共查询到20条相似文献,搜索用时 15 毫秒
1.
Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated
by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X
1,…,X
n
} from [0,1]
d
, L({X
1,…,X
n
})/n
(d−p)/d
converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X
1,…,X
n
})/n
(d−p)/d
.
Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University.
S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University. 相似文献
2.
This work emerges from a study of the extremal behavior of a daily maximum sea water levels series, {X
i
} , presented in Draisma (Duration of extremes at sea. In: Parametric and semi-parametric methods in E. V. T., pp. 137–143.
PhD thesis, Erasmus, University, 2001). In its approach, a new series, {Y
i
}, is defined, consisting of water levels that persist for a fixed period of time. In this paper, we study the tail behavior
of {Y
i
} , in case {X
i
} is independent and identically distributed (i.i.d.) and in case {X
i
} is a max-autoregressive sequence (we will consider two different max-autoregressive processes), whose distribution function
is in the Fréchet domain of attraction. We also determine Ledford and Tawn tail dependence index (Ledford and Tawn, Biometrika
83:169–187, 1996, J. R. Stat. Soc. B 59:475–499, 1997) and we analyze the asymptotic tail dependence of the random pair (Y
i
, Y
i + m
), in all considered cases. According to Drees (Bernoulli 9:617–657, 2003), we obtain the limit behavior of the tail empirical quantile function associated with a random sample (Y
1, Y
2,...Y
n
) and hence the asymptotic normality of a class of estimators of the tail index that includes Hill estimator.
Research partially supported by FCT/POCTI and POCI/FEDER. 相似文献
3.
For each n≥1, let {X j,n }1≤j≤n be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions for the convergence in distribution of the point process $N_{n}=\sum_{j=1}^{n}\delta_{X_{j,n}}For each n≥1, let {X
j,n
}1≤j≤n
be a sequence of strictly stationary random variables. In this article, we give some asymptotic weak dependence conditions
for the convergence in distribution of the point process
Nn=?j=1ndXj,nN_{n}=\sum_{j=1}^{n}\delta_{X_{j,n}}
to an infinitely divisible point process. From the point process convergence we obtain the convergence in distribution of
the partial sum sequence S
n
=∑
j=1
n
X
j,n
to an infinitely divisible random variable whose Lévy measure is related to the canonical measure of the limiting point process.
As examples, we discuss the case of triangular arrays which possess known (row-wise) dependence structures, like the strong
mixing property, the association, or the dependence structure of a stochastic volatility model. 相似文献
4.
Carla Henriques Paulo Eduardo Oliveira 《Statistical Inference for Stochastic Processes》2008,11(1):77-91
Let X
n
, n ≥ 1, be a strictly stationary associated sequence of random variables, with common continuous distribution function F. Using histogram type estimators we consider the estimation of the two-dimensional distribution function of (X
1,X
k+1) as well as the estimation of the covariance function of the limit empirical process induced by the sequence X
n
, n ≥ 1. Assuming a convenient decrease rate of the covariances Cov(X
1,X
n+1), n ≥ 1, we derive uniform strong convergence rates for these estimators. The condition on the covariance structure of the variables
is satisfied either if Cov(X
1,X
n+1) decreases polynomially or if it decreases geometrically, but as we could expect, under the latter condition we are able
to establish faster convergence rates. For the two-dimensional distribution function the rate of convergence derived under
a geometrical decrease of the covariances is close to the optimal rate for independent samples.
相似文献
5.
For a fixed integer n ≥ 2, let X
1
,…, X
n
be independent random variables (r.v.s) with distributions F
1,…,F
n
, respectively. Let Y be another random variable with distribution G belonging to the intersection of the longtailed distribution class and the O-subexponential distribution class. When each
tail of F
i
, i = 1,…,n, is asymptotically less than or equal to the tail of G, we derive asymptotic lower and upper bounds for the ratio of the tail probabilities of the sum X
1 + ⋯ + X
n
and Y. By taking different G’s, we obtain general forms of some existing results. 相似文献
6.
We fix a prime p and let f(X) vary over all monic integer polynomials of fixed degree n. Given any possible shape of a tamely ramified splitting of p in an extension of degree n, we prove that there exists a rational function φ(X)∈ℚ(X) such that the density of the monic integer polynomials f(X) for which the splitting of p has the given shape in ℚ[X]/f(X) is φ(p) (here reducible polynomials can be neglected). As a corollary, we prove that, for p≥n, the density of irreducible monic polynomials of degree n in ℤ
p
[X] is the value at p of a rational function φ
n
(X)∈ℚ(X). All rational functions involved are effectively computable.
Received: 15 September 1998 / Revised version: 21 October 1999 相似文献
7.
M. Ahsanullah 《Annals of the Institute of Statistical Mathematics》1978,30(1):429-433
A sequence {X
n,n≧1} of independent and identically distributed random variables with continuous cumulative distribution functionF(x) is considered.X
j is a record value of this sequence ifX
j>max (X
1, …,X
j−1). Let {X
L(n) n≧0} be the sequence of such record values. Some properties ofX
L(n) andX
L(n)−XL(n−1) are studied when {X
n,n≧1} has the exponential distribution. Characterizations of the exponential distribution are given in terms of the sequence
{X
L(n),n≧0}
The work was partly completed when the author was at the Department of Statistics, University of Brasilia, Brazil. 相似文献
8.
Zukang Zheng 《中国科学A辑(英文版)》1997,40(9):932-944
The stability of testing hypotheses is discussed. Differing from the usual tests measured by Neyman-Pearson lemma, the regret
and correction of the tests are considered. After the decision is made based on the observationsX
1,X
2, ⋅⋅⋅,X
n, one more piece of datumX
n+1 is picked and the test is done again in the same way but based onX
1,X
2, ⋅⋅⋅,X
n,X
n+l There are three situations: (i) The previous decision is right but the new decision is wrong; (ii) the previous decision
is wrong but the new decision is right; (iii) both of them are right or both of them are wrong. Of course, it is desired that
the probability of the occurrence of (i) is as small as possible and the probability of the occurrence of (ii) is as large
as possible. Since the sample size is sometimes not chosen very precisely after the type I error and the type II error are
determined in practice, it seems more urgent to consider the above problem. Some optimal plans are also given.
Project supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation. 相似文献
9.
M. Ahsanullah 《Annals of the Institute of Statistical Mathematics》1978,30(1):163-166
Summary LetX be a non-negative random variable with probability distribution functionF. SupposeX
i,n (i=1,…,n) is theith smallest order statistics in a random sample of sizen fromF. A necessary and sufficient condition forF to be exponential is given which involves the identical distribution of the random variables (n−i)(X
i+1,n−Xi,n) and (n−j)(X
j+1,n−Xj,n) for somei, j andn, (1≦i<j<n).
The work was partly completed when the author was at the Dept. of Statistics, University of Brasilia, Brazil. 相似文献
10.
Ervin Győri 《Combinatorica》1981,1(4):377-380
The problem is the following: How many questions are necessary in the worst case to determine whether a pointX in then-dimensional Euclidean spaceR
n
belongs to then-dimensional unit cubeQ
n, where we are allowed to ask which halfspaces of (n−1)-dimensional hyperplanes contain the pointX? It is known that ⌌3n/2⌍ questions are sufficient. We prove here thatcn questions are necessary, wherec≈1.2938 is the solution of the equationx log2
x−(x−1) log2 (x−1)=1. 相似文献
11.
This paper is devoted to the study of specific statistical methods for extremal events in the markovian setup, based on the regenerative method and the Nummelin technique. Exploiting ideas developed in Rootzén (Adv Appl Probab 20:371–390, 1988), the principle underlying our methodology consists of first generating a random number l of approximate pseudo-renewal times τ 1, τ 2, ..., τ l for a sample path X 1, ..., X n drawn from a Harris chain X with state space E, from the parameters of a minorization condition fulfilled by its transition kernel, and then computing submaxima over the approximate cycles thus obtained: $\max_{1+\tau_1\leq i \leq \tau_2}f(X_i),\;\ldots ,\;\max_{1+\tau_{l-1}\leq i \leq \tau_l}f(X_i)This paper is devoted to the study of specific statistical methods for extremal events in the markovian setup, based on the
regenerative method and the Nummelin technique. Exploiting ideas developed in Rootzén (Adv Appl Probab 20:371–390, 1988), the principle underlying our methodology consists of first generating a random number l of approximate pseudo-renewal times τ
1, τ
2, ..., τ
l
for a sample path X
1, ..., X
n
drawn from a Harris chain X with state space E, from the parameters of a minorization condition fulfilled by its transition kernel, and then computing submaxima over the approximate cycles thus obtained: max1+t1 £ i £ t2f(Xi), ?, max1+tl-1 £ i £ tlf(Xi)\max_{1+\tau_1\leq i \leq \tau_2}f(X_i),\;\ldots ,\;\max_{1+\tau_{l-1}\leq i \leq \tau_l}f(X_i) for any measurable function f:E→ℝ. Estimators of tail features of the sample maximum max1 ≤ i ≤ n
f(X
i
) are then constructed by applying standard statistical methods, tailored for the i.i.d. setting, to the submaxima as if they
were independent and identically distributed. In particular, the asymptotic properties of extensions of popular inference
procedures based on the conditional maximum likelihood theory, such as Hill’s method for the index of regular variation, are
thoroughly investigated. Using the same approach, we also consider the problem of estimating the extremal index of the sequence
{f(X
n
)}
n ∈ ℕ under suitable assumptions. Eventually, practical issues related to the application of the methodology we propose are discussed
and preliminary simulation results are displayed. 相似文献
12.
For X
1 , X
2 , ..., X
n
a sequence of non-negative independent random variables with common distribution function F(t), X
(n) denotes the maximum and S
n
denotes the sum. The ratio variate R
n
= X
(n) / S
n
is a quantity arising in the analysis of process speedup and the performance of scheduling. O’Brien (J. Appl. Prob. 17:539–545,
1980) showed that as n → ∞, R
n
→0 almost surely iff is finite. Here we show that, provided either (1) is finite, or (2) 1 − F (t) is a regularly varying function with index ρ < − 1, then . An integral representation for the expected ratio is derived, and lower and upper asymptotic bounds are developed to obtain
the result. Since is often known or estimated asymptotically, this result quantifies the rate of convergence of the ratio’s expected value.
The result is applied to the performance of multiprocessor scheduling.
相似文献
13.
V. M. Korchevsky 《Vestnik St. Petersburg University: Mathematics》2011,44(4):268-271
New sufficient conditions for the applicability of the strong law of large numbers to a sequence of dependent random variables
X
1, X
2, …, with finite variances are established. No particular type of dependence between the random variables in the sequence
is assumed. The statement of the theorem involves the classical condition Σ
n
∞ (log2
n)2/n
2 < ∞, which appears in various theorems on the strong law of large numbers for sequences of random variables without the independence
condition. 相似文献
14.
Oleg T. Izhboldin 《manuscripta mathematica》2000,102(1):41-52
Let F be a field of characteristic ≠2 and φ be a quadratic form over F. By X
φ we denote the projective variety given by the equation φ=0. For each positive even integer d≥8 (except for d=12) we construct a field F and a pair φ, ψ of anisotropic d-dimensional forms over F such that the Chow motives of X
φ and X
ψ coincide but . For a pair of anisotropic (2
n
-1)-dimensional quadrics X and Y, we prove that existence of a rational morphism Y→X is equivalent to existence of a rational morphism Y→X.
Received: 27 September 1999 / Revised version: 27 December 1999 相似文献
15.
Given a connected spaceX, we consider the effect of Quillen’s plus construction on the homotopy groups ofX in terms of its Postnikov decomposition. Specifically, using universal properties of the fibration sequenceAX→X→X
+, we explain the contribution of π
n
X to π
n
X
+, π
n+1
X
+ and π
n
AX, π
n+1
AX explicitly in terms of the low dimensional homology of π
n
X regarded as a module over π1
X. Key ingredients developed here for this purpose are universal II-central fibrations and a theory of universal central extensions
of modules, analogous to universal central extensions of perfect groups.
Research partially supported by NSERC of Canada. 相似文献
16.
Etsuko Bannai 《Journal of Algebraic Combinatorics》2006,24(4):391-414
Neumaier and Seidel (1988) generalized the concept of spherical designs and defined Euclidean designs in ℝ
n
. For an integer t, a finite subset X of ℝ
n
given together with a weight function w is a Euclidean t-design if holds for any polynomial f(x) of deg(f)≤ t, where {S
i
, 1≤ i ≤ p} is the set of all the concentric spheres centered at the origin that intersect with X, X
i
= X∩ S
i
, and w:X→ ℝ> 0. (The case of X⊂ S
n−1 with w≡ 1 on X corresponds to a spherical t-design.) In this paper we study antipodal Euclidean (2e+1)-designs. We give some new examples of antipodal Euclidean tight 5-designs. We also give the classification of all antipodal Euclidean tight 3-designs, the classification of antipodal Euclidean tight 5-designs supported by 2 concentric spheres. 相似文献
17.
Parviz Sahandi 《Ricerche di matematica》2009,58(2):219-242
Given a stable semistar operation of finite type ⋆ on an integral domain D, we show that it is possible to define in a canonical way a stable semistar operation of finite type ⋆[X] on the polynomial ring D[X], such that, if n := ⋆-dim(D), then n+1 ≤ ⋆[X]-dim(D[X]) ≤ 2n+1. We also establish that if D is a ⋆-Noetherian domain or is a Prüfer ⋆-multiplication domain, then ⋆[X]-dim(D[X]) = ⋆- dim(D)+1. Moreover we define the semistar valuative dimension of the domain D, denoted by ⋆-dim
v
(D), to be the maximal rank of the ⋆-valuation overrings of D. We show that ⋆-dim
v
(D) = n if and only if ⋆[X
1, . . . , X
n
]-dim(D[X
1, . . . , X
n
]) = 2n, and that if ⋆-dim
v
(D) < ∞ then ⋆[X]-dim
v
(D[X]) = ⋆-dim
v
(D) + 1. In general ⋆-dim(D) ≤ ⋆-dim
v
(D) and equality holds if D is a ⋆-Noetherian domain or is a Prüfer ⋆-multiplication domain. We define the ⋆-Jaffard domains as domains D such that ⋆-dim(D) < ∞ and ⋆-dim(D) = ⋆-dim
v
(D). As an application, ⋆-quasi-Prüfer domains are characterized as domains D such that each (⋆, ⋆′)-linked overring T of D, is a ⋆′-Jaffard domain, where ⋆′ is a stable semistar operation of finite type on T. As a consequence of this result we obtain that a Krull domain D, must be a w
D
-Jaffard domain. 相似文献
18.
LU Chuanrong QIU Jin & XU Jianjun School of Mathematics Statistics Zhejiang University of Finance Economics Hangzhou China Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2006,49(12):1788-1799
Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn Rn, where supn E|Rn| <∞and Rn = o(n~(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc. 相似文献
19.
K. Marton 《Israel Journal of Mathematics》1987,58(3):288-304
Let {(X
i,Z
i)} be an i.i.d. sequence of random pairs in a finite set × x ℒ; we will call it a discrete memoryless stationary correlated
(DMSC) source with generic distribution dist(X
1,Z
1). Two DMSC sources {(X
i,Z
i)} and {(X
i′,Z
i′)} are called asymptotically isomorphic in the weak sense if for every ε>0 and sufficiently largen, there exists a joint distribution dist(X
n,Z
n,X′
n,Z′
n) ofn-length blocks of the two sources such that
. For single sources of equal entropy, McMillan’s theorem implies asymptotic isomorphy in the sense suggested by this definition.
For correlated sources, however, no nontrivial cases of weak asymptotic isomorphy are known. We show that some spectral properties
of the generic distributions are invariant for weak asymptotic isomorphy, and these properties wholly determine the generic
distribution in many cases. 相似文献
20.
Tim Austin 《Journal d'Analyse Mathématique》2010,111(1):131-150
We offer a new proof of the Furstenberg-Katznelson multiple recurrence theorem for several commuting probability-preserving
transformations T
1, T
2, …, T
d
: ℤ ↷ (X, ∑, μ) ([6]), and so, via the Furstenberg correspondence principle introduced in [5], a new proof of the multi-dimensional Szemerédi Theorem. We bypass the careful manipulation of certain towers of factors
of a probability-preserving system that underlies the Furstenberg-Katznelson analysis, instead modifying an approach recently
developed in [1] to pass to a large extension of our original system in which this analysis greatly simplifies. The proof is then completed
using an adaptation of arguments developed by Tao in [13] for his study of an infinitary analog of the hypergraph removal lemma. In a sense, this addresses the difficulty, highlighted
by Tao, of establishing a direct connection between his infinitary, probabilistic approach to the hypergraph removal lemma
and the infinitary, ergodic-theoretic approach to Szemerédi’s Theorem set in motion by Furstenberg [5]. 相似文献