共查询到20条相似文献,搜索用时 15 毫秒
1.
Marie Hušková 《Journal of multivariate analysis》1975,5(4):487-496
In the present paper there is proposed a rank statistic for multivariate testing of randomness conceriing some marginal distributions. The asymptotic distribution of this statistic under hypothesis and “near” alternatives is treated. 相似文献
2.
Consider a right-invariant sub-Laplacian L on an exponential solvable Lie group G, endowed with a left-invariant Haar measure. Depending on the structure of G and possibly also that of L, L may admit differentiable Lp-functional calculi, or may be of holomorphic Lp-type for a given p≠2, as recent studies of specific classes of groups G and sub-Laplacians L have revealed. By “holomorphic Lp-type” we mean that every Lp-spectral multiplier for L is necessarily holomorphic in a complex neighborhood of some point in the L2-spectrum of L. This can only arise if the group algebra L1(G) is non-symmetric. In this article we prove that, for large classes of exponential groups, including all rank one AN-groups, a certain Lie algebraic condition, which characterizes the non-symmetry of L1(G) [37], also suffices for L to be of holomorphic L1-type. Moreover, if this condition, which was first introduced by J. Boidol [6] in a different context, holds for generic points in the dual
* of the Lie algebra of G, then L is of holomorphic Lp-type for every p≠2. Besides the non-symmetry of L1(G), also the closedness of coadjoint orbits plays a crucial role. We also discuss an example of a higher rank AN-group. This example and our results in the rank one case suggest that sub-Laplacians on exponential Lie groups may be of holomorphic L1-type if and only if there exists a closed coadjoint orbit Ω
* such that the points of Ω satisfy Boidol's condition. In the course of the proof of our main results, whose principal strategy is similar as in [8], we develop various tools which may be of independent interest and largely apply to more general Lie groups. Some of them are certainly known as “folklore” results. For instance, we study subelliptic estimates on representation spaces, the relation between spectral multipliers and unitary representations, and develop some “holomorphic” and “continuous” perturbation theory for images of sub-Laplacians under “smoothly varying” families of irreducible unitary representations. 相似文献
3.
In the univariate case it is well known that the one sided t test is uniformly most powerful for the null hypothesis against all one sided alternatives. Such a property does not easily extend to the multivariate case. In this paper, a test derived for the hypothesis that the mean of a vector random variable is zero against specified alternatives, when the covariance matrix is unknown. This test depends on the given alternatives and is more powerful than Hotelling's T2. The results are derived both for real and complex vector observations and under normal and spherical distributions. The properties of the proposed tests are investigated in detail when a single alternative is specified. 相似文献
4.
A new series representation of the exact distribution of Hotelling's generalized T02 statistic is obtained. Unlike earlier work, the series representation given here is everywhere convergent. Explicit formulae are given for both the null and the non-central distributions. Earlier results by [1], 215–225), which are convergent on the interval [0, 1), are also derived quite simply from our formulae. The paper therefore provides a solution to the long standing problem of the exact distribution of the T02 statistic in the general case. 相似文献
5.
Eugenia Stoimenova 《Applications of Mathematics》2007,52(4):345-352
Simple rank statistics are used to test that two samples come from the same distribution. Šidák’s E-test (Apl. Mat. 22 (1977), 166–175) is based on the number of observations from one sample that exceed all observations from the other sample.
A similar test statistic is defined in Ann. Inst. Stat. Math. 52 (1970), 255–266. We study asymptotic behavior of the moments of both statistics. 相似文献
6.
Yoshihiko Maesono 《Annals of the Institute of Statistical Mathematics》1987,39(1):363-375
Summary Distribution-free statistics are proposed for one-sample location test, and are compared with the Wilcoxon signed rank test.
It is shown that one of the statistics is superior to the Wilcoxon test in terms of approximate Bahadur efficiency. And we
compare that statistic with the Wilcoxon test from the viewpoint of asymptotic expansion of power function under contiguous
alternatives. 相似文献
7.
Ken-ichi Yoshihara 《Journal of multivariate analysis》1978,8(4):584-588
In 1974, Sen proved weak convergence of the empirical processes (in the J1-topology on Dp[0, 1]) for a stationary φ-mixing sequence of stochastic p( 1)-vectors. In this note, we show that Sen's theorem on weak convergence of the multidimensional empirical process for a stationary φ-mixing sequence of stochastic vectors remains true under a less restrictive condition on the mixing constants {φn}, i.e., φn = O(n−1−δ) for some δ > 0. 相似文献
8.
Nobuhiro Taneichi Yuri Sekiya Hideyuki Imai 《Annals of the Institute of Statistical Mathematics》2003,55(4):831-848
We consider multinomial goodness-of-fit tests for a specified simple hypothesis under the assumption of sparseness. It is
shown that the asymptotic normality of the PearsonX
2 statistic (X
k
2
) and the log-likelihood ratio statistic (G
k
2
) assuming sparseness. In this paper, we improve the asymptotic normality ofX
k
2
andG
k
2
statistics based on two kinds of normalizing transformation. The performance of the transformed statistics is numerically
investigated. 相似文献
9.
Let p be a prime divisor of the order of a finite group G. Thompson (1970, J. Algebra14, 129–134) has proved the following remarkable result: a finite group G is p-nilpotent if the degrees of all its nonlinear irreducible characters are divisible by p (in fact, in that case G is solvable). In this note, we prove that a group G, having only one nonlinear irreducible character of p′-degree is a cyclic extension of Thompson's group. This result is a consequence of the following theorem: A nonabelian simple group possesses two nonlinear irreducible characters χ1 and χ2 of distinct degrees such that p does not divide χ1(1)χ2(1) (here p is arbitrary but fixed). Our proof depends on the classification of finite simple groups. Some properties of solvable groups possessing exactly two nonlinear irreducible characters of p′-degree are proved. Some open questions are posed. 相似文献
10.
We study the complexity of automatic structures via well-established concepts from both logic and model theory, including ordinal heights (of well-founded relations), Scott ranks of structures, and Cantor–Bendixson ranks (of trees). We prove the following results: (1) The ordinal height of any automatic well-founded partial order is bounded by ωω. (2) The ordinal heights of automatic well-founded relations are unbounded below , the first non-computable ordinal. (3) For any computable ordinal α, there is an automatic structure of Scott rank at least α. Moreover, there are automatic structures of Scott rank . (4) For any computable ordinal α, there is an automatic successor tree of Cantor–Bendixson rank α. 相似文献
11.
Liudas Giraitis Piotr Kokoszka Remigijus Leipus Gilles Teyssière 《Acta Appl Math》2003,78(1-3):285-299
The paper deals with the power and robustness of the R/S type tests under contiguous alternatives. We briefly review some long memory models in levels and volatility, and describe the R/S-type tests used to test for the presence of long memory. The empirical power of the tests is investigated when replacing the fractional difference operator (1–L)
d
by the operator (1–rL)
d
, with r<1 close to 1, in the FARIMA, LARCH and ARCH time series models. We also investigate the Gegenbauer process with a pole of the spectral density at frequency close to zero. 相似文献
12.
Marie Hušková 《Journal of multivariate analysis》1977,7(1):63-73
The rates of convergence of the distribution function of quadratic rank statistics to the X2-distribution under hypothesis and near alternatives are investigated. The considered quadratic rank statistics are used for testing the multivariate hypothesis of randomness. The method suggested by Jure?ková [7] is applied. 相似文献
13.
Summary The members of the power divergence family of statistics
all have an asymptotically equivalent χ2 distribution (Cressie and Read [1]). An asymptotic expansion for the distribution function is derived which shows that the
speed of convergence to this asymptotic limit is dependent on λ. Known results for Pearson'sX
2 statistic and the log-likelihood ratio statistic then appear as special cases in a continuum rather than as separate (unrelated)
expansions. 相似文献
14.
Yasunori Fujikoshi 《Journal of multivariate analysis》2000,72(2):249
Suppose that a nonnegative statistic T is asymptotically distributed as a chi-squared distribution with f degrees of freedom, χ2f, as a positive number n tends to infinity. Bartlett correction T was originally proposed so that its mean is coincident with the one of χ2f up to the order O(n−1). For log-likelihood ratio statistics, many authors have shown that the Bartlett corrections are asymptotically distributed as χ2f up to O(n−1), or with errors of terms of O(n−2). Bartlett-type corrections are an extension of Bartlett corrections to other statistics than log-likelihood ratio statistics. These corrections have been constructed by using their asymptotic expansions up to O(n−1). The purpose of the present paper is to propose some monotone transformations so that the first two moments of transformed statistics are coincident with the ones of χ2f up to O(n−1). It may be noted that the proposed transformations can be applied to a wide class of statistics whether their asymptotic expansions are available or not. A numerical study of some test statistics that are not a log-likelihood ratio statistic is discribed. It is shown that the proposed transformations of these statistics give a larger improvement to the chi-squared approximation than do the Bartlett corrections. Further, it is seen that the proposed approximations are comparable with the approximation based on an Edgeworth expansion. 相似文献
15.
We consider a family of basic nonstationary wavelet packets generated using the Haar filters except for a finite number of scales where we allow the use of arbitrary filters. Such a system, which we call a system of Walsh-type wavelet packets, can be considered as a smooth generalization of the Walsh functions. We show that the basic Walsh-type wavelet packets share a number of metric properties with the Walsh system. We prove that the system constitutes a Schauder basis for Lp(
), 1<p<∞, and we construct an explicit function in L1(
) for which the expansion fails. Then we prove that expansions of Lp(
)-functions, 1<p<∞, in the Walsh-type wavelet packets converge pointwise a.e. Finally, we prove that the analogous results are true for periodic Walsh-type wavelet packets in Lp[0,1). 相似文献
16.
In this paper we develop a criterion for existence or non-existence of self-intersection local time (SILT) for a wide class of Gaussian
′(
d)-valued processes, we show that quite generally the SILT process has continuous paths, and we give several examples which illustrate existence of SILT for different ranges of dimensions (e.g., d ≤ 3, d ≤ 7 and 5 ≤ d ≤ 11 in the Brownian case). Some of the examples involve branching and exhibit “dimension gaps”. Our results generalize the work of Adler and coauthors, who studied the special case of “density processes” and proved that SILT paths are cadlag in the Brownian case making use of a “particle picture” approximation (this technique is not available for our general formulation). 相似文献
17.
Shashikala Sukhatme 《Journal of multivariate analysis》1983,13(4):539-549
Let Y1,…, Yn be independent identically distributed random variables with distribution function F(x, θ), θ = (θ′1, θ′2), where θi (i = 1, 2) is a vector of pi components, p = p1 + p2 and for θI, an open interval in
p, F(x, θ) is continuous. In the present paper the author shows that the asymptotic distribution of modified Cramér-Smirnov statistic under Hn: θ1 = θ10 + n−1/2γ, θ2 unspecified, where γ is a given vector independent of n, is the distribution of a sum of weighted noncentral χ12 variables whose weights are eigenvalues of a covariance function of a Gaussian process and noncentrality parameters are Fourier coefficients of the mean function of the Gaussian process. Further, the author exploits the special form of the covariance function by using perturbation theory to obtain the noncentrality parameters and the weights. The technique is applicable to other goodness-of-fit statistics such as U2 [G. S. Watson, Biometrika 48 (1961), 109–114]. 相似文献
18.
We consider two basic potential theoretic problems in Riemannian manifolds: Hodge decompositions and Maxwell's equations. Here we are concerned with smoothness and integrability assumptions. In the context of Lp forms in Lipschitz domains, we show that both are well posed provided that 2−<p<2+, for some >0, depending on the domain. Our approach is constructive (in the sense that we produce integral representation formulas for the solutions) and emphasizes the intimate connections between the two problems at hand. Applications to other related PDEs, such as boundary problems for the Hodge Dirac operator, are also presented. 相似文献
19.
Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C : K → 2Y a point-to-set mapping such that for any χ ε K, C(χ) is a pointed, closed, and convex cone in Y and int C(χ) ≠ 0. Given a mapping g : K → K and a vector valued bifunction f : K × K → Y, we consider the implicit vector equilibrium problem (IVEP) of finding χ* ε K such that f g(χ*), y) -int C(χ) for all y ε K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. 相似文献
20.
Recently, active research has been performed on constructing t-designs from linear codes over Z
4. In this paper, we will construct a new simple 3 – (2
m
, 7, 14/3 (2
m
– 8)) design from codewords of Hamming weight 7 in the Z
4-Goethals code for odd m 5. For 3 arbitrary positions, we will count the number of codewords of Hamming weight 7 whose support includes those 3 positions. This counting can be simplified by using the double-transitivity of the Goethals code and divided into small cases. It turns out interestingly that, in almost all cases, this count is related to the value of a Kloosterman sum. As a result, we can also prove a new Kloosterman sum identity while deriving the 3-design. 相似文献