共查询到20条相似文献,搜索用时 31 毫秒
1.
Haruhiko Ogasawara 《Journal of multivariate analysis》2009,100(5):902-912
Asymptotic expansions of the distributions of parameter estimators in mean and covariance structures are derived. The parameters may be common to, or specific in means and covariances of observable variables. The means are possibly structured by the common/specific parameters. First, the distributions of the parameter estimators standardized by the population asymptotic standard errors are expanded using the single- and the two-term Edgeworth expansions. In practice, the pivotal statistic or the Studentized estimator with the asymptotically distribution-free standard error is of interest. An asymptotic distribution of the pivotal statistic is also derived by the Cornish-Fisher expansion. Simulations are performed for a factor analysis model with nonzero factor means to see the accuracy of the asymptotic expansions in finite samples. 相似文献
2.
An implicit function approach to constrained optimization with applications to asymptotic expansions
Robert J. Boik 《Journal of multivariate analysis》2008,99(3):465-489
In this article, an unconstrained Taylor series expansion is constructed for scalar-valued functions of vector-valued arguments that are subject to nonlinear equality constraints. The expansion is made possible by first reparameterizing the constrained argument in terms of identified and implicit parameters and then expanding the function solely in terms of the identified parameters. Matrix expressions are given for the derivatives of the function with respect to the identified parameters. The expansion is employed to construct an unconstrained Newton algorithm for optimizing the function subject to constraints.Parameters in statistical models often are estimated by solving statistical estimating equations. It is shown how the unconstrained Newton algorithm can be employed to solve constrained estimating equations. Also, the unconstrained Taylor series is adapted to construct Edgeworth expansions of scalar functions of the constrained estimators. The Edgeworth expansion is illustrated on maximum likelihood estimators in an exploratory factor analysis model in which an oblique rotation is applied after Kaiser row-normalization of the factor loading matrix. A simulation study illustrates the superiority of the two-term Edgeworth approximation compared to the asymptotic normal approximation when sampling from multivariate normal or nonnormal distributions. 相似文献
3.
YuZhaoping 《高校应用数学学报(英文版)》2000,15(2):167-172
Abstract. In this paper ,Edgeworth expansion for the nearest neighbor-kernel and random weighting approximation of conditional density are given and the consistency and convergence rate are proved 相似文献
4.
Vsevolod K. Malinovskii 《Acta Appl Math》1994,34(1-2):261-281
Edgeworth expansions for the distribution of a sequential least squares estimator in the random coefficient autoregressive (RCA) model are derived. The regenerative approach to second-order asymptotic analysis of Markov-type statistical models is developed. 相似文献
5.
部分线性模型中的Edgeworth展开 总被引:8,自引:0,他引:8
本文在相当一般的条件下,首先给出了部分线性模型中有关参数β的标准化统计量的一阶Edgeworth展开,然后构造了误差方差的一个非残差型相合估计,最后给出了相应的学生化统计量的Edgeworth展开. 相似文献
6.
Shi Jian 《数学学报(英文版)》1998,14(3):303-314
In this paper, under some fairly general conditions, a first-order Edgeworth expansion for the standardized statistic of β
in partial linear models is given, then a non-residual type of consistent estimation for the error variance is constructed,
and finally an Edgeworth expansion for the corresponding studentized version is presented. 相似文献
7.
Haruhiko Ogasawara 《Journal of multivariate analysis》2007,98(9):1726-1750
Asymptotic expansions of the distributions of typical estimators in canonical correlation analysis under nonnormality are obtained. The expansions include the Edgeworth expansions up to order O(1/n) for the parameter estimators standardized by the population standard errors, and the corresponding expansion by Hall's method with variable transformation. The expansions for the Studentized estimators are also given using the Cornish-Fisher expansion and Hall's method. The parameter estimators are dealt with in the context of estimation for the covariance structure in canonical correlation analysis. The distributions of the associated statistics (the structure of the canonical variables, the scaled log likelihood ratio and Rozeboom's between-set correlation) are also expanded. The robustness of the normal-theory asymptotic variances of the sample canonical correlations and associated statistics are shown when a latent variable model holds. Simulations are performed to see the accuracy of the asymptotic results in finite samples. 相似文献
8.
Summary. A simple mapping approach is proposed to study the bootstrap accuracy in a rather general setting. It is demonstrated that
the bootstrap accuracy can be obtained through this method for a broad class of statistics to which the commonly used Edgeworth
expansion approach may not be successfully applied. We then consider some examples to illustrate how this approach may be
used to find the bootstrap accuracy and show the advantage of the bootstrap approximation over the Gaussian approximation.
For the multivariate Kolmogorov–Smirnov statistic, we show the error of bootstrap approximation is as small as that of the
Gaussian approximation. For the multivariate kernel type density estimate, we obtain an order of the bootstrap error which
is smaller than the order of the error of the Gaussian approximation given in Rio (1994). We also consider an application
of the bootstrap accuracy for empirical process to that for the copula process.
Received: 23 June 1995 / In revised form: 18 June 1996 相似文献
9.
Kenichiro Tamaki 《Journal of multivariate analysis》2007,98(3):638-659
We consider the second order asymptotic properties of an efficient frequency domain regression coefficient estimator proposed by Hannan [Regression for time series, Proc. Sympos. Time Series Analysis (Brown Univ., 1962), Wiley, New York, 1963, pp. 17-37]. This estimator is a semiparametric estimator based on nonparametric spectral estimators. We derive the second order Edgeworth expansion of the distribution of . Then it is shown that the second order asymptotic properties are independent of the bandwidth choice for residual spectral estimator, which implies that has the same rate of convergence as in regular parametric estimation. This is a sharp contrast with the general semiparametric estimation theory. We also examine the second order Gaussian efficiency of . Numerical studies are given to confirm the theoretical results. 相似文献
10.
M. Bloznelis 《Lithuanian Mathematical Journal》2001,41(3):207-218
For symmetric asymptotically linear statistics based on simple random samples, we construct a one–term empirical Edgeworth expansion, where the moments defining the true Edgeworth expansion are replaced by their jackknife estimators. In order to establish the validity of the empirical Edgeworth expansion (in probability) we prove the consistency of the jackknife estimators. 相似文献
11.
M. Bloznelis 《Acta Appl Math》2003,78(1-3):51-60
We show the validity of the one-term Edgeworth expansion for Studentized asymptotically linear statistics based on samples drawn without replacement from finite populations. Replacing the moments defining the expansion by their estimators we obtain an empirical Edgeworth expansion. We show the validity of the empirical Edgeworth expansion in probability. 相似文献
12.
We show the validity of the one-term Edgeworth expansion for Studentized asymptotically linear statistics based on samples drawn without replacement from finite populations. Replacing the moments defining the expansion by their estimators, we obtain an empirical Edgeworth expansion. We show the validity of the empirical Edgeworth expansion in probability. 相似文献
13.
For symmetric asymptotically linear statistics based on simple random samples, we construct the one-term empirical Edgeworth expansion, where the moments defining the true Edgeworth expansion are replaced by their jackknife estimators. In order to establish the validity of the empirical Edgeworth expansion (in probability), we prove the consistency of the jackknife estimators. 相似文献
14.
Ryoichi Shimizu 《Annals of the Institute of Statistical Mathematics》1974,26(1):195-201
Summary An upper bound for the remainder term of the Edgeworth expansion for the distribution of the normalized sum of independent
and identically distributed random variables is given in terms of 3rd and 4th order moments, together with the total variation
of the probability density function of the underlying distribution.
The Institute of Statistical mathematics 相似文献
15.
W. C. M. Kallenberg 《Annals of the Institute of Statistical Mathematics》1993,45(2):341-351
With a given Edgeworth expansion sequences of i.i.d. r.v.'s are associated such that the Edgeworth expansion for the standardized sum of these r.v.'s agrees with the given Edgeworth expansion. This facilitates interpretation and manipulation of Edgeworth expansions. The theory is applied to the power of linear rank statistics and to the combination of such statistics based on subsamples. Complicated expressions for the power become more transparent. As a consequence of the sum-structure it is seen why splitting the sample causes no loss of first order efficiency and only a small loss of second order efficiency. 相似文献
16.
Robert J. Boik 《Journal of multivariate analysis》2005,96(1):136-171
Edgeworth expansions and saddlepoint approximations for the distributions of estimators of certain eigenfunctions of covariance and correlation matrices are developed. These expansions depend on second-, third-, and fourth-order moments of the sample covariance matrix. Expressions for and estimators of these moments are obtained. The expansions and moment expressions are used to construct second-order accurate confidence intervals for the eigenfunctions. The expansions are illustrated and the results of a small simulation study that evaluates the finite-sample performance of the confidence intervals are reported. 相似文献
17.
Andrius ?iginas 《Lithuanian Mathematical Journal》2012,52(1):40-52
We consider the one-term Edgeworth expansion for finite-population L-statistics. We provide an explicit formula for the Edgeworth correction term and give sufficient conditions for the validity
of the expansion that are expressed in terms of the weight function defining the statistics and moment conditions. 相似文献
18.
In the Koziol-Green or proportional hazards random censorship model, the asymptotic accuracy of the estimated one-term Edgeworth
expansion and the smoothed bootstrap approximation for the Studentized Abdushukurov-Cheng-Lin estimator is investigated. It
is shown that both the Edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact
distribution of the Studentized Abdushukurov-Cheng-Lin estimator than the normal approximation. 相似文献
19.
Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depend on not only geometric features of the underlying graphs but also the modified harmonic embedding of the graph into a certain nilpotent Lie group. Moreover, we apply the rate of convergence in Trotter’s approximation theorem to establish the Berry–Esseen-type bound for the random walks.
相似文献20.
The approximation of integral functionals with respect to a stationary Markov process by a Riemann sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to explicitly calculate the estimation error and to prove a general finite sample error bound. The presented approach admits general integrands and gives a unifying explanation for different rates obtained in the literature. Several examples demonstrate how the general bound can be related to well-known function spaces. 相似文献