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1.
A multivariate empirical characteristic function test of independence with normal marginals 总被引:1,自引:0,他引:1
This paper proposes a semi-parametric test of independence (or serial independence) between marginal vectors each of which is normally distributed but without assuming the joint normality of these marginal vectors. The test statistic is a Cramér–von Mises functional of a process defined from the empirical characteristic function. This process is defined similarly as the process of Ghoudi et al. [J. Multivariate Anal. 79 (2001) 191] built from the empirical distribution function and used to test for independence between univariate marginal variables. The test statistic can be represented as a V-statistic. It is consistent to detect any form of dependence. The weak convergence of the process is derived. The asymptotic distribution of the Cramér–von Mises functionals is approximated by the Cornish–Fisher expansion using a recursive formula for cumulants and inversion of the characteristic function with numerical evaluation of the eigenvalues. The test statistic is finally compared with Wilks statistic for testing the parametric hypothesis of independence in the one-way MANOVA model with random effects. 相似文献
2.
Adolfo J. Quiroz Miguel Nakamura Francisco J. Pérez 《Annals of the Institute of Statistical Mathematics》1996,48(4):687-709
Let X=(X
1, X
2,..., X
d
)
t
be a random vector of positive entries, such that for some =(1,2,...,
d
)
t
, the vector X
() defined by % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GaamiwamaaDaaaleaamiaadMgaaSqaaWGaaiikaiabeU7aSnaaBaaa% baGaamyAaiaacMcaaeqaaaaakiabg2da9iaacIcadaWcgaqaaiaadI% fadaqhaaWcbaadcaWGPbaaleaamiabeU7aSnaaBaaabaGaamyAaaqa% baaaaOGaeyOeI0IaaGymaiaacMcaaeaacqaH7oaBdaWgaaWcbaadca% WGPbGaaiilaaWcbeaakiaadMgacqGH9aqpcaaIXaGaeSOjGSKaaiil% aiaadsgaaaaaaa!53BB!\[X_i^{(\lambda _{i)} } = ({{X_i^{\lambda _i } - 1)} \mathord{\left/ {\vphantom {{X_i^{\lambda _i } - 1)} {\lambda _{i,} i = 1 \ldots ,d}}} \right. \kern-\nulldelimiterspace} {\lambda _{i,} i = 1 \ldots ,d}}\]is elliptically symmetric. We describe a procedure based on the multivariate empirical characteristic function for estimating the i's. Asymptotic results regarding consistency of the estimators are given and we evaluate their performance in simulated data. In a one-dimensional setting, comparisons are made with other available transformations to symmetry.Adolfo Quiroz and Miguel Nakamura's research was partially supported by CONACYT (Mexico) grants numbers 1858E9219 and 4224E9405, while Dr. Quiroz was visiting Centro de Investigación en Matemáticas at Guanajuato, Mexico. 相似文献
3.
E. M. Sukhanova 《Mathematical Methods of Statistics》2008,17(1):74-86
The paper presents a new nonparametric test for independence of two vectors. The idea is based on zonotope approach by G.
Koshevoy, H. Oja and others, see [4, 5]. Under the independence hypothesis the test statistic converges in distribution to
the supremum of a certain Gaussian field, and its asymptotic distribution is found using the theory of extrema of random Gaussian
fields developed by V. Piterbarg and Yu. Tyurin, see [6, 8]. In contrast to traditional correlation coefficients the formula
is not symmetric.
相似文献
4.
This paper considers the independence test for two stationary infinite order autoregressive processes. For a test, we follow
the empirical process method and construct the Cramér-von Mises type test statistics based on the least squares residuals.
It is shown that the proposed test statistics behave asymptotically the same as those based on true errors. Simulation results
are provided for illustration. 相似文献
5.
Summary Independent measurements are taken from distinct populations which may differ in mean, variance and in shape, for instance
in the number of modes and the heaviness of the tails. Our goal is to characterize differences between these different populations.
To avoid pre-judging the nature of the heterogeneity, for instance by assuming a parametric form, and to reduce the loss of
information by calculating summary statistics, the observations are transformed to the empirical characteristic function (ECF).
An eigen decomposition is applied to the ECFs to represent the populations as points in a low dimensional space and the choice
of optimal dimension is made by minimising a mean square error. Interpretation of these plots is naturally provided by the
corresponding density estimate obtained by inverting the ECF projected on the reduced dimension space. Some simulated examples
indicate the promise of the technique and an application to the growth of Mirabilis plants is given. 相似文献
6.
Sigeo Aki 《Annals of the Institute of Statistical Mathematics》1986,38(1):1-21
Summary It is proved that the martingale term of the empirical distribution function converges weakly to a Gaussian process inD[0, 1]. Some statistics for goodness-of-fit tests based on the martingale term of the empirical distribution function are
proposed. Asymptotic distributions of these statistics under the null hypothesis are given. The approximate Bahadur efficiencies
of the statistics to the Kolmogorov-Smirnov statistic and to the Cramér-von Mises statistic are also calculated.
The Institute of Statistical Mathematics 相似文献
7.
Terence J ONeill 《Statistics & probability letters》1985,3(5):269-274
Several bivariate exponential distributions have been proposed in the literature. A common problem for independent exponentials is to test the quality of the two distributions. The analogous problem for bivariate exponentials is to test for symmetry. For the bivariate exponential model of Freund (1961, Journal of the American Statistical Association 56, 971–977), tests of symmetry and independence are derived and the small sample distributions of the test statistics are found. The power function of the tests are calculated. The efficiency of the tests is found to be high on both an asymptotic and small sample basis. 相似文献
8.
John Kellermeier 《Journal of multivariate analysis》1980,10(1):78-87
The empirical characteristic function is considered as a tool for large sample testing of a hypothesis that can be characterized in terms of the characteristic function. Two test statistics based upon the empirical characteristic function are proposed. The limiting distributions of these test statistics are obtained and methods are suggested for using these limiting distributions to calculate critical regions. 相似文献
9.
Multivariate generalizations of Bhuchongkul's bivariate rank statistics [Ann. Math. Statist.35 (1964)] have been introduced and studied in this paper for the purpose of testing mulitvariate independence. It is shown that the test statistics can be expressed as rank statistics which are easy to compute, have asymptotic normal distributions, and can detect mutual dependence in alternatives which are pairwise independent. The tests are compared to the Puri-Sen-Gokhale [[8]] tests and a normal theory test [ [1]] using Pitman efficiency. 相似文献
10.
祁永成 《应用数学学报(英文版)》1997,13(2):167-175
ThisresearchissupportedbytheNationalNaturalScienceFoundationofChina.1.IntroductionandTheoremsSupposethatF(x,y)isabivariatedistributionfunctionwithtwocontinuousmarginaldistributionfunctions,say,FIandF2.DefineFissaidtohaveastabletaildependencefunction(STDF)l(x,y)ifforx20andy20,whereF(x,y)~1--F(QI(x),QZ(y)).TheconceptofSTDFwasintroducedin[6].Supposethat{(Xi,K),i21}isasequenceofi.i.d.randomvectorswithdistributionF(x,y).Ifthereedestsomesequencesofconstantsan>0,on>0,b.ERandd.ER,n>1.suc… 相似文献
11.
Youri Davydov Ricardas Zitikis 《Proceedings of the American Mathematical Society》2004,132(4):1203-1210
We consider weak convergence of empirical measures generated by stationary random process perturbed by deterministic noise . We assume that the noise has asymptotic distribution. In particular, we demonstrate that if the process is ergodic, or satisfies some mixing assumptions, then the influence of deterministic noise on is the same as it would be if were stochastic. Such results are of importance when investigating fluctuations and convex rearrangements of stochastic processes.
12.
Let (X, Y) be an
d ×
-valued random vector and let (X1, Y1),…,(XN, YN) be a random sample drawn from its distribution. Divide the data sequence into disjoint blocks of length l1, …, ln, find the nearest neighbor to X in each block and call the corresponding couple (Xi*, Yi*). It is shown that the estimate mn(X) = Σi = 1n wniYi*/Σi = 1n wni of m(X) = E{Y|X} satisfies E{|mn(X) − m(X)|p}
0 (p ≥ 1) whenever E{|Y|p} < ∞, ln
∞, and the triangular array of positive weights {wni} satisfies supi ≤ nwni/Σi = 1n wni
0. No other restrictions are put on the distribution of (X, Y). Also, some distribution-free results for the strong convergence of E{|mn(X) − m(X)|p|X1, Y1,…, XN, YN} to zero are included. Finally, an application to the discrimination problem is considered, and a discrimination rule is exhibited and shown to be strongly Bayes risk consistent for all distributions. 相似文献
13.
A modification of a test for independence based on the empirical characteristic function is investigated. The initial test
is not consistent in the general case. The modification makes the test always consistent and asymptotically distribution free.
It is based on a special transformation of the data.
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I. 相似文献
14.
LI Dong 《中国科学 数学(英文版)》2014,57(1):173-180
This paper studies the weak convergence of the sequential empirical process K n of the residuals in the threshold autoregressive(TAR)model of order p.Under some mild conditions,it is shown that K n converges weakly to a Kiefer process plus a random variable which converges to a multivariate normal.This differs from that given by Bai(1994)for a stationary autoregressive and moving average(ARMA)model. 相似文献
15.
Jerzy Rudnicki 《Statistics & probability letters》1984,2(2):83-89
The problem of testing the hypothesis of independence against multiparametrical set of alternatives is considered. Rank tests, having some locally maximin property are studied and a certain characterization of these tests is given. Finite sample and asymptotic test statistics in a restricted class of tests are derived. 相似文献
16.
Sigeo Aki 《Annals of the Institute of Statistical Mathematics》1987,39(1):457-472
Summary This paper is concerned with an extension of the problem of testing symmetry about zero of a distribution function. In order
to obtain the asymptotic null distribution of test statistics for the problem, a limit theorem is proved, which indeed plays
an essential role in the asymptotic theory of testing, problem for symmetry.
The Institute of Statistical Mathematics 相似文献
17.
Let X1, X2, …, Xn be random vectors that take values in a compact set in Rd, d ≥ 1. Let Y1, Y2, …, Yn be random variables (“the responses”) which conditionally on X1 = x1, …, Xn = xn are independent with densities f(y | xi, θ(xi)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θq,d of real valued functions, an optimal L1-consistent estimator
of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θq,d. 相似文献
18.
在加权线性损失下导出了刻度指数族中参数单调的Bayes检验函数,利用同分布负相协(NA)样本情形概率密度函数及其导数的核估计构造了经验Bayes(EB)检验函数,获得了EB检验函数的收敛速度.在适当的条件下,这一收敛速度可任意接近O(n~(-1)),改进了文献中已有的结果.对同分布正相协(PA)样本和独立同分布(iid)样本情形,亦可获得类似结论.最后给出了一个满足文中主要结果的例子. 相似文献
19.
负相伴样本情形连续型单参数指数族参数的经验Bayes检验问题 总被引:1,自引:0,他引:1
在加权"线性损失"下讨论了负相伴样本情形连续型单参数指数族参数的经验Bayes(EB)检验问题.利用概率密度函数的核估计构造了参数的经验Bayes检验函数,并获得了它的渐近最优(a.o.)性,在适当的条件下证明了所提出的经验Bayes检验函数的收敛速度可任意接近O(n-1/2). 相似文献
20.
Sangyeol Lee Okyoung Na Seongryong Na 《Annals of the Institute of Statistical Mathematics》2003,55(3):467-485
In this paper we consider the problem of testing for a variance change in nonstationary and nonparametric time series models.
The models under consideration are the unstable AR(q) model and the fixed design nonparametric regression model with a strong mixing error process. In order to perform a test,
we employ the cusum of squares test introduced by Inclán and Tiao (1994,J. Amer. Statist. Assoc.,89, 913–923). It is shown that the limiting distribution of the test statistic is the sup of a standard Brownian bridge as seen
in iid random samples. Simulation results are provided for illustration. 相似文献