共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
Dale Umbach 《Journal of multivariate analysis》1978,8(4):518-531
The behavior of the posterior for a large observation is considered. Two basic situations are discussed; location vectors and natural parameters.Let X = (X1, X2, …, Xn) be an observation from a multivariate exponential distribution with that natural parameter Θ = (Θ1, Θ2, …, Θn). Let θx* be the posterior mode. Sufficient conditions are presented for the distribution of Θ − θx* given X = x to converge to a multivariate normal with mean vector 0 as |x| tends to infinity. These same conditions imply that E(Θ | X = x) − θx* converges to the zero vector as |x| tends to infinity.The posterior for an observation X = (X1, X2, …, Xn is considered for a location vector Θ = (Θ1, Θ2, …, Θn) as x gets large along a path, γ, in Rn. Sufficient conditions are given for the distribution of γ(t) − Θ given X = γ(t) to converge in law as t → ∞. Slightly stronger conditions ensure that γ(t) − E(Θ | X = γ(t)) converges to the mean of the limiting distribution.These basic results about the posterior mean are extended to cover other estimators. Loss functions which are convex functions of absolute error are considered. Let δ be a Bayes estimator for a loss function of this type. Generally, if the distribution of Θ − E(Θ | X = γ(t)) given X = γ(t) converges in law to a symmetric distribution as t → ∞, it is shown that δ(γ(t)) − E(Θ | X = γ(t)) → 0 as t → ∞. 相似文献
3.
Abstract Let X = {X(t), t ? ?+} be an operator stable Lévy process on ? d with the exponent B, where B is a diagonal matrix. In the present paper, we consider the asymptotic behavior of the first passage time out of a sphere, and of the sojourn time in a sphere. We shall also determine the exact Hausdorff measure function for the range of X over unit time interval [0, 1]. 相似文献
4.
We show that the joint distribution of the degrees of a random graph can be accurately approximated by several simpler models derived from a set of independent binomial distributions. On the one hand, we consider the distribution of degree sequences of random graphs with n vertices and ½m edges. For a wide range of values of m, this distribution is almost everywhere in close correspondence with the conditional distribution {(X1,…,Xn) | ∑ Xi=m}, where X1,…,Xn are independent random variables, each having the same binomial distribution as the degree of one vertex. We also consider random graphs with n vertices and edge probability p. For a wide range of functions p=p(n), the distribution of the degree sequence can be approximated by {(X1,…,X>n) | ∑ Xi is even}, where X1,…,Xn are independent random variables each having the distribution Binom (n−1, p′), where p′ is itself a random variable with a particular truncated normal distribution. To facilitate computations, we demonstrate techniques by which statistics in this model can be inferred from those in a simple model of independent binomial random variables. Where they apply, the accuracy of our method is sufficient to determine asymptotically all probabilities greater than n−k for any fixed k. In this first paper, we use the geometric mean of degrees as a tutorial example. In the second paper, we will determine the asymptotic distribution of the tth largest degree for all functions t=t(n) as n→∞. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 97–117 (1997) 相似文献
5.
We consider the M/G/1 queue with an arrival rate λ that depends weakly upon time, as λ = λ(εt) where ε is a small parameter. In the asymptotic limit ε → 0, we construct approximations to the probability p
n(t)that η customers are present at time t. We show that the asymptotics are different for several ranges of the (slow) time scale Τ= εt. We employ singular perturbation techniques and relate the various time scales by asymptotic matching.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
《随机分析与应用》2013,31(3):719-735
When a new software is produced it is usually tested for failure several times in succession (whenever a failure is detected the software is rectified and tested again for failure). Suppose X 1,X 2,…,X k denote the times between failures. For the customer the main characteristic of interest is T=max(X 1,X 2,…,X k ). In particular, one would be interested in t α for which Pr{T≤t α }=1?α for small α. In this paper we consider four models for T based on the class of extreme value distributions (Gumbel, Fre´chet, Weibull and Pareto) and provide methods for estimating t α . In addition to numerical estimation of t α , we perform sensitivity analysis of t α with respect to the four models considered. 相似文献
7.
Jean Picard 《Probability Theory and Related Fields》1996,105(4):481-511
Summary We consider a Lévy processX
t and the solutionY
t of a stochastic differential equation driven byX
t; we suppose thatX
t has infinitely many small jumps, but its Lévy measure may be very singular (for instance it may have a countable support). We obtain sufficient conditions ensuring the existence of a smooth density forY
t: these conditions are similar to those of the classical Malliavin calculus for continuous diffusions. More generally, we study the smoothness of the law of variablesF defined on a Poisson probability space; the basic tool is a duality formula from which we estimate the characteristic function ofF. 相似文献
8.
The Increment Ratio (IR) statistic (see (1.1) below) was introduced in Surgailis et al. [16]. The IR statistic can be used for testing nonparametric hypotheses for d-integrated (−1/2 < d < 5/4) behavior of time series, including short memory (d = 0), (stationary) long-memory (0 < d < 1/2), and unit roots (d = 1). For stationary/stationary increment Gaussian observations, in [16], a rate of decay of the bias of the IR statistic
and a central limit theorem are obtained. In this paper, we study the asymptotic distribution of the IR statistic under the
model X
t = X
t0 + g
N(t) (t = 1, …, N), where X
t0 is a stationary/stationary increment Gaussian process as in [16], and g
N(t) is a slowly varying deterministic trend. In particular, we obtain sufficient conditions on X
t0 and g
N(t) under which the IR test has the same asymptotic confidence intervals as in the absence of the trend. We also discuss the
asymptotic distribution of the IR statistic under change-points in mean and scale parameters.
Partially supported by the bilateral France-Lithuania scientific project Gilibert and Lithuanian State Science and Studies
Foundation, grant No. T-25/08. 相似文献
9.
A well known application of Ramsey’s Theorem to Banach Space Theory is the notion of a spreading model
of a normalized basic sequence (x
i) in a Banach spaceX. We show how to generalize the construction to define a new creature (e
i), which we call an asymptotic model ofX. Every spreading model ofX is an asymptotic model ofX and in most settings, such as ifX is reflexive, every normalized block basis of an asymptotic model is itself an asymptotic model. We also show how to use
the Hindman-Milliken Theorem—a strengthened form of Ramsey’s Theorem—to generate asymptotic models with a stronger form of
convergence.
Research supported by NSF. 相似文献
10.
Patrícia A. Filipe Carlos A. Braumann Carlos J. Roquete 《Methodology and Computing in Applied Probability》2012,14(1):49-56
The evolution of the growth of an individual in a random environment can be described through stochastic differential equations
of the form dY
t
= β(α − Y
t
)dt + σdW
t
, where Y
t
= h(X
t
), X
t
is the size of the individual at age t, h is a strictly increasing continuously differentiable function, α = h(A), where A is the average asymptotic size, and β represents the rate of approach to maturity. The parameter σ measures the intensity of the effect of random fluctuations on growth and W
t
is the standard Wiener process. We have previously applied this monophasic model, in which there is only one functional form
describing the average dynamics of the complete growth curve, and studied the estimation issues. Here, we present the generalization
of the above stochastic model to the multiphasic case, in which we consider that the growth coefficient β assumes different values for different phases of the animal’s life. For simplicity, we consider two phases with growth coefficients
β
1 and β
2. Results and methods are illustrated using bovine growth data. 相似文献
11.
Yoichi Nishiyama 《Probability Theory and Related Fields》1997,108(4):459-494
Summary. This paper is devoted to the generalization of central limit theorems for empirical processes to several types of ℓ∞(Ψ)-valued continuous-time stochastic processes t⇝X
t
n
=(X
t
n
,ψ|ψ∈Ψ), where Ψ is a non-empty set. We deal with three kinds of situations as follows. Each coordinate process t⇝X
t
n
,ψ is: (i) a general semimartingale; (ii) a stochastic integral of a predictable function with respect to an integer-valued
random measure; (iii) a continuous local martingale. Some applications to statistical inference problems are also presented.
We prove the functional asymptotic normality of generalized Nelson-Aalen's estimator in the multiplicative intensity model
for marked point processes. Its asymptotic efficiency in the sense of convolution theorem is also shown. The asymptotic behavior
of log-likelihood ratio random fields of certain continuous semimartingales is derived.
Received: 6 May 1996 / In revised form: 4 February 1997 相似文献
12.
We consider fluid models with infinite buffer size. Let {Z
N
(t)} be the net input rate to the buffer, where {{Z
N
(t)} is a superposition of N homogeneous alternating on–off flows. Under heavy traffic environment {{Z
N
(t)} converges in distribution to a centred Gaussian process with covariance function of a single flow. The aim of this paper
is to prove the convergence of the stationary buffer content process {X
N
*
(t)} in the fNth model to the buffer content process {X
N
(t)} in the limiting Gaussian model.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
13.
Masafumi Akahira 《Annals of the Institute of Statistical Mathematics》1976,28(1):35-48
Summary Let {X
t
} be defined recursively byX
t
=θX
t−1+U
t
(t=1,2, ...), whereX
0=0 and {U
t
} is a sequence of independent identically distributed real random variables having a density functionf with mean 0 and varianceσ
2. We assume that |θ|<1. In the present paper we obtain the bound of the asymptotic distributions of asymptotically median
unbiased (AMU) estimators of θ and the sufficient condition that an AMU estimator be asymptotically efficient in the sense
that its distribution attains the above bound. It is also shown that the least squares estimator of θ is asymptotically efficient
if and only iff is a normal density function.
University of Electro-Communications 相似文献
14.
We consider a diffusion process {x(t)} on a compact Riemannian manifold with generator δ/2 + b. A current‐valued continuous stochastic process {X t} in the sense of Itô [8] corresponds to {x(t)} by considering the stochastic line integral X t(a) along {x(t)} for every smooth 1-form a. Furthermore {X t} is decomposed into the martingale part and the bounded variation part as a current-valued continuous process. We show the central limit theorems for {X t} and the martingale part of {X t}. Occupation time laws for recurrent diffusions and homogenization problems of periodic diffusions are closely related to these theorems 相似文献
15.
Rong-mao ZHANG & Zheng-yan LIN Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2007,50(1):35-46
Let {W(t),t∈R}, {B(t),t∈R } be two independent Brownian motions on R with W(0) = B(0) = 0. In this paper, we shall consider the exact Hausdorff measures for the image and graph sets of the d-dimensional iterated Brownian motion X(t), where X(t) = (Xi(t),... ,Xd(t)) and X1(t),... ,Xd(t) are d independent copies of Y(t) = W(B(t)). In particular, for any Borel set Q (?) (0,∞), the exact Hausdorff measures of the image X(Q) = {X(t) : t∈Q} and the graph GrX(Q) = {(t, X(t)) :t∈Q}are established. 相似文献
16.
Roberto Paoletti 《manuscripta mathematica》2002,107(2):145-150
We study the stability of a compact Lagrangian submanifold of a symplectic manifold under perturbation of the symplectic
structure. If X is a compact manifold and the ω
t
are cohomologous symplectic forms on X, then by a well-known theorem of Moser there exists a family Φ
t
of diffeomorphisms of X such that ω
t
=Φ
t
*(ω0). If L⊂X is a Lagrangian submanifold for (X,ω0), L
t
=Φ
t
-1(L) is thus a Lagrangian submanifold for (X,ω
t
). Here we show that if we simply assume that L is compact and ω
t
|
L
is exact for every t, a family L
t
as above still exists, for
sufficiently small t. Similar results are proved concerning the stability of special Lagrangian and Bohr–Sommerfeld special Lagrangian submanifolds,
under perturbation of the ambient Calabi–Yau structure.
Received: 29 May 2001/ Revised version: 17 October 2001 相似文献
17.
Gea Hwa Kwoun Yoshihiro Yajima 《Annals of the Institute of Statistical Mathematics》1986,38(1):297-309
Summary As one of the non-stationary time series model, we consider a firstorder autoregressive model in which the autoregressive
coefficient is assumed to be a function,f
t
(θ), of timet. We establish several assumptions onf
t
(θ), not on the terms in the Taylor expansion of log-likelihood function, and show that the estimators of unknown parameters
involved inf
t
(θ) have strong consistency and asymptotic normality under these assumptions when sample size tends to infinity. 相似文献
18.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):313-341
In this paper, we consider a filtering problem where the signal X t satisfies a slightly nonlinear stochastic differential equation and we want to obtain estimates of X t. To this end, we decompose the nonlinearity with two techniques—a deterministic one and a stochastic one—and this leads us to two sequences of estimates which can be computed by solving finite dimensional equations. We want to compare their performances: we solve this problem in most cases if we restrict ourselves to sufficiently small times t and we give conditions which permit to conclude also for larger times 相似文献
19.
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
20.
Logic Regression 总被引:1,自引:0,他引:1
《Journal of computational and graphical statistics》2013,22(3):475-511
Logic regression is an adaptive regression methodology that attempts to construct predictors as Boolean combinations of binary covariates. In many regression problems a model is developed that relates the main effects (the predictors or transformations thereof) to the response, while interactions are usually kept simple (two- to three-way interactions at most). Often, especially when all predictors are binary, the interaction between many predictors may be what causes the differences in response. This issue arises, for example, in the analysis of SNP microarray data or in some data mining problems. In the proposed methodology, given a set of binary predictors we create new predictors such as “X1, X2, X3, and X4 are true,” or “X5 or X6 but not X7 are true.” In more specific terms: we try to fit regression models of the form g(E[Y]) = b0 + b1 L1 + · · · + bn Ln , where Lj is any Boolean expression of the predictors. The Lj and bj are estimated simultaneously using a simulated annealing algorithm. This article discusses how to fit logic regression models, how to carry out model selection for these models, and gives some examples. 相似文献