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1.
We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which possibly depends on the time and the latent diffusion processes, while the sampling times also possibly depend on the observed processes. In a high-frequency setting, we consider a modified version of the pre-averaged Hayashi–Yoshida estimator, and we show that such a kind of estimator has the consistency and the asymptotic mixed normality, and attains the optimal rate of convergence. 相似文献
2.
Summary In the problem of estimating the covariance matrix of a multivariate normal population, James and Stein (Proc. Fourth Berkeley Symp. Math. Statist. Prob.,1, 361–380, Univ. of California Press) obtained a minimax estimator under a scale invariant loss. In this paper we propose
an orthogonally invariant trimmed estimator by solving certain differential inequality involving the eigenvalues of the sample
covariance matrix. The estimator obtained, truncates the extreme eigenvalues first and then shrinks the larger and expands
the smaller sample eigenvalues. Adaptive version of the trimmed estimator is also discussed. Finally some numerical studies
are performed using Monte Carlo simulation method and it is observed that the trimmed estimate shows a substantial improvement
over the minimax estimator.
The second author's research was supported by NSF Grant Number MCS 82-12968. 相似文献
3.
S. N. Elogne O. Perrin C. Thomas-Agnan 《Statistical Inference for Stochastic Processes》2008,11(2):177-205
In this paper we introduce a nonparametric approach for the estimation of the covariance function of a stationary stochastic
process X
t
indexed by The data consist of a finite number of observations of the process at irregularly spaced time points and the aim is to estimate
the covariance at any lag point without parametric assumptions and in such a way that it is a positive definite function.
After interpolating the process, we use the estimator designed by Parzen (Technometrics 3:167–190,1961) for continuous-time
data. Our estimator is shown to be consistent under smoothness assumptions on the covariance. Its performance is evaluated
by simulations. 相似文献
4.
We consider a linear multivariate errors-in-variables model AX ≈ B, where the matrices A and B are observed with errors and the matrix parameter X is to be estimated. In the case of lack of information about the error covariance structure, we propose an estimator that
converges in probability to X as the number of rows in A tends to infinity. Sufficient conditions for this convergence and for the asymptotic normality of the estimator are found.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1026–1033, August, 2007. 相似文献
5.
Salim Lardjane 《Statistical Inference for Stochastic Processes》2007,10(3):209-221
The author deals with nonparametric density estimation for stochastic processes which satisfy the L
∞-approximability property. He considers a Parzen–Rosenblatt estimator of the density for general stationary L
∞-approximable processes. He states conditions under which it is consistent and investigates its rate of convergence. Finally,
he applies his results to general nonmixing linear processes and nonmixing nonlinear autoregressive processes. 相似文献
6.
GemaiChen Jin-hongYou 《应用数学学报(英文版)》2005,21(2):177-192
Consider a repeated measurement partially linear regression model with an unknown vector parameter β, an unknown function g(.), and unknown heteroscedastic error variances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of β, we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that it improves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given to determine the number of iterations. We also show that when the number of replicates is less than or equal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of those in [2] to the case of semiparametric regressions. 相似文献
7.
Tomohito Naito Kohei Asai Tomoyuki Amano Masanobu Taniguchi 《Statistical Inference for Stochastic Processes》2010,13(3):163-174
In this paper, we propose a local Whittle likelihood estimator for spectral densities of non-Gaussian processes and a local
Whittle likelihood ratio test statistic for the problem of testing whether the spectral density of a non-Gaussian stationary
process belongs to a parametric family or not. Introducing a local Whittle likelihood of a spectral density f
θ
(λ) around λ, we propose a local estimator [^(q)] = [^(q)] (l){\hat{\theta } = \hat{\theta } (\lambda ) } of θ which maximizes the local Whittle likelihood around λ, and use f[^(q)] (l) (l){f_{\hat{\theta } (\lambda )} (\lambda )} as an estimator of the true spectral density. For the testing problem, we use a local Whittle likelihood ratio test statistic
based on the local Whittle likelihood estimator. The asymptotics of these statistics are elucidated. It is shown that their
asymptotic distributions do not depend on non-Gaussianity of the processes. Because our models include nonlinear stationary
time series models, we can apply the results to stationary GARCH processes. Advantage of the proposed estimator is demonstrated
by a few simulated numerical examples. 相似文献
8.
Denis Bosq 《Statistical Inference for Stochastic Processes》2002,5(3):287-306
The autoregressive model in a Banach space (ARB) contains many continuous time processes used in practice, for example, processes that satisfy linear stochastic differential
equations of order k, a very particular case being the Ornstein–Uhlenbeck process. In this paper we study empirical estimators for ARB processes. In particular we show that, under some regularity conditions, the empirical mean is asymptotically optimal with
respect to a.s. convergence and convergence of order 2. Limit in distribution and the law of the iterated logarithm are also
presented. Concerning the empirical covariance operator we note that, if (X
n, n ∈ ℤ) is ARB then (X
n ⊗ X
n, n ∈ ℤ) is AR in a suitable space of linear operators. This fact allows us to interpret the empirical covariance operator as a sample mean
of an AR and to derive similar results for it.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
9.
Takeaki Kariya Koichi Maekawa 《Annals of the Institute of Statistical Mathematics》1982,34(1):281-297
This paper first develops a valid method for approximations to the pdf's and cdf's of GLSE in linear models and, applying
this method to the Zellner estimator with an unrestricted sample covariance in the seemingly unrelated regression model, obtains
an approximate pdf with a bound of ordern
−2 and an approximate covariance matrix with a bound of ordern
−3
This research was done at the London School of Economics while the authors were British Council scholars. Kariya is grateful
to Professor J. Durbin for a general discussion on asymptotic expansions. Further the authors deeply appreciate Professor
Y. Kataoka and anonymous referee for their invaluable comments and suggestions. 相似文献
10.
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
11.
Delete-group Jackknife Estimate in
Partially Linear Regression Models with Heteroscedasticity 总被引:3,自引:0,他引:3
Abstract Consider a partially linear regression model with an unknown vector parameter β,an unknownfunction g(.),and unknown heteroscedastic error variances.Chen,You proposed a semiparametric generalizedleast squares estimator(SGLSE)for β,which takes the heteroscedasticity into account to increase efficiency.Forinference based on this SGLSE,it is necessary to construct a consistent estimator for its asymptotic covariancematrix.However,when there exists within-group correlation, the traditional delta method and the delete-1jackknife estimation fail to offer such a consistent estimator.In this paper, by deleting grouped partial residualsa delete-group jackknife method is examined.It is shown that the delete-group jackknife method indeed canprovide a consistent estimator for the asymptotic covariance matrix in the presence of within-group correlations.This result is an extension of that in[21]. 相似文献
12.
Mihai Anitescu Jie Chen Michael L. Stein 《Journal of computational and graphical statistics》2017,26(1):98-107
One of the scalability bottlenecks for the large-scale usage of Gaussian processes is the computation of the maximum likelihood estimates of the parameters of the covariance matrix. The classical approach requires a Cholesky factorization of the dense covariance matrix for each optimization iteration. In this work, we present an estimating equations approach for the parameters of zero-mean Gaussian processes. The distinguishing feature of this approach is that no linear system needs to be solved with the covariance matrix. Our approach requires solving an optimization problem for which the main computational expense for the calculation of its objective and gradient is the evaluation of traces of products of the covariance matrix with itself and with its derivatives. For many problems, this is an O(nlog?n) effort, and it is always no larger than O(n2). We prove that when the covariance matrix has a bounded condition number, our approach has the same convergence rate as does maximum likelihood in that the Godambe information matrix of the resulting estimator is at least as large as a fixed fraction of the Fisher information matrix. We demonstrate the effectiveness of the proposed approach on two synthetic examples, one of which involves more than 1 million data points. 相似文献
13.
A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the
finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.
Zhang Mei, Functional central limit theorem for the super-brownian motion with super-Brownian immigration, J. Theoret. Probab.,
to appear. 相似文献
14.
Model selection for regression on a fixed design 总被引:1,自引:0,他引:1
Yannick Baraud 《Probability Theory and Related Fields》2000,117(4):467-493
We deal with the problem of estimating some unknown regression function involved in a regression framework with deterministic
design points. For this end, we consider some collection of finite dimensional linear spaces (models) and the least-squares
estimator built on a data driven selected model among this collection. This data driven choice is performed via the minimization
of some penalized model selection criterion that generalizes on Mallows' C
p
. We provide non asymptotic risk bounds for the so-defined estimator from which we deduce adaptivity properties. Our results
hold under mild moment conditions on the errors. The statement and the use of a new moment inequality for empirical processes
is at the heart of the techniques involved in our approach.
Received: 2 July 1997 / Revised version: 20 September 1999 / Published online: 6 July 2000 相似文献
15.
Let (X,Y) be a bivariate random vector. The estimation of a probability of the form P(Y ≤ y |X > t) is challenging when t is large, and a fruitful approach consists in studying, if it exists, the limiting conditional distribution of the random
vector (X,Y), suitably normalized, given that X is large. There already exists a wide literature on bivariate models for which this limiting distribution exists. In this
paper, a statistical analysis of this problem is done. Estimators of the limiting distribution (which is assumed to exist)
and the normalizing functions are provided, as well as an estimator of the conditional quantile function when the conditioning
event is extreme. Consistency of the estimators is proved and a functional central limit theorem for the estimator of the
limiting distribution is obtained. The small sample behavior of the estimator of the conditional quantile function is illustrated
through simulations. Some real data are analysed. 相似文献
16.
Dennis D. Cox 《Annals of the Institute of Statistical Mathematics》1985,37(1):271-288
Summary Given a random sample of sizen from a densityf
0 on the real line satisfying certain regularity conditions, we propose a nonparametric estimator forψ
0=−f
0
′
/f0. The estimate is the minimizer of a quadratic functional of the formλJ(ψ)+∫[ψ
2−2ψ′]dFn where λ>0 is a smoothing parameter,J(·) is a roughness penalty, andF
n
is the empirical c.d.f. of the sample. A characterization of the estimate (useful for computational purposes) is given which
is related to spline functions. A more complete study of the caseJ(ψ)=∫[d
2ψ/dx2]2 is given, since it has the desirable property of giving the maximum likelihood normal estimate in the infinite smoothness
limit (λ→∞). Asymptotics under somewhat restrictive assumptions (periodicity) indicate that the estimator is asymptotically
consistent and achieves the optimal rate of convergence. This type of estimator looks promising because the minimization problem
is simple in comparison with the analogous penalized likelihood estimators.
This research was supported by the Office of Naval Research under Grant Number N00014-82-C-0062. 相似文献
17.
Martin Ohlson Zhanna Andrushchenko Dietrich von Rosen 《Annals of the Institute of Statistical Mathematics》2011,63(1):29-42
The problem of estimating parameters of a multivariate normal p-dimensional random vector is considered for a banded covariance structure reflecting m-dependence. A simple non-iterative estimation procedure is suggested which gives an explicit, unbiased and consistent estimator
of the mean and an explicit and consistent estimator of the covariance matrix for arbitrary p and m. 相似文献
18.
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
19.
Many applied problems require a covariance matrix estimator that is not only invertible, but also well-conditioned (that is, inverting it does not amplify estimation error). For large-dimensional covariance matrices, the usual estimator—the sample covariance matrix—is typically not well-conditioned and may not even be invertible. This paper introduces an estimator that is both well-conditioned and more accurate than the sample covariance matrix asymptotically. This estimator is distribution-free and has a simple explicit formula that is easy to compute and interpret. It is the asymptotically optimal convex linear combination of the sample covariance matrix with the identity matrix. Optimality is meant with respect to a quadratic loss function, asymptotically as the number of observations and the number of variables go to infinity together. Extensive Monte Carlo confirm that the asymptotic results tend to hold well in finite sample. 相似文献
20.
This paper is a continuation of the work in [11] and [2] on the problem of estimating by a linear estimator, N unobservable input vectors, undergoing the same linear transformation, from noise-corrupted observable output vectors. Whereas
in the aforementioned papers, only the matrix representing the linear transformation was assumed uncertain, here we are concerned
with the case in which the second order statistics of the noise vectors (i.e., their covariance matrices) are also subjected to uncertainty. We seek a robust mean-squared error estimator immuned against
both sources of uncertainty. We show that the optimal robust mean-squared error estimator has a special form represented by
an elementary block circulant matrix, and moreover when the uncertainty sets are ellipsoidal-like, the problem of finding
the optimal estimator matrix can be reduced to solving an explicit semidefinite programming problem, whose size is independent
of N.
The research was partially supported by BSF grant #2002038 相似文献