共查询到20条相似文献,搜索用时 78 毫秒
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Eugenia Stoimenova 《Annals of the Institute of Statistical Mathematics》2000,52(2):255-266
Rank tests based on the maximum number of exceeding observations for several standard nonparametric hypotheses are proposed. An approach to constructing nonparametric rank tests via metrics on the permutation group is used. The test statistics are based on a metric induced by Chebyshev's norm. 相似文献
3.
Gianna M. Del Corso Federico Poloni Leonardo Robol Raf Vandebril 《Numerical Linear Algebra with Applications》2019,26(6)
Hermitian and unitary matrices are two representatives of the class of normal matrices whose full eigenvalue decomposition can be stably computed in quadratic computing complexity once the matrix has been reduced, for instance, to tridiagonal or Hessenberg form. Recently, fast and reliable eigensolvers dealing with low‐rank perturbations of unitary and Hermitian matrices have been proposed. These structured eigenvalue problems appear naturally when computing roots, via confederate linearizations, of polynomials expressed in, for example, the monomial or Chebyshev basis. Often, however, it is not known beforehand whether or not a matrix can be written as the sum of a Hermitian or unitary matrix plus a low‐rank perturbation. In this paper, we give necessary and sufficient conditions characterizing the class of Hermitian or unitary plus low‐rank matrices. The number of singular values deviating from 1 determines the rank of a perturbation to bring a matrix to unitary form. A similar condition holds for Hermitian matrices; the eigenvalues of the skew‐Hermitian part differing from 0 dictate the rank of the perturbation. We prove that these relations are linked via the Cayley transform. Then, based on these conditions, we identify the closest Hermitian or unitary plus rank k matrix to a given matrix A, in Frobenius and spectral norm, and give a formula for their distance from A. Finally, we present a practical iteration to detect the low‐rank perturbation. Numerical tests prove that this straightforward algorithm is effective. 相似文献
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Ming-Tan M. Tsai Pranas Kumar Sen 《Annals of the Institute of Statistical Mathematics》1990,42(2):375-385
In a randomized block design MANOVA model, for intrablock as well as aligned rank tests for homogeneity of treatment effects against some restricted alternatives, asymptotic optimality is studied by reference to the corresponding restrieted likelihood ratio tests. Tests based on aligned ranks are better than intra-block rank tests when the error distributions are homogeneous aeross the blocks.Work of this author was partially supported by the Office of Naval Research, Contract No. N00014-83-K-0987. 相似文献
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The paper presents some permutation test procedures for multivariate location. The tests are based on projected univariate versions of multivariate data. For one-sample cases, the tests are affine invariant and strictly distribution-free for the symmetric null distribution with elliptical direction and their permutation counterparts are conditionally distribution-free when the underlying null distribution of the sample is angularly symmetric. For multi-sample cases, the tests are also affine invariant and permutation counterparts of the tests are conditionally distribution-free for any null distribution with certain continuity. Hence all of the tests in this paper are exactly valid. Furthermore, the equivalence, in the large sample sense, between the tests and their permutation counterparts are established. The power behavior of the tests and of their permutation counterparts under local alternative are investigated. A simulation study shows the tests to perform well compared with some existing tests in the literature, particularly when the underlying null distribution is symmetric whether light-tailed or heavy-tailed. For revealing the influence of data sparseness on the effect of the test, some simulations with different dimensions are also performed. 相似文献
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A Monte Carlo comparison of studentized bootstrap and permutation tests for heteroscedastic two-sample problems 总被引:1,自引:0,他引:1
The present Monte Carlo study compares bootstrap and permutation tests for semiparametric heteroscedastic two-sample testing
problems of Behrens-Fisher type. The underlying functionals to be tested are (a) the difference of the means and (b) the Wilcoxon
functionalP(Y < X) which is invariant under strictly increasing transformations. The consideration leads to semiparametric modifications of
Welch type tests for the Behrens-Fisher model and an extended two-sample Wilcoxon test which also works under some null hypothesis
with non-exchangeable distributions. The present Monte Carlo study confirms the high quality of studentized permutation tests
at finite sample size. They are typically better than tests with asymptotic critical values and for many situations and they
are also better than two-sample bootstrap tests when their type I error probabilities are compared. 相似文献
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Lanh Tat Tran 《Annals of the Institute of Statistical Mathematics》1988,40(2):247-260
Some invariance principles are obtained for the one-sample rank order statistics of a -mixing or strong mixing type time series. The estimation of the center of symmetry of the time series and tests for serial dependence are considered as applications. 相似文献
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Simos Meintanis George Iliopoulos 《Annals of the Institute of Statistical Mathematics》2003,55(1):137-151
In this paper a class of goodness-of-fit tests for the Rayleigh distribution is proposed. The tests are based on a weighted
integral involving the empirical Laplace transform. The consistency of the tests as well as their asymptotic distribution
under the null hypothesis are investigated. As the decay of the weight function tends to infinity the test statistics approach
limit values. In a particular case the resulting limit statistic is related to the first nonzero component of Neyman’s smooth
test for this distribution. The new tests are compared with other omnibus tests for the Rayleigh distribution. 相似文献
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We computed the test rank of a free solvable Lie algebra of finite rank. 相似文献
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Ram C. Tripathi Ramesh C. Gupta Robert K. Pair 《Annals of the Institute of Statistical Mathematics》1993,45(4):773-786
Statistical tests are developed regarding linear combinations of the parameters of several independent gamma populations. The tests are based on a generalized minimum chi-square procedure. On utilizing these, one can test hypotheses regarding the means or the scale parameters when the shape parameters are unknown. In these tests there is no need to assume the equality of the shape parameters of the underlying populations. Tests for comparing coefficients of variation of several gamma populations have also been developed. For the two population case, a power comparison of these tests with some existing tests is also presented. Two examples are provided to explain the procedure. 相似文献
11.
James A Koziol 《Statistics & probability letters》1985,3(4):227-230
A simple yet general technique is presented for the problem of assessing symmetry about an unknown point with linear rank statistics. 相似文献
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K. Krishnamoorthy Maruthy K. Pannala 《Annals of the Institute of Statistical Mathematics》1998,50(3):531-542
The problem of testing normal mean vector when the observations are missing from subsets of components is considered. For a data matrix with a monotone pattern, three simple exact tests are proposed as alternatives to the traditional likelihood ratio test. Numerical power comparisons between the proposed tests and the likelihood ratio test suggest that one of the proposed tests is indeed comparable to the likelihood ratio test and the other two tests perform better than the likelihood ratio test over a part of the parameter space. The results are extended to a nonmonotone pattern and illustrated using an example. 相似文献
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In this article a new approach for checking the adequacy of GARCH-type models in time series was proposed. The resulted tests involve weight functions, which provide them with the flexibility in choosing scores to enhance power performance. The choice of weight functions and the power properties of the tests are studied. For a large number of alternatives, asymptotically distribution-free maximin test is constructed. The tests are asymptotically chi-squared under the null hypothesis and easy to implement. Simulation results indicate that the tests perform well. 相似文献
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We calculate the test rank of a finite rank free metabelian Lie algebra over an arbitrary field and characterize the test sets for these algebras. We prove that each automorphism that is the identity modulo the derived subalgebra and that acts as the identity on some test set is an inner automorphism. 相似文献
15.
The purpose of this paper is to provide limit laws for semiparametric estimators of copulas. Some statistical tests of independence
are introduced as a consequence of this methodology. We are primarily concernedwith the case where the parameter lies on the
boundary of the admissible domain.
相似文献
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For some mixed models (involving both stochastic and nonstochastic predictors), a general class of permutationally distribution-free rank tests for some restricted alternative problems is considered. The proposed tests are asymptotically optimal in the light of the restricted likelihood ratio tests. For an ordered alternative problem in a two-way analysis of covariance model, the proposed tests are asymptotically optimal. 相似文献
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Günter Rothe 《Statistics & probability letters》1984,2(4):197-201
The efficiency of nonparametric trend tests is considered in the randomized block design: For a large number of rank test statistics the projection on the subset of linear rank statistics defines an even uniformly more efficient rank test than the original test statistics. 相似文献
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In this paper, we suggest the conditional test procedures for testing elliptical symmetry of multivariate distribution. The conditional tests are exactly valid if the symmetric center and the shape matrix are given and are asymptotically valid if they are unknowns to be estimated. The equivalence, in the large sample sense, between the conditional tests and their unconditional counterparts is established. The power behavior of the tests under global as well as local alternatives is investigated theoretically. A small simulation study is performed. 相似文献
19.
Ashis Sen Gupta 《Statistics & probability letters》1982,1(1):46-50
Given a set of data, very little is known about tests to determine number of clusters and/or elements of the clusters. Even in the simplest case of detecting between only one or two clusters with multivariate normal data, theoretically the number of tests needed seems to be infinite. Alternatively, suppose N independent estimates of generalized variances (GVs) are computed from a given set of p-dimensional vector observations. Assuming multivariate normality, tests based on GVs are proposed which objectively and uniquely determine, simultaneously, the number of clusters and their corresponding elements. Only a reasonably small nunber of tests are required for this stepwise procedure. The exact percentage points are either available from existing tables or can be computed from a result presented. 相似文献
20.
By modifying the method of projection, the results of Hajek and Huskova are extended to show the asymptotic normality of signed and linear rank statistics under general alternatives for dependent random variables that can be expressed as independent vectors of fixed equal length. The score function is twice differentiable; the regression constants are arbitrary; and the distribution functions are continuous, but arbitrary. As an application, a rank transform statistic is proposed for the one-sample multivariate location model. The ranks of the absolute values of the observations are calculated without regard to component membership, and the scored ranks are substituted in place of the observed values. The limiting distribution of the proposed test statistic is shown to be χ2 divided by the degrees of freedom under the null hypothesis, and noncentral χ2 divided by the degrees of freedom under the sequence of Pitman alternatives. 相似文献