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1.
Testing the equality of several gamma means: a parametric bootstrap method with applications 总被引:2,自引:0,他引:2
We apply a recently developed ‘Computational Approach Test’ (CAT), a variant of the parametric bootstrap method, to test the
equality of means of several gamma distributions. All parameters are assumed to be unknown, and we consider two cases-(i)
the shape parameters, though unknown, are assumed to be equal; and (ii) the shape parameters are all unknown and possibly
unequal. The CAT, as applied to the above two cases, doesn’t require the knowledge of any sampling distribution, depends heavily
on numerical computations and Monte-Carlo simulation, and figures out the critical region automatically. The power and/or
size of our proposed CAT is quite encouraging compared with the other tests reported in the literature. The proposed method
can be used as a logical alternative approach to classical one-way ANOVA when one is not sure about normality, and positively
skewed distribution is a possibility for the observed data. Though the proposed CAT has been used recently to compare normal
means by the present authors, its usefulness for comparing gamma means hadn’t been studied before. This paper shows that the
CAT can be as good as, if not better than, the other proposed methods discussed in the literature to test the equality of
several gamma means. Real life datasets have been used to illustrate the applicability of this method. Also, our comprehensive
numerical study reveals that some of the frequently cited methods are not as good as they are claimed to be. 相似文献
2.
For several decades, much attention has been paid to the two-sample Behrens-Fisher (BF) problem which tests the equality of
the means or mean vectors of two normal populations with unequal variance/covariance structures. Little work, however, has
been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal
populations with unequal covariance structures. In this paper we study this challenging problem via extending the famous Scheffe’s
transformation method, which reduces the k-sample BF problem to a one-sample problem. The induced one-sample problem can be easily tested by the classical Hotelling’s
T
2 test when the size of the resulting sample is very large relative to its dimensionality. For high dimensional data, however,
the dimensionality of the resulting sample is often very large, and even much larger than its sample size, which makes the
classical Hotelling’s T
2 test not powerful or not even well defined. To overcome this difficulty, we propose and study an L
2-norm based test. The asymptotic powers of the proposed L
2-norm based test and Hotelling’s T
2 test are derived and theoretically compared. Methods for implementing the L
2-norm based test are described. Simulation studies are conducted to compare the L
2-norm based test and Hotelling’s T
2 test when the latter can be well defined, and to compare the proposed implementation methods for the L
2-norm based test otherwise. The methodologies are motivated and illustrated by a real data example.
The work was supported by the National University of Singapore Academic Research Grant (Grant No. R-155-000-085-112) 相似文献
3.
Júlia Volaufová 《Mathematica Slovaca》2009,59(6):679-692
Seemingly, testing for fixed effects in linear models with variance-covariance components has been solved for decades. However,
even in simple situations such as in fixed one-way model with heteroscedastic variances (a multiple means case of the Behrens-Fisher
problem) the questions of statistical properties of various approximations of test statistics are still alive. Here we present
a brief overview of several approaches suggested in the literature as well as those available in statistical software, accompanied
by a simulation study in which the accuracy of p-values is studied. Our interest is limited here to the Welch’s test, the
Satterthwaite-Fai-Cornelius test, the Kenward-Roger test, the simple ANOVA F-test, and the parametric bootstrap test. We conclude that for small sample sizes, regardless the number of compared means
and the heterogeneity of variance, the ANOVA F-test p-value performs the best. For higher sample sizes (at least 5 per group), the parametric bootstrap performs well, and the
Kenward-Roger test also performs well. 相似文献
4.
S. R. Kulkarni 《Annals of the Institute of Statistical Mathematics》1973,25(1):187-203
Summary Suppose we have two independent experiments conducted with a set of ‘t’ treatments each, at different places. This paper deals with two interesting problems of testing of hypotheses associated
with these experiments. The first problem deals with the test of the equality of the respective treatment effects in the two
experiments. The second problem is concerned with the testing of the equality of treatment into places interactions. Though
we assume normality, the variance σ
1
2
in one experiment is assumed different from the variance σ
2
2
in the other experiment. When no information is available aboutR=σ
1
2
/(σ
1
2
+σ
2
2
) except that 0≦R≦1, tests known as ‘bilateral tests’ are proposed in the literature, to test the hypotheses mentioned above. This paper studies
some important small sample properties of these bilateral tests. More specifically we study the probability of the first and
second kind of error of these bilateral tests as a function ofR. When the two experiments have the same number of observations on each treatment, the bilateral test is shown to control
the first kind of error. Fort=1,2, the level of these tests is a strictly convex function ofR and hence these tests can be very conservative. Some power properties of these tests are also obtained. Two tests which are
equivalent to the bilateral tests for large sample sizes, and which are superior to the bilateral tests for small sample sizes,
are obtained. 相似文献
5.
Hossein Ghodosi 《Designs, Codes and Cryptography》2011,60(1):63-66
Detection of cheating and identification of cheaters in threshold schemes has been well studied, and several solid solutions
have been provided in the literature. This paper analyses Harn and Lin’s recent work on cheating detection and identification
of cheaters in Shamir’s threshold scheme. We will show that, in a broad area, Harn–Lin’s scheme fails to detect cheating and
even if the cheating is detected cannot identify the cheaters. In particular, in a typical Shamir (t, n)-threshold scheme, where n = 2t − 1 and up to t − 1 of participants are corrupted, their scheme neither can detect nor can identify the cheaters. Moreover, for moderate
size of groups their proposed cheaters identification scheme is not practical. 相似文献
6.
Abraham Zaks 《Israel Journal of Mathematics》1980,37(4):281-302
LetR be a commutative domain with 1. We termR an HFD (Half-Factorial-Domain) provided the equality Π
i=1
n
χi=Π{f=1/m}y
f impliesm=n, whenever thex’s and they’s are non-zero, non-unit and irreducible elements ofR. The purpose of this note is to study HFD’s, in particular, Krull domains that are HFD’s, and to provide examples of HFD’s,
that contradict a conjecture of Narkiewicz. 相似文献
7.
Koen Thas 《Designs, Codes and Cryptography》2008,47(1-3):221-224
We show that a generalized quadrangle of order (s, t) with a center of transitivity is an elation generalized quadrangle if s ≤ t. In order to obtain this result, we generalize Frohardt’s result on Kantor’s conjecture from elation quadrangles to the more
general case of quadrangles with a center of transitivity.
相似文献
8.
9.
F. Carbonell K. J. Worsley L. Galan 《Annals of the Institute of Statistical Mathematics》2011,63(1):1-27
The statistical problem addressed in this paper is to approximate the P value of the maximum of a smooth random field of Wilks’s Λ statistics. So far results are only available for the usual univariate
statistics (Z, t, χ2, F) and a few multivariate statistics (Hotelling’s T
2, maximum canonical correlation, Roy’s maximum root). We derive results for any differentiable scalar function of two independent
Wishart random fields, such as Wilks’s Λ random field. We apply our results to a problem in brain shape analysis. 相似文献
10.
In this paper we propose a method to construct more general fuzzy sets using ordinary fuzzy sets as building blocks. We introduce
the concept of multi-fuzzy sets in terms of ordered sequences of membership functions. The family of operations T, S, M of multi-fuzzy sets are introduced by coordinate wise t-norms, s-norms and aggregation operations. We define the notion of coordinate wise conjugation of multifuzzy sets, a method for obtaining
Atanassov’s intuitionistic fuzzy operations from multi-fuzzy sets. We show that various binary operations in Atanassov’s intuitionistic
fuzzy sets are equivalent to some operations in multi-fuzzy sets like M operations, 2-conjugates of the T and S operations. It is concluded that multi-fuzzy set theory is an extension of Zadeh’s fuzzy set theory, Atanassov’s intuitionsitic
fuzzy set theory and L-fuzzy set theory. 相似文献
11.
Soichi Okada 《Journal of Algebraic Combinatorics》2010,32(3):399-416
We generalize multivariate hook product formulae for P-partitions. We use Macdonald symmetric functions to prove a (q,t)-deformation of Gansner’s hook product formula for the generating functions of reverse (shifted) plane partitions. (The unshifted
case has also been proved by Adachi.) For a d-complete poset, we present a conjectural (q,t)-deformation of Peterson–Proctor’s hook product formula. 相似文献
12.
Remmers (Adv. Math. 36:283–296, 1980) uses group diagrams in the Euclidean plane to demonstrate how equality in a semigroup S “mirrors” that inside the group G sharing the same presentation with S, when S satisfies Adyan’s condition—no cycles in the left/right graphs of the semigroup’s presentation. Goldstein and Teymouri (Semigroup
Forum 47:299–304, 1993) introduce a conjugacy equivalence relation for semigroups S. By closely examining the geometry of annular group diagrams in the plane, they show how their equivalence relation mirrors
conjugacy inside G, for S satisfying Adyan’s. In this article we introduce two cancellative commutative congruences. Following their leads, we examine
the geometry of group diagrams on closed surfaces of higher genera to demonstrate how these congruences mirror equality inside
two naturally associated Abelian quotient groups G/[G,G] and G/G
2, respectively. In these instances we can drop Adyan’s condition. 相似文献
13.
This paper studies the possibility to calculate efficiently compounds of real matrices which have a special form or structure.
The usefulness of such an effort lies in the fact that the computation of compound matrices, which is generally noneffective
due to its high complexity, is encountered in several applications. A new approach for computing the Singular Value Decompositions
(SVD’s) of the compounds of a matrix is proposed by establishing the equality (up to a permutation) between the compounds
of the SVD of a matrix and the SVD’s of the compounds of the matrix. The superiority of the new idea over the standard method
is demonstrated. Similar approaches with some limitations can be adopted for other matrix factorizations, too. Furthermore,
formulas for the n − 1 compounds of Hadamard matrices are derived, which dodge the strenuous computations of the respective numerous large determinants.
Finally, a combinatorial counting technique for finding the compounds of diagonal matrices is illustrated.
相似文献
14.
In this paper we generalize and sharpen D. Sullivan’s logarithm law for geodesics by specifying conditions on a sequence of
subsets {A
t
| t∈ℕ} of a homogeneous space G/Γ (G a semisimple Lie group, Γ an irreducible lattice) and a sequence of elements f
t
of G under which #{t∈ℕ | f
t
x∈A
t
} is infinite for a.e. x∈G/Γ. The main tool is exponential decay of correlation coefficients of smooth functions on G/Γ. Besides the general (higher rank) version of Sullivan’s result, as a consequence we obtain a new proof of the classical
Khinchin-Groshev theorem on simultaneous Diophantine approximation, and settle a conjecture recently made by M. Skriganov.
Oblatum 27-VII-1998 & 2-IV-1999 / Published online: 5 August 1999 相似文献
15.
Z. Ditzian 《Israel Journal of Mathematics》1971,9(4):541-553
Rate of convergence in terms of the modulus of continuity of eitherT(t)f or ofT(t)Af, whereT(t) is a strongly continuous semi-group of operators, is obtained for Phillips’ and for Widder’s exponential formula. 相似文献
16.
Peter Müller 《Israel Journal of Mathematics》1999,109(1):319-337
Letf (X, t)εℚ[X, t] be an irreducible polynomial. Hilbert’s irreducibility theorem asserts that there are infinitely manyt
0εℤ such thatf (X, t
0) is still irreducible. We say thatf (X, t) isgeneral if the Galois group off (X, t) over ℚ(t) is the symmetric group in its natural action. We show that if the degree off with respect toX is a prime ≠ 5 or iff is general of degree ≠ 5, thenf (X, t
0) is irreducible for all but finitely manyt
0εℤ unless the curve given byf (X, t)=0 has infinitely many points (x
0,t
0) withx
0εℚ,t
0εℤ. The proof makes use of Siegel’s theorem about integral points on algebraic curves, and classical results about finite
groups, going back to Burnside, Schur, Wielandt, and others.
Supported by the DFG. 相似文献
17.
We say that f: ℝ → ℝ is LIF if it is linearly independent over ℚ as a subset of ℝ2 and that it is a Hamel function (HF) if it is a Hamel basis of ℝ2. We construct an example of HF bijection and use a similar method to prove that any function can be represented as the composition
of three HF’s as well as the limit of uniformly convergent sequence of HF’s. Finally we consider products of HF’s, maximal
invariant classes (with respect to several algebraic operations) and pose some open problems concerning sets of continuity
points of HF’s. 相似文献
18.
A. S. Gordienko 《Journal of Mathematical Sciences》2010,164(2):188-194
Let A be a finite-dimensional associative algebra over a field of characteristic 0. Then there exist C ∈ ℚ+ and t ∈ ℤ+ such that gc
n
(A) ∼ Cn
t
d
n
as n → ∞, where d = PIexp(A). In particular, Amitsur’s and Regev’s conjectures hold for the codimensions gc
n
(A) of generalized polynomial identities. 相似文献
19.
We add two sections to [8] and answer some questions asked there. In the first section we give another derivation of Theorem
1.1 of [8], which reveals the relation between the entropy formula, (1.4) of [8], and the well-known Li-Yau ’s gradient estimate.
As a by-product we obtain the sharp estimates on ‘Nash’s entropy’ for manifolds with nonnegative Ricci curvature. We also
show that the equality holds in Li-Yau’s gradient estimate, for some positive solution to the heat equation, at some positive
time, implies that the complete Riemannian manifold with nonnegative Ricci curvature is isometric to ℝ
n
.In the second section we derive a dual entropy formula which, to some degree, connects Hamilton’s entropy with Perelman ’s
entropy in the case of Riemann surfaces. 相似文献
20.
V. I. Dmitriev E. S. Kurkina O. E. Simakova 《Computational Mathematics and Modeling》2011,22(1):54-68
The article models the distribution of cities by population. Two approaches are considered to mathematical modeling of urban
growth: a probability model in which the number of cities depends on the population and the rank model of distribution of
cities by their population. Five population censuses are analyzed for Russia’s cities. The probability density function n(x, α) for the number of cities as a function of their population x is fitted to all the available censuses with a time-dependent coefficient α . The function α(t ) is approximated and a prediction for the nearest future is computed. In particular, it is shown that in 2010 compared with
2002 the number of large cities should increase, while the number of small town should decrease. A model is also proposed
for the interaction of urban areas linked into a single hierarchical system. The model is based on a system of ordinary differential
equations describing the change in urban population. Independently of the initial distribution, all the cities and town line
up by the rank–size law and deviations from this law, as in real life, are observed only for some large and very small cities.
Model parameters are fitted for Russia’s cities. 相似文献