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1.
We present an exact formula for moments and cumulants of several real compound Wishart matrices in terms of an Euler characteristic
expansion, similar to the genus expansion for complex random matrices. We consider their asymptotic values in the large matrix
limit: as in a genus expansion, the terms which survive in the large matrix limit are those with the greatest Euler characteristic,
that is, either spheres or collections of spheres. This topological construction motivates an algebraic expression for the
moments and cumulants in terms of the symmetric group. We examine the combinatorial properties distinguishing the leading
order terms. By considering higher cumulants, we give a central-limit-type theorem for the asymptotic distribution around
the expected value. 相似文献
2.
In this article, multivariate density expansions for the sample correlation matrix R are derived. The density of R is expressed through multivariate normal and through Wishart distributions. Also, an asymptotic expansion of the characteristic function of R is derived and the main terms of the first three cumulants of R are obtained in matrix form. These results make it possible to obtain asymptotic density expansions of multivariate functions of R in a direct way. 相似文献
3.
In this paper we obtain an asymptotic expansion for the distribution of Hotelling's T2-statistic T2under nonnormality when the sample size is large. In the derivation we find an explicit Edgeworth expansion of the multivariate t-statistic. Our method is to use the Edgeworth expansion and to expand the characteristic function of T2. 相似文献
4.
Asymptotic cumulants of the distributions of the sample singular vectors and values of cross covariance and correlation matrices
are obtained under nonnormality. The asymptotic cumulants are used to have the approximations of the distributions of the
estimators by the Edgeworth expansions up to order O(1/ n) and Hall’s method with variable transformation. The cases of Studentized estimators are also considered. As an application
of the method, the distributions of the parameter estimators in the model of inter-battery factor analysis are expanded. Interpreting
the singular vectors and values in the context of the factor model with distributional conditions, the asymptotic robustness
of some lower-order normal-theory cumulants of the distributions of the sample singular vectors and values under nonnormality
is shown. 相似文献
5.
In this paper, we construct an asymptotic expansion of a time-harmonic wave scattered by N small spheres. This construction is based on the method of matched asymptotic expansions. Error estimates give a theoretical
background to the approach. 相似文献
6.
An asymptotic expansion of the null distribution of the Wilks’ lambda statistic is derived when some of the parameters are large. Cornish-Fisher expansions of the upper percent points are also obtained. A monotone transformation which reduces the third and the fourth order cumulants is also derived. In order to study the accuracy of the approximation formulas, some numerical experiments are done, with comparing to the classical expansions when only the sample size tends to infinity. 相似文献
7.
We prove a convergence acceleration result by the E-algorithm for sequences whose error has an asymptotic expansion on the scale of comparison for which a determinantal relation holds. This result is generalized to the vector case. Moreover we prove a result which contains an acceleration property for columns and diagonals of the E array. This result is applied to some alternating series. 相似文献
8.
In this paper we derive the asymptotic expansion of the null distribution of the F-statistic in one-way ANOVA under non-normality. The asymptotic framework is when the number of treatments is moderate but
sample size per treatment (replication size) is small. This kind of asymptotics will be relevant, for example, to agricultural
screening trials where large number of cultivars are compared with few replications per cultivar. There is also a huge potential
for the application of this kind of asymptotics in microarray experiments. Based on the asymptotic expansion we will devise
a transformation that speeds up the convergence to the limiting distribution. The results indicate that the approximation
based on limiting distribution are unsatisfactory unless number of treatments is very large. Our numerical investigations
reveal that our asymptotic expansion performs better than other methods in the literature when there is skewness in the data
or even when the data comes from a symmetric distribution with heavy tails. 相似文献
9.
The ε-Markov process is a general model of stochastic processes which includes nonlinear time series models, diffusion processes
with jumps, and many point processes. With a view to applications to the higher-order statistical inference, we will consider
a functional of the ε-Markov process admitting a stochastic expansion. Arbitrary order asymptotic expansion of the distribution
will be presented under a strong mixing condition. Applying these results, the third order asymptotic expansion of the M-estimator for a general stochastic process will be derived. The Malliavin calculus plays an essential role in this article.
We illustrate how to make the Malliavin operator in several concrete examples. We will also show that the thirdorder expansion
formula (Sakamoto and Yoshida (1998, ISM Cooperative Research Report, No. 107, 53–60; 1999, unpublished)) of the maximum likelihood
estimator for a diffusion process can be obtained as an example of our result. 相似文献
10.
In an abstract Wiener space setting, we construct a rigorous mathematical model of the one-loop approximation of the perturbative Chern–Simons integral, and derive its explicit asymptotic expansion for stochastic Wilson lines. 相似文献
11.
An “ m-consecutive- k-out-of- n: F system” consists of n components ordered on a line; the system fails if and only if there are at least m nonoverlapping runs of k consecutive failed components. In this paper, we give a recursive formula to compute the reliability of such a system. Thereafter,
we state two asymptotic results concerning the failure time Z
n
of the system. The first result concerns a limit theorem for Z
n
when the failure times of components are not necessarily with identical failure distributions. In the second one, we prove
that, for an arbitrary common failure distribution of components, the limit system failure distribution is always of the Poisson
class.
相似文献
12.
The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with
statistical inference on cosmological data. In this paper, we analyze its moments and cumulants of arbitrary order and we
use these results to establish a multivariate central limit theorem and higher order approximations. The results rely upon
combinatorial methods from graph theory and a detailed investigation for the asymptotic behavior of coefficients arising in
matrix representation theory for the group of rotations SO(3).
I am very grateful to an associate editor and two referees for many useful comments, and to M. W. Baldoni and P. Baldi for
discussions on an earlier version. 相似文献
13.
The purpose of the paper is three-fold: (a) we prove that every sequence which is a multidimensional sum of a balanced hypergeometric term has an asymptotic expansion of Gevrey type-1 with rational exponents, (b) we construct a class of G-functions that come from enumerative combinatorics, and (c) we give a counterexample to a question of Zeilberger that asks whether holonomic sequences can be written as multisums of balanced hypergeometric terms. The proofs utilize the notion of a G-function, introduced by Siegel, and its analytic/arithmetic properties shown recently by André. 相似文献
14.
In this note, we study the asymptotic properties of the ?-distribution of traces of some matrices, with respect to the free Haar trace on the unitary dual group. The considered matrices are powers of the unitary matrix generating the Brown algebra. We proceed in two steps, first computing the free cumulants of any R-cyclic family, then characterizing the asymptotic ?-distributions of the traces of powers of the generating matrix, thanks to these free cumulants. In particular, we obtain that these traces are asymptotic ?-free circular variables. 相似文献
15.
A system of equations that arises in a singularly perturbed optimal control problem is studied. We give conditions under which a formal asymptotic solution exists. This formal asymptotic solution consists of an outer expansion and left and right boundary-layer expansions. A feature of our procedure is that we do not a priori eliminate the control function from the problem. In particular, we construct a formal asymptotic expansion for the control directly. We apply our procedure to a Mayer-type problem. The paper concludes with a worked example. 相似文献
16.
Relations between moments and cumulants play a central role in both classical and non-commutative probability theory. The latter allows for several distinct families of cumulants corresponding to different types of independences: free, Boolean and monotone. Relations among those cumulants have been studied recently. In this work, we focus on the problem of expressing with a closed formula multivariate monotone cumulants in terms of free and Boolean cumulants. In the process, we introduce various constructions and statistics on non-crossing partitions. Our approach is based on a pre-Lie algebra structure on cumulant functionals. Relations among cumulants are described in terms of the pre-Lie Magnus expansion combined with results on the continuous Baker–Campbell–Hausdorff formula due to A. Murua. 相似文献
17.
In this paper we consider the sampling properties of the bootstrap process, that is, the empirical process obtained from a random sample of size n (with replacement) of a fixed sample of size n of a continuous distribution. The cumulants of the bootstrap process are given up to the order n
–1 and their unbiased estimation is discussed. Furthermore, it is shown that the bootstrap process has an asymptotic minimax property for some class of distributions up to the order n
–1/2. 相似文献
18.
We consider the classical M/G/1 queue with two priority classes and the nonpreemptive and preemptive-resume disciplines. We show that the low-priority steady-state
waiting-time can be expressed as a geometric random sum of i.i.d. random variables, just like the M/G/1 FIFO waiting-time distribution. We exploit this structures to determine the asymptotic behavior of the tail probabilities.
Unlike the FIFO case, there is routinely a region of the parameters such that the tail probabilities have non-exponential
asymptotics. This phenomenon even occurs when both service-time distributions are exponential. When non-exponential asymptotics
holds, the asymptotic form tends to be determined by the non-exponential asymptotics for the high-priority busy-period distribution.
We obtain asymptotic expansions for the low-priority waiting-time distribution by obtaining an asymptotic expansion for the
busy-period transform from Kendall's functional equation. We identify the boundary between the exponential and non-exponential
asymptotic regions. For the special cases of an exponential high-priority service-time distribution and of common general
service-time distributions, we obtain convenient explicit forms for the low-priority waiting-time transform. We also establish
asymptotic results for cases with long-tail service-time distributions. As with FIFO, the exponential asymptotics tend to
provide excellent approximations, while the non-exponential asymptotics do not, but the asymptotic relations indicate the
general form. In all cases, exact results can be obtained by numerically inverting the waiting-time transform.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
19.
This article shows an analytically tractable small noise asymptotic expansion with a sharp error estimate for the expectation of the solution to Young’s pathwise stochastic differential equations (SDEs) driven by fractional Brownian motions with the Hurst index H > 1/2. In particular, our asymptotic expansion can be regarded as small noise and small time asymptotics by the error estimate with Malliavin culculus. As an application, we give an expansion formula in one-dimensional general Young SDE driven by fractional Brownian motion. We show the validity of the expansion through numerical experiments. 相似文献
20.
In this paper, we provide an asymptotic expansion for the mean integrated squared error (MISE) of nonlinear wavelet estimator of survival density for a censorship model when the data exhibit some kind of dependence. It is assumed that the observations form a stationary and α‐mixing sequence. This asymptotic MISE expansion, when the density is only piecewise smooth, is same. However, for the kernel estimators, the MISE expansion fails if the additional smoothness assumption is absent. Also, we establish the asymptotic normality of the nonlinear wavelet estimator. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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