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1.
S. Sylvia Chu K. C. S. Pillai 《Annals of the Institute of Statistical Mathematics》1979,31(1):185-205
Power studies of tests of equality of covariance matrices of twop-variate normal populations Σ1=Σ2 against two-sided alternatives have been made based on the following six criteria: 1) Roy's largest root, 2) Hotelling's
trace, 3) Pillai's trace, 4) Wilks' criterion, 5) Roy's largest-smallest roots and 6) modified likelihood ratio. A general
theorem has been proved establishing the local unbiasedness conditions connecting the two critical values for tests 1) to
5). Extensive unbiased power tabulations have been made forp=2, for various values ofn
1,n
2, λ1 and λ2 wheren
i
is the df of the SP matrix from theith sample and λ
i
is theith latent root of Σ1Σ
2
−1
(i=1,2). Further, comparisons of powers of tests 1) to 5) have been made with those of the modified likelihood ratio after obtaining
the exact distribution of the latter forn
2=2n
1 andp=2. Equal tail areas approach has also been used further to compute powers of tests 1) to 4) forp=2 for studying the bias. Again, a separate study has been made to compare the powers of the largest-smallest roots test with
its three biased approximate approaches as well as the largest root. Since the largest root test was observed to have some
advantage over the others, critical values were also obtained for this test in the unbiased as well as equal tail areas case
forp=3.
This research was supported by David Ross Grant from Purdue University.
S. Sylvia Chu is now with Northwestern University. 相似文献
2.
B. M. Bennett 《Annals of the Institute of Statistical Mathematics》1965,17(1):55-61
Summary As a test for the hypothesis of equality of means in a sample ofn matched pairs of observations from a single bivariate population in(x, y), Wilcoxon ([4], [5]) proposed a signed rank sum testU involving the differencesz=x\t-y. Tables of valuesUs have been provided forn of 50 or less and four significance levelsε. The following paper considers some generalizations of the Wilcoxon test for the case of matched bivariate or trivariate populations.
These tests utilize certain properties of thep-variate normal distribution when integrated over certain regions for the cases:p=2,3. 相似文献
3.
Jeff Kahn 《Combinatorica》1985,5(4):319-323
The following statement fork=1, 2, 3 has been proved by Tutte [4], Bixby [1] and Seymour [3] respectively: IfM is ak-connected non-binary matroid andX a set ofk-1 elements ofM, thenX is contained in someU
4
2
minor ofM. Seymour [3] asks whether this statement remains true fork=4; the purpose of this note is to show that it does not and to suggest some possible alternatives.
Supported in part by the National Science Foundation 相似文献
4.
Summary Wilks'L
mvc
is the likelihood ratio criterion for testing the hypothesis that the mean values are equal, the variances are equal and
the covariances are equal, in ap-variate normal population. In this article the exact null distribution as well as the exact percentage points are given for
the first time. The distribution is obtained for the most general cases and the inverse tables, namely, the values ofu for given values ofF(u) are computed for the values ofF(u)=0.01, 0.02, 0.05 and for the various values ofn andp whereF(u) is the exact distribution function of the test statistic,n=N−1 andN is the sample size. The exact tables are given forp=2, 3, 4, 5, 6, 7, 8, 9. 相似文献
5.
In [7], for the casesq even andq=3, a characterisation of the Buekenhout-Metz unitals inPG(2,q
2) was given. We complete this characterisation by proving the result forq>3. 相似文献
6.
In this paper we address the problem of testing the equality ofk intraclass correlation coefficients based on samples from independentp-variate normal populations, and explore various aspects of optimality through invariance. A UMPIU test is derived fork=2, and LMMPIU test of SenGupta and Vermeire (1986) is indicated fork>2. Several approximately optimum invariant tests are also proposed. The tests are compared with the approximate LR tests and Fisher'sZ-tests derived in Konishi and Gupta (1987, 1989). As expected, the performance of the proposed tests turns out to be quite satisfactory and superior to the LR tests andZ-tests. 相似文献
7.
Summary For estimating the mean of ap-variate normal distribution under a quadratic loss, a class of estimators, known as Stein's estimators, is known to dominate
the maximum likelihood estimator (MLE) forp≧3. But, whereas the risk of the MLE has the same value, equal to a constant, for each component, the maximum component risk
of Stein's estimator is large for large values ofp. Certain modification of Stein's rule has been proposed in the literature for reducing the maximum component risk. In this
paper, a new rule is given for reducing the maximum component risk. The new rule yields larger reduction in the maximum component
risk, compared to its competitor. 相似文献
8.
Alexander Abian 《Rendiconti del Circolo Matematico di Palermo》1990,39(2):307-314
Let the rows of an infinite square matrixM be elements ofl
p
-space (p>1) andX be an infinite column vector of unknowns andC an infinite column vector of real numbers. To our knowledge the solvability ofMX=C has nowhere been satisfactorily studied in the literature. This is also true of Riesz’classical work [2]. A reason for this
is that not until recently [1] an appropriate inner product and the corresponding orthonormalization forp≠2 has been introduced. In this paper, based on [1], it is shown thatMX=C has a solution which is an element ofl
q
if and only if upon our process of orthonormalization of the rows ofM the system yields an equivalent systemAX=K where the rows ofA form an orthonormal sequence (in our sense) of elements ofl
p
andK becomes an element ofl
q
withp
−1+q
−1=1. A solution is then given byX=(A
(q)
(AA
(q)
)−1)K whereA
(q)
is ourq-transpose ofA. This solution is the solution of the minimall
q
-norm. Otherwise, the obvious dual concept of the best approximating solution inl
q
-norm is introduced and obtained.
1980 Mathematics Subject Classification: Primary 46C10, Secondary 15A06 相似文献
9.
Summary The joint density function of the latent roots ofS
1
S
2
−1
under violations is obtained whereS
1 has a complex non-central Wishart distributionW
c
(p,n
1,Σ
1,Ω) andS
2, an independent complex central Wishart,W
c
(p,n
2,Σ
2, 0). The density and moments of Hotelling's trace are also derived under violations. Further, the non-null distributions
of the following four criteria in the two-roots case are studied for tests of three hypotheses: Hotelling's trace, Pillai's
trace, Wilks' criterion and Roy's largest root. In addition, tabulations of powers are carried out and power comparisons for
tests of each of three hypotheses based on the four criteria are made in the complex case extending such work of Pillai and
Jayachandran in the classical Gaussian case. The findings in the complex Gaussian are generally similar to those in the classical. 相似文献
10.
Kaiming Zhao 《数学学报(英文版)》1999,15(2):145-152
In this paper, automorphisms of the algebra ofq-difference operators, as an associative algebra for arbitraryq and as a Lie algebra forq being not a root of unity, are determined.
Project supported by the NNSF of China 相似文献
11.
On the generators of subgroups of unit groups of group rings 总被引:1,自引:0,他引:1
Ashwani K. Bhandari 《Bulletin of the Brazilian Mathematical Society》1990,20(2):87-93
In this paper we find the generators of a subgroup of finite index in the unit group of the integral group ring of the metacyclic
group of orderpq given byG=(a,x:a
p=1=x
q
,xax
−1=a
f
), wherep is an odd prime,q>2 a divisor ofp-1, andf belongs to the exponentq modulop. 相似文献
12.
For testing the independence of q-sets in a p-variate normal population, the asymptotic distributions of the likelihood ratio test, and the test proposed by the author under local alternatives are derived in terms of noncentral χ2 variates. 相似文献
13.
LetX be a Banach space and leta, b, q be real numbers such thata<b,q>0. Denote byD a locally closed subset ofX. A necessary and sufficient condition for the existence of a mild solutionu∈C([a−q, b
1],X),a<b
1<b, to the differential equationdu(t)/dt=Au(t)+f(t, u
t), such thatu:[a,b
1]→D, u
a=ϕ is given. The linear operatorA is the generator of aC
0 semigroupT(t), t≧0, withT(t) compact fort>0,f: [a, b)×C([−q,0],D
λ)→X is continuous and ϕ∈C([−q,0],D
λ) with ϕ(0)∈D. D
λ is a neighbourhood ofD. Applications to parabolic partial differential equations with retarded argument are given. 相似文献
14.
M. D. Atkinson 《Archiv der Mathematik》1979,32(1):530-532
Transitive permutation groups of degrees 43, 67, 79, 103 and 139 are classified.In this note we consider insoluble transitive permutation groups of degreeq = 6q+1 wherep andq are primes and summarise the computations whereby these groups have been classified for some small values ofq. The result which allows progress on this problem is due to McDonough [1]; he showed that if such a group has a Sylowp-normaliser of order 3p then it is isomorphic either toPSL(3, 3) orPAL(3, 5) (of degrees 13, 31 respectively). Using this theorem machine computations along the lines of those done by Parker, Nikolai and Appel [3, 2] for degreesp=2q+1 andp=4q+1 give the following 相似文献
15.
Ingrid Debroey 《Journal of Geometry》1980,14(2):159-163
In [1] S. ILKKA conjectured that pqeudoregular points of an elliptic quadric ofAG(2,q),q odd, only exist for small values ofq. In [3] B. SEGRE proves that an elliptic quadric ofAG(2,q),q odd, has pseudoregular points iffq=3 or 5. In [2], however, F. KáRTESZI shows that an elliptic quadric ofAG(2,7) has eight pseudoregular points. In this note we prove that part of B. Segre's proof is not correct, and that an elliptic quadric ofAG(2,q),q odd, has pseudoregular points iffq=3, 5 or 7. 相似文献
16.
H. Markšaitis 《Lithuanian Mathematical Journal》2000,40(1):39-47
LetK
p (p, q) be the maximalp-extension of the field ℚ of rational numbers with ramification pointsp andq. LetG
p (p, q) be the Galois group of the extensionK
p(p.q)/ℚ. It is known thatG
p(p, q) can be presented by two generators which satisfy a single relation. The form of this relation is known only modulo
the second member of the descending central series ofG
p(p, q). In this paper, we find an arithmetical-type condition on which the form of the relation modulo the third member of
the descending central series ofG
p(p, q) depends. We also consider two examples withp=3,q=19 andp=3,q=37.
Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 1, pp. 48–60, January–March, 2000.
Translated by H. Markšaitis 相似文献
17.
Summary We consider linear systems whose associated block Jacobi matricesJ
p are weakly cyclic of indexp. In a recent paper, Pierce, Hadjidimos and Plemmons [13] proved that the block two-cyclic successive overrelaxation (SOR) iterative method is numerically more effective than the blockq-cyclic SOR-method, 2<qp, if the eigenvalues ofJ
p
p
are either all non-negative or all non-positive. Based on the theory of stationaryp-step methods, we give an alternative proof of their theorem. We further determine the optimal relaxation parameter of thep-cyclic SOR method under the assumption that the eigenvalues ofJ
p
p
are contained in a real interval, thereby extending results due to Young [19] (for the casep=2) and Varga [15] (forp>2). Finally, as a counterpart to the result of Pierce, Hadjidimos and Plemmons, we show that, under this more general assumption, the two-cyclic SOR method is not always superior to theq-cyclic SOR method, 2<qp.Dedicated to R. S. Varga on the occasion of his 60th birthdayResearch supported in part by the Deutsche Forschungsgemeinschaft 相似文献
18.
Turán's problem is to determine the maximum numberT(n,k,t) oft-element subsets of ann-set without a complete sub-hypergraph onk vertices, i.e., allt-subsets of ak-set. It is proved that fora≥1 fixed andt sufficiently largeT(n, t+a,t)>(1-a(a+4+o(1))logt/(
a
t
)(
t
n
holds 相似文献
19.
20.
Carl G. Wagner 《Studies in Applied Mathematics》1994,93(1):15-27
The elementary problem of counting surjections from an n-set to a k-set is generalized to that of enumerating solutions of a1 ∨ ? ∨ an = y, with each ai an atom of the k-interval [x, y] in a binomial lattice L. When L is modular, the number of such solutions is representable as a q-difference and satisfies a simple recurrence. 相似文献