共查询到20条相似文献,搜索用时 15 毫秒
1.
Multivariate tree-indexed Markov processes are discussed with applications. A Galton-Watson super-critical branching process is used to model the random tree-indexed process. Martingale estimating functions are used as a basic framework to discuss asymptotic properties and optimality of estimators and tests. The limit distributions of the estimators turn out to be mixtures of normals rather than normal. Also, the non-null limit distributions of standard test statistics such as Wald, Rao’s score, and likelihood ratio statistics are shown to have mixtures of non-central chi-square distributions. The models discussed in this paper belong to the local asymptotic mixed normal family. Consequently, non-standard limit results are obtained. 相似文献
2.
Jugal Ghorai 《Annals of the Institute of Statistical Mathematics》1980,32(1):341-350
LetX
1,...,X
n
be i.i.d. random variable with a common densityf. Let
be an estimate off(x) based on a complete orthonormal basis {φ
k
:k≧0} ofL
2[a, b]. A Martingale central limit theorem is used to show that
, where
and
. 相似文献
3.
We develop a martingale-based decomposition for a general class of quadratic forms of Markov chains, which resembles the well-known Hoeffding decomposition of U-statistics of i.i.d. data up to a reminder term. To illustrate the applicability of our results, we discuss how this decomposition may be used to studying the large-sample properties of certain statistics in two problems: (i) we examine the asymptotic behavior of lag-window estimators in time series, and (ii) we derive an asymptotic linear representation and limiting distribution of U-statistics with varying kernels in time series. We also discuss simplified examples of interest in statistics and econometrics. 相似文献
4.
We consider statistics of the form
, where the Xj are i.i.d. random variables with finite sixth moment. We obtain the rate of convergence in the central limit theorem for
the one-term Edgeworth expansion. Furthermore, applications to Toeplitz matrices, quadratic form of ARMA-processes, goodness-of-fit,
as well as spacing statistics are included. Bibliography: 16 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 81–114. 相似文献
5.
6.
Sadanori Konishi Naoto Niki Arjun K. Gupta 《Annals of the Institute of Statistical Mathematics》1988,40(2):279-296
Higher order asymptotic expansions for the distribution of quadratic forms in normal variables are obtained. The Cornish-Fisher inverse expansions for the percentiles of the distribution are also given. The resulting formula for a definite quadratic form guarantees accuracy almost up to fourth decimal place if the distribution is not very skew. The normalizing transformation investigated by Jensen and Solomon (1972, J. Amer. Statist. Assoc., 67, 898–902) is reconsidered based on the rate of convergence to the normal distribution.Faculty of Science, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812 Japan 相似文献
7.
Rainer Dahlhaus 《Journal of multivariate analysis》1985,16(3):412-431
The asymptotic normality of some spectral estimates, including a functional central limit theorem for an estimate of the spectral distribution function, is proved for fourth-order stationary processes. In contrast to known results it is not assumed that all moments exist or that the process is linear. The data are allowed to be tapered. Using some recent results on the central limit theorem for stationary processes, corollaries are obtained for strong and φ-mixing sequences and linear transformations of martingale differences. 相似文献
8.
Stefan Jaschke Claudia Klüppelberg Alexander Lindner 《Journal of multivariate analysis》2004,88(2):252-273
We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension. 相似文献
9.
10.
The paper considers higher-order cumulant spectral estimates obtained by directly Fourier transforming weighted cumulant estimates. Such estimates computationally are different from those based on the finite Fourier transform. These estimates can be looked at continuously as well as directly on submanifolds. The estimates of cumulants are based on unbiased moment estimates. Asymptotic normality is obtained for these estimates and is based on a strong mixing condition and only a finite number of cumulant summability conditions. 相似文献
11.
12.
Dinh Tuan Pham Joachim Möcks Lothar Sroka 《Annals of the Institute of Statistical Mathematics》1989,41(3):415-427
The paper provides sufficient conditions for the asymptotic normality of statistics of the form a
ijbRiRj, wherea
ijandb
ijare real numbers andR
iis a random permutation. 相似文献
13.
U. M. Pachev 《Journal of Mathematical Sciences》2007,146(2):5717-5722
Asymptotic formulas for the number of classes of positive binary quadratic forms with conditions of divisibility of extreme
coefficients are obtained by the discrete ergodic method.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 123–130, 2005. 相似文献
14.
Acta Mathematica Hungarica - We consider weakenings of normality in $$\Psi$$ -spaces and prove that the existence of an AD family whose $$\Psi$$ -space is almost-normal but not normal follows from... 相似文献
15.
16.
Svetozar Kurepa 《Aequationes Mathematicae》1987,34(2-3):125-138
The present paper is related to the Jordan—von Neumann characterization of inner product spaces, to the Halperin problem concerning quadratic forms, to some results of the present author on quadratic and sesquilinear forms and to recently obtained results of C. T. Ng and of J. Vukman.Dedicated to Professor Otto Haupt with best wishes on his 100th birthday. 相似文献
17.
18.
《Applied and Computational Harmonic Analysis》2020,48(1):321-342
This current paper shows the asymptotic normality for wavelet deconvolution density estimators, when a density function belongs to some and the noises are moderately ill-posed with the index β. The estimators include both the linear and non-linear wavelet ones. It turns out that the situation for is more complicated than that for . 相似文献
19.
Docent Bengt Rosén 《Probability Theory and Related Fields》1969,13(3-4):256-279
Summary Let {a
s
, s=1, 2, ..., N} be a set of reals and {p
s
, s=1, 2, ..., N} be a set of probabilities, i.e. p
s0 and p
1+p
2+...+p
N
=1. Let I
1
I
2,... be independent random variables, all with the distribution P(I=s)=p
s
, s=1, 2, ..., N. Put U
v
=l if I
v
{I
1, I
2, ..., I
v
–1} and U
v
=0 otherwise, v=1, 2, .... The random variable Z
n
=
is called the bonus sum after ncoupons for a coupon collector in the situation {(p
s
, a
s
), s=1, 2, ..., N}.Consider a sequence {(p
ks
, a
ks
), s=l, 2, ..., N
k
}, k=1, 2, ..., of collector situations, and let {Z
n
(k)
, n=1, 2, ...}, k=1, 2, ..., be the corresponding sequence of bonus sum variables. Let d be an arbitrary natural number and let
, k=1, 2, ..., where 1 n
k
(1)<n
k
(2)<< n
k
(d)
.We assume that N
(k)
t8 and that
.It is shown that the random vector V
(k)
is, under general conditions, asymptotically (as kt8) normally distributed. An asymptotic expression for the covariance matrix of V
(k)
is derived.Research supported in part at Stanford University, Stanford, California under contract N0014-67-A-0112-0015. 相似文献
20.
Burton W Jones 《Journal of Number Theory》1977,9(4):393-412
Let f be a quadratic form in n variables (n > 1) with nonzero determinant d. A prime p is said to be exceptional with respect to f if every automorph of f with rational elements, determinant ±1 and denominator prime to 2d has a denominator which is a quadratic residue of p. (Throughout, slight modifications must be made if p = 2.) Except for certain binary forms, each exceptional prime induces a splitting of the genus into two quasi-genera. Building on previous results, necessary and sufficient conditions are given that a prime p be exceptional for n = 2 and n = 3 and necessary conditions for n > 3. It is proved that there are no exceptional primes for n > 4 and only possibly in special cases for n = 4. A connection is shown between representations of integers by certain ternary forms and the existence of quasi-genera. Possible connections with spinor genera are mentioned and a few unanswered questions are posed. 相似文献