共查询到20条相似文献,搜索用时 31 毫秒
1.
Hans M. Dietz 《Statistical Inference for Stochastic Processes》2001,4(3):249-258
Suppose one observes a path of a stochastic processX = (Xt)t≥0 driven by the equation
dXt=θ a(Xt)dt + dWt, t≥0, θ ≥ 0
with a(x) = x or a(x) = |x|α for some α ∈ [0,1) and given initial condition X
0. If the true but unknown parameter θ0 is positive then X is non-ergodic. It is shown that in this situation a trajectory fitting estimator for θ0 is strongly consistent and has the same limiting distribution as the maximum likelihood estimator, but converges of minor
order.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
2.
A polynomial Q = Q(X
1, …, X
n
) of degree m in independent identically distributed random variables with distribution function F is an unbiased estimator of a functional q(α
1(F), …, α
m
(F)), where q(u
1, …, u
m
) is a polynomial in u
1, …, u
m
and α
j
(F) is the jth moment of F (assuming the necessary moment of F exists). It is shown that the relation E(Q | X
1 + … + X
n) = 0 holds if and only if q(α
1(θ), …, α
m
(θ)) ≡ 0, where α
j
(θ) is the jth moment of the natural exponential family generated by F. This result, based on the fact that X
1 + … + X
n is a complete sufficient statistic for a parameter θ in a sample from a natural exponential family of distributions F
θ(x) = ∫−∞
x
e
θu−k(θ)
dF(u), explains why the distributions appearing as solutions of regression problems are the same as solutions of problems for
natural exponential families though, at the first glance, the latter seem unrelated to the former. 相似文献
3.
Bin Zhao 《高校应用数学学报(英文版)》2009,24(2):237-244
In this paper, the hereditarily almost expandability of inverse limits is investigated, with two results obtained. Let X be the inverse limit space of an inverse system (Xα, π^αβ, ∧}. (1) Suppose X is hereditarily κ-metacompact, if each Xα is hereditarily pointwise collectionwise normal (almost θ-expandable, almost discrete θ-expandable), then so is X; (2) Suppose X is hereditarily κ-σ-metacompact, if each Xα is hereditarily almost σ-expandable (almost discrete σ-expandable = σ-pointwise collectionwise normal), then so is X. 相似文献
4.
Summary LetX be the observed vector of thep-variate (p≧3) normal distribution with mean θ and covariance matrix equal to the identity matrix. Denotey
+=max{0,y} for any real numbery. We consider the confidence set estimator of θ of the formC
δa,φ={θ:|θ−δa,φ(X)}≦c}, whereδ
a,φ=[1−aφ({X})/{X}2]+X is the positive part of the Baranchik (1970,Ann. Math. Statist.,41, 642–645) estimator. We provide conditions on ϕ(•) anda which guarantee thatC
δa.φ has higher coverage probability than the usual one, {θ:|θ−X|≦c}. This dominance result will be shown to hold for spherically symmetric distributions, which include the normal distribution,t-distribution and double exponential distribution. The latter result generalizes that of Hwang and Chen (1983,Technical Report, Dept. of Math., Cornell University). 相似文献
5.
Elizabeth Meckes 《Journal of Theoretical Probability》2012,25(2):333-352
Let X be a d-dimensional random vector and X
θ
its projection onto the span of a set of orthonormal vectors {θ
1,…,θ
k
}. Conditions on the distribution of X are given such that if θ is chosen according to Haar measure on the Stiefel manifold, the bounded-Lipschitz distance from X
θ
to a Gaussian distribution is concentrated at its expectation; furthermore, an explicit bound is given for the expected distance,
in terms of d, k, and the distribution of X, allowing consideration not just of fixed k but of k growing with d. The results are applied in the setting of projection pursuit, showing that most k-dimensional projections of n data points in ℝ
d
are close to Gaussian, when n and d are large and k=clog (d) for a small constant c. 相似文献
6.
Longcheen Huwang Y. H. Steve Huang Yi-Hua Tina Wang 《Annals of the Institute of Statistical Mathematics》2009,61(4):789-810
Consider an ordinary errors-in-variables model. The true level α
n
(θ*) of a test at nominal level α and sample size n is said to be pointwise robust if α
n
(θ*) → α as n → ∞ for each parameter θ*. Let Ω* be a set of values of θ*. Define α
n
= sup
θ*
∈Ω*α
n
(θ*). The test is said to be uniformly robust over Ω* if α
n
→ α as n → ∞. Corresponding definitions apply to the coverage probabilities of confidence sets. It is known that all existing large-sample
tests for the parameters of the errors-in-variables model are pointwise robust. However, they might not be uniformly robust
over certain null parameter spaces. In this paper, we construct uniformly robust tests for testing the vector coefficient
parameter and vector slope parameter in the functional errors-in-variables model. These tests are established through constructing
the confidence sets for the same parameters in the model with similar desirable property. Power comparisons based on simulation
studies between the proposed tests and some existing tests in finite samples are also presented. 相似文献
7.
Any regular mixed Tsirelson spaceT(θ
n
,S
n
)N for whichθ
n
/θ
n
→ 0, whereθ=lim
n
θ
n
1n
, is shown to be arbitrarily distortable. Certain asymptoticl
1 constants for those and other mixed Tsirelson spaces are calculated. Also, a combinatorial result on the Schreier families
(S
α
)
α<ω
1 is proved and an application is given to show that for every Banach spaceX with a basis (e
i
), the two Δ-spectrums Δ(X) and Δ(X, (e
i
)) coincide.
Part of this paper also appears in the first author’s Ph.D. thesis which is being prepared under the supervision of Prof.
H. Rosenthal at the University of Texas at Austin. 相似文献
8.
S. P. Yadav 《Acta Mathematica Hungarica》2003,98(1-2):21-30
Let X represent either the space C[-1,1] L
p
(α,β) (w), 1 ≦ p < ∞ on [-1, 1]. Then Xare Banach spaces under the sup or the p norms, respectively. We prove that there exists a normalized Banach subspace X
1
αβ of Xsuch that every f ∈ X
1
αβ can be represented by a linear combination of Jacobi polynomials to any degree of accuracy. Our method to prove such an approximation
problem is Fourier–Jacobi analysis based on the convergence of Fourier–Jacobi expansions.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
9.
A. D. Kolesnik 《Ukrainian Mathematical Journal》2008,60(12):1915-1926
A symmetric random evolution X(t) = (X
1 (t), …, X
m
(t)) controlled by a homogeneous Poisson process with parameter λ > 0 is considered in the Euclidean space ℝ
m
, m ≥ 2. We obtain an asymptotic relation for the transition density p(x, t), t > 0, of the process X(t) as λ → 0 and describe the behavior of p(x, t) near the boundary of the diffusion domain in spaces of different dimensions.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1631 – 1641, December, 2008. 相似文献
10.
Shmuel Glasner 《Israel Journal of Mathematics》1979,32(2-3):161-172
We establish some “number theoretical” results about a continuous functionh from the circleT into itself, which generalize Kronecker’s theorem in several ways. These results are used to characterize the almost periodic
sets of the flow on the torusT
2 generated by (θ, φ) → (θ+α, φ+h(θ)), where α is irrational. The almost periodic measures are characterized in the caseh(θ)=θ. 相似文献
11.
For two collections of nonnegative and suitably normalized weights W = (Wj) and V = (Vn,k), a probability distribution on the set of partitions of the set {1, …, n} is defined by assigning to a generic partition
{Aj, j ≤ k} the probability Vn,k
, where |Aj| is the number of elements of Aj. We impose constraints on the weights by assuming that the resulting random partitions Π n of [n] are consistent as n varies, meaning that they define an exchangeable partition of the set of all natural numbers.
This implies that the weights W must be of a very special form depending on a single parameter α ∈ [− ∞, 1]. The case α =
1 is trivial, and for each value of α ≠ = 1 the set of possible V-weights is an infinite-dimensional simplex. We identify
the extreme points of the simplex by solving the boundary problem for a generalized Stirling triangle. In particular, we show
that the boundary is discrete for − ∞ ≤ α < 0 and continuous for 0 ≤ α < 1. For α ≤ 0 the extremes correspond to the members
of the Ewens-Pitman family of random partitions indexed by (α,θ), while for 0 < α < 1 the extremes are obtained by conditioning
an (α,θ)-partition on the asymptotics of the number of blocks of Πn as n tends to infinity. Bibliography: 29 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 325, 2005, pp. 83–102. 相似文献
12.
Khursheed Alam James R. Thompson 《Annals of the Institute of Statistical Mathematics》1973,25(1):57-64
Summary LetX be normally distributed with mean θ and variance σ2. We consider the problem of estimating θ with squared error as the loss function. A priori the true value of θ is known to
be close to θ0, say. Several estimates are considered which might be preferred toX, the unbiased estimate of θ, as their risks are smaller in the neighborhood of θ0. The admissibility of these estimates is discussed in this paper.
This research was supported in part by ONR Grants NR-042-271 and NR-042-283 at Clemson University and Rice University respectively. 相似文献
13.
In this paper, we consider a multidimensional diffusion process with jumps whose jump term is driven by a compound Poisson
process. Let a(x,θ) be a drift coefficient, b(x,σ) be a diffusion coefficient respectively, and the jump term is driven by a Poisson random measure p. We assume that its intensity measure qθ has a finite total mass. The aim of this paper is estimating the parameter α = (θ,σ) from some discrete data. We can observe
n + 1 data at tin = ihn,
. We suppose hn → 0, nhn → ∞, nhn2 → 0.
Final version 20 December 2004 相似文献
14.
Toyoaki Akai 《Annals of the Institute of Statistical Mathematics》1986,38(1):85-99
Summary LetX
i
,i=1,..., p be theith component of thep×1 vectorX=(X
1,X
2,...,X
p
)′. Suppose thatX
1,X
2,...,X
p
are independent and thatX
i
has a probability density which is positive on a finite interval, is symmetric about θ
i
and has the same variance. In estimation of the location vector θ=(θ1, θ2,...,θ
p
)′ under the squared error loss function explicit estimators which dominateX are obtained by using integration by parts to evaluate the risk function. Further, explicit dominating estimators are given
when the distributions ofX
i
′s are mixture of two uniform distributions. For the loss function
such an estimator is also given when the distributions ofX
i
′s are uniform distributions. 相似文献
15.
16.
We will study the following problem.Let X_t,t∈[0,T],be an R~d-valued process defined on atime interval t∈[0,T].Let Y be a random value depending on the trajectory of X.Assume that,at each fixedtime t≤T,the information available to an agent(an individual,a firm,or even a market)is the trajectory ofX before t.Thus at time T,the random value of Y(ω) will become known to this agent.The question is:howwill this agent evaluate Y at the time t?We will introduce an evaluation operator ε_t[Y] to define the value of Y given by this agent at time t.Thisoperator ε_t[·] assigns an (X_s)0(?)s(?)T-dependent random variable Y to an (X_s)0(?)s(?)t-dependent random variableε_t[Y].We will mainly treat the situation in which the process X is a solution of a SDE (see equation (3.1)) withthe drift coefficient b and diffusion coefficient σcontaining an unknown parameter θ=θ_t.We then consider theso called super evaluation when the agent is a seller of the asset Y.We will prove that such super evaluation is afiltration consistent nonlinear expectation.In some typical situations,we will prove that a filtration consistentnonlinear evaluation dominated by this super evaluation is a g-evaluation.We also consider the correspondingnonlinear Markovian situation. 相似文献
17.
Let X
1, X
2, ...X
n
be independent and identically distributed random variables with common distribution function F. Necessary and sufficient conditions for F to belong to the domains of attraction of Φ
α
and Ψ
α
are derived in terms of conditional moments.
相似文献
18.
S. A. Ould Abdi S. Dabo-Niang A. Diop A. Ould Abdi 《Mathematical Methods of Statistics》2010,19(1):1-21
Given a stationary multidimensional spatial process (Z
i
= (X
i
, Y
i
) ∈ ℝ
d
× ℝ, i ∈ ℤ
N
), we investigate a kernel estimate of the spatial conditional quantile function of the response variable Y
i
given the explicative variable X
i
. Almost complete convergence and consistency in L
2r
norm (r ∈ ℕ*) of the kernel estimate are obtained when the sample considered is an α-mixing sequence. 相似文献
19.
E. I. Pancheva 《Journal of Mathematical Sciences》1998,92(3):3911-3920
Given an extremal process X: [0,∞)→[0,∞)d with lower curve C and associated point process N={(tk, Xk):k≥0}, tk distinct and Xk independent, given a sequence ζ
n
=(τ
n
, ξ
n
), n≥1, of time-space changes (max-automorphisms of [0,∞)d+1), we study the limit behavior of the sequence of extremal processes Yn(t)=ξ
n
-1
○ X ○ τn(t)=Cn(t) V max {ξ
n
-1
○ Xk: tk ≤ τn(t){ ⇒ Y under a regularity condition on the norming sequence ζn and asymptotic negligibility of the max-increments of Yn. The limit class consists of self-similar (with respect to a group ηα=(σα, Lα), α>0, of time-space changes) extremal processes. By self-similarity here we mean the property Lα ○ Y(t)
=
d
Y ○ αα(t) for all α>0. The univariate marginals of Y are max-self-decomposable. If additionally the initial extremal process X is
assumed to have homogeneous max-increments, then the limit process is max-stable with homogeneous max-increments.
Supported by the Bulgarian Ministry of Education and Sciences (grant No. MM 234/1996).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I. 相似文献
20.
Nedžad Limić 《Applied Mathematics and Optimization》2011,64(1):101-133
Consider a non-symmetric generalized diffusion X(⋅) in ℝ
d
determined by the differential operator $A(\mbox{\boldmath{$A(\mbox{\boldmath{. In this paper the diffusion process is approximated by Markov jump processes X
n
(⋅), in homogeneous and isotropic grids G
n
⊂ℝ
d
, which converge in distribution in the Skorokhod space D([0,∞),ℝ
d
) to the diffusion X(⋅). The generators of X
n
(⋅) are constructed explicitly. Due to the homogeneity and isotropy of grids, the proposed method for d≥3 can be applied to processes for which the diffusion tensor $\{a_{ij}(\mbox{\boldmath{$\{a_{ij}(\mbox{\boldmath{ fulfills an additional condition. The proposed construction offers a simple method for simulation of sample paths of non-symmetric
generalized diffusion. Simulations are carried out in terms of jump processes X
n
(⋅). For piece-wise constant functions a
ij
on ℝ
d
and piece-wise continuous functions a
ij
on ℝ2 the construction and principal algorithm are described enabling an easy implementation into a computer code. 相似文献