, a seemingly unrelated regression model, and a serial correlation model. 相似文献

6.

Several results involving a product of two orthogonal projectors (i.e., Hermitian idempotent matrices) are established by exploring a representation of the product as a partitioned matrix. These results concern, for instance, rank, trace, range, null space, generalized inverses, and spectral properties of the product and its various functions. Particular attention is paid to the conditions equivalent to the requirement that the product of two orthogonal projectors is an orthogonal projector itself, and these characterizations refer to such known classes of matrices as Hermitian, involutory, normal, star-dagger, unitary as well as partial isometries and semi-orthogonal projectors. Moreover, some results dealing with the notions of parallel sum and spectral norm are obtained. The variety of problems considered shows that the approach utilized in the paper provides a powerful tool of wide applicability. 相似文献

7.

Invertibility of the Difference of Idempotents

**总被引：5，自引：0，他引：5**We study conditions equivalent to the invertibility of f -g when f and g are idempotents in a unital ring, and give applications to bounded linear operators in Banach and Hilbert spaces. In the setting of rings we are able to show that many conditions previously linked to finite dimensionality, rank equalities, norm topology of bounded linear operators or to properties of C *-algebras can be in fact proved by simple algebraic arguments. 相似文献

8.

证得:在Banach空间中,相对紧集上的恒等算子可由一列有限秩连续拟线性投影算子一致逼近.由此得到:线性算子为紧线性算子必须且仅须它可由一列有限秩连续齐性算子一致逼近. 相似文献

9.

Yong Ge Tian 《数学学报(英文版)》2010,26(10):1927-1942

Estimations of parametric functions under a system of linear regression equations with correlated errors across equations involve many complicated operations of matrices and their generalized inverses. In the past several years, a useful tool -- the matrix rank method was utilized to simplify various complicated operations of matrices and their generalized inverses. In this paper, we use the matrix rank method to derive a variety of new algebraic and statistical properties for the best linear unbiased estimators （BLUEs） of parametric functions under the system. In particular, we give the necessary and sufficient conditions for some equalities, additive and block decompositions of BLUEs of parametric functions under the system to hold. 相似文献

10.

Some necessary and sufficient conditions are given for two equalities of ordinary least-squares estimators and best linear unbiased estimators of an estimable vector of parametric functions under a general linear model and its transformed linear model to hold 相似文献

11.

12.

Method of elementary transformation to compute Moore-Penrose inverse is given by applying the rank equalities of matrix. The inheritable properties of Moore-Penrose inverse on rank are also discussed. 相似文献

13.

为了确定多重线性回归模型中回归系数矩阵的秩， 本文提出了一个基于Ｍ估计的模型选择程序， 且在较弱的条件下建立了回归系数矩阵的秩的估计的强相合性。 相似文献

14.

Heung Wong W. K. Li Shiqing Ling 《Annals of the Institute of Statistical Mathematics》2005,57(1):83-103

A cointegrated vector AR-GARCH time series model is introduced. Least squares estimator, full rank maximum likelihood estimator
(MLE), and reduced rank MLE of the model are presented. Monte Carlo experiments are conducted to illustrate the finite sample
properties of the estimators. Its applicability is then demonstrated with the modeling of international stock indices and
exchange rates. The model leads to reasonable financial interpretations. 相似文献

15.

Heinz H. Bauschke Caifang Wang Xianfu Wang Jia Xu 《Set-Valued and Variational Analysis》2018,26(4):1009-1078

Subgradient projectors play an important role in optimization and for solving convex feasibility problems. For every locally Lipschitz function, we can define a subgradient projector via generalized subgradients even if the function is not convex. The paper consists of three parts. In the first part, we study basic properties of subgradient projectors and give characterizations when a subgradient projector is a cutter, a local cutter, or a quasi-nonexpansive mapping. We present global and local convergence analyses of subgradent projectors. Many examples are provided to illustrate the theory. In the second part, we investigate the relationship between the subgradient projector of a prox-regular function and the subgradient projector of its Moreau envelope. We also characterize when a mapping is the subgradient projector of a convex function. In the third part, we focus on linearity properties of subgradient projectors. We show that, under appropriate conditions, a linear operator is a subgradient projector of a convex function if and only if it is a convex combination of the identity operator and a projection operator onto a subspace. In general, neither a convex combination nor a composition of subgradient projectors of convex functions is a subgradient projector of a convex function. 相似文献

16.

泛最小二乘法的改进及其容许性

**总被引：1，自引：0，他引：1**考虑线性回归模型,当设计阵呈病态或秩亏时,我们用泛最小二乘法给出参数的估计,并证明其容许性;然后针对泛最小二乘估计对最小二乘估计过度压缩的缺点加以改进,使之更合理,有效. 相似文献

17.

Yongge Tian 《Annals of the Institute of Statistical Mathematics》2010,62(5):929-941

The weighted least-squares estimator of parametric functions

**K****under a general linear regression model {***β***y**,**X**b, s^{2}S }{\{ {\bf y},\,{\bf X \beta}, \sigma^2{\bf \Sigma} \}} is defined to be**K**[^(b)]{{\bf K}{\hat{\bf {\beta}}}}, where [^(b)]{\hat{{\bf \beta}}} is a vector that minimizes (**y**−**X****)′***β***V**(**y**−**X****) for a given nonnegative definite weight matrix***β***V**. In this paper, we study some algebraic and statistical properties of**K**[^(b)]{{\bf K}\hat{{\bf \beta}}} and the projection matrix associated with the estimator, such as, their ranks, unbiasedness, uniqueness, as well as equalities satisfied by the projection matrices. 相似文献18.

A number of characterizations involving column and null spaces of various functions of a pair of oblique projectors are established. Particular attention is paid to properties of a product of the two projectors, but other functions of the pair (such as sum, difference or sum and difference of products) are considered as well. In many cases, the results obtained generalize those already known to be valid for orthogonal projectors. 相似文献

19.

This paper concerns the study of asymptotic properties of the maximum likelihood estimator (MLE) for the general hidden semi-Markov
model (HSMM) with backward recurrence time dependence. By transforming the general HSMM into a general hidden Markov model,
we prove that under some regularity conditions, the MLE is strongly consistent and asymptotically normal. We also provide
useful expressions for asymptotic covariance matrices, involving the MLE of the conditional sojourn times and the embedded
Markov chain of the hidden semi-Markov chain. Bibliography: 17 titles. 相似文献

20.

A general non-stationary point process whose intensity function is given up to unknown numerical factor λ is considered. As
an alternative to the conventional estimator of λ based on counting the points, we consider general linear unbiased estimators
of λ given by sums of weights associated with individual points. A necessary and sufficient condition for a linear, unbiased
estimator for the intensity λ to have the minimum variance is determined. It is shown that there are “nearly” no other processes
than Poisson and Cox for which the unweighted estimator of λ, which counts the points only, is optimal. The properties of
the optimal estimator are illustrated by simulations for the Matérn cluster and the Matérn hard-core processes.
This research was partially supported by Grant Agency of Czech Republic, project No. 201/03/D062. 相似文献