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1.
We propose a score statistic to test the null hypothesis that the two-component density functions are equal under a semiparametric finite mixture model. The proposed score test is based on a partial empirical likelihood function under an I-sample semiparametric model. The proposed score statistic has an asymptotic chi-squared distribution under the null hypothesis and an asymptotic noncentral chi-squared distribution under local alternatives to the null hypothesis. Moreover, we show that the proposed score test is asymptotically equivalent to a partial empirical likelihood ratio test and a Wald test. We present some results on a simulation study.  相似文献   

2.
We show that for every uncountable regular κ and every κ-complete Boolean algebra B of density ≤ κ there is a filter F ? B such that the number of partitions of length < modulo κF is ≤2. We apply this to Boolean algebras of the form P(X)/I, where I is a κ-complete κ-dense ideal on X. Mathematics Subject Classification: 06E05, 03C20.  相似文献   

3.
We consider the inverse limit space (I,f) of a unimodal bonding map f as fixed bonding map. If f has a periodic turning point, then (I,f) has a finite non-empty set of asymptotic arc-components. We show how asymptotic arc-components can be determined from the kneading sequence of f. This gives an alternative to the substitution tiling space approach taken by Barge and Diamond [Ergodic Theory Dynamical Systems 21 (2001) 1333].  相似文献   

4.
We give an alternative and direct approach to the Choquet integral representability of a comonotonically additive, bounded, monotone functional I defined on the space of all continuous, real-valued functions on a locally compact space X with compact support and on the space of all continuous, real-valued functions on X vanishing at infinity. To this end, we introduce the notion of the asymptotic translatability of the functional I and show that this simple notion is equivalent to the Choquet integral representability of I with respect to a monotone measure on X with appropriate regularity.  相似文献   

5.
In this paper recent results of Gregory [(1977)Ann. Statist.5 110–123] are used to obtain the asymptotic null distribution of a weighted Cramér-von Mises type test for independence. We use approximate Bahadur slopes to find good weight functions for certain alternatives. Some percentage points of the asymptotic distribution are given.  相似文献   

6.
A test of uniformity on the shape space Σmk is presented, together with modifications of the test statistic which bring its null distribution close to the large-sample asymptotic distribution. The asymptotic distribution under suitable local alternatives to uniformity is given. A family of distributions on Σmk is proposed, which is suitable for modelling shapes given by landmarks which are almost collinear.  相似文献   

7.
Let {Xn,n?1} be iid elliptical random vectors in Rd,d≥2 and let I,J be two non-empty disjoint index sets. Denote by Xn,I,Xn,J the subvectors of Xn with indices in I,J, respectively. For any aRd such that aJ is in the support of X1,J the conditional random sample Xn,I|Xn,J=aJ,n≥1 consists of elliptically distributed random vectors. In this paper we investigate the relation between the asymptotic behaviour of the multivariate extremes of the conditional sample and the unconditional one. We show that the asymptotic behaviour of the multivariate extremes of both samples is the same, provided that the associated random radius of X1 has distribution function in the max-domain of attraction of a univariate extreme value distribution.  相似文献   

8.
In the framework of ARMA models, we consider testing the reliability of the standard asymptotic covariance matrix (ACM) of the least-squares estimator. The standard formula for this ACM is derived under the assumption that the errors are independent and identically distributed, and is in general invalid when the errors are only uncorrelated. The test statistic is based on the difference between a conventional estimator of the ACM of the least-squares estimator of the ARMA coefficients and its robust HAC-type version. The asymptotic distribution of the HAC estimator is established under the null hypothesis of independence, and under a large class of alternatives. The asymptotic distribution of the proposed statistic is shown to be a standard χ2 under the null, and a noncentral χ2 under the alternatives. The choice of the HAC estimator is discussed through asymptotic power comparisons. The finite sample properties of the test are analyzed via Monte Carlo simulation.  相似文献   

9.
The asymptotic scattering matrix s ε(λ) for a Dirac-Krein system with signature matrix J = diag{ I p ,-I p }, integrable potential, and the boundary condition u 1(0, λ) = u 2(0, λ)ε(λ) with a coefficient ε(λ) that belongs to the Schur class of holomorphic contractive p × p matrix-valued functions in the open upper half-plane is defined. The inverse asymptotic scattering problem for a given s ε is analyzed by Krein’s method. Earlier studies by Krein and others focused on the case in which ε = I p (or a constant unitary matrix).  相似文献   

10.
An object is hidden in box i with probability Pi, for i = 1, 2,…, I. A search of a box detects the object, given that it is in the box, with probability d. The detection probability d is fixed but unknown. The asymptotic form of an optimal search policy is related to the behaviour near zero of the prior distribution for d.  相似文献   

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