共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
C Hipp 《Journal of multivariate analysis》1983,13(1):67-108
As is well known, in full rank multivariate exponential families, tests of Neyman structure are uniformly most powerful unbiased for one-sided problems. For the case of lattice distributions, the power of these tests—evaluated at contiguous alternatives—is approximated by asymptotic expansions up to errors of order o(n?1). Surprisingly the tests with Neyman structure are not third-order efficient in the class of all asymptotically similar tests unless the problem is univariate. 相似文献
3.
Summary It is shown that the relative error of the bootstrap quantile variance estimator is of precise order n
-1/4, when n denotes sample size. Likewise, the error of the bootstrap sparsity function estimator is of precise order n
-1/4. Therefore as point estimators these estimators converge more slowly than the Bloch-Gastwirth estimator and kernel estimators,
which typically have smaller error of order at most n
-2/5. 相似文献
4.
Asymptotic expansions are made for the distributions of the Maximum Empirical Likelihood (MEL) estimator and the Estimating Equation (EE) estimator (or the Generalized Method of Moments (GMM) in econometrics) for the coefficients of a single structural equation in a system of linear simultaneous equations, which corresponds to a reduced rank regression model. The expansions in terms of the sample size, when the non-centrality parameters increase proportionally, are carried out to O(n−1). Comparisons of the distributions of the MEL and GMM estimators are made. Also, we relate the asymptotic expansions of the distributions of the MEL and GMM estimators to the corresponding expansions for the Limited Information Maximum Likelihood (LIML) and the Two-Stage Least Squares (TSLS) estimators. We give useful information on the higher order properties of alternative estimators including the semi-parametric inefficiency factor under the homoscedasticity assumption. 相似文献
5.
We consider the problem of estimating the discriminant coefficients, η=∑1-(θ(1)-θ(2)) based on two independent normal samples fromN
p
(θ(1),∑) andN
p
(θ(2),∑). We are concerned with the estimation of η as the gradient of log-odds between two extreme situations. A decision theoretic
approach is taken with the quadratic loss function. We derive the unbiased estimator of the essential part of the risk which
is applicable for general estimators. We propose two types of new estimators and prove their dominance over the traditional
estimator using this unbiased estimator. 相似文献
6.
Let θ(n) denote the maximum likelihood estimator of a vector parameter, based on an i.i.d. sample of size n. The class of estimators θ(n) + n?1q(θ(n)), with q running through a class of sufficiently smooth functions, is essentially complete in the following sense: For any estimator T(n) there exists q such that the risk of θ(n) + n?1q(θ(n)) exceeds the risk of T(n) by an amount of order o(n?1) at most, simultaneously for all loss functions which are bounded, symmetric, and neg-unimodal. If is chosen such that is unbiased up to , then this estimator minimizes the risk up to an amount of order o(n?1) in the class of all estimators which are unbiased up to .The results are obtained under the assumption that T(n) admits a stochastic expansion, and that either the distributions have—roughly speaking—densities with respect to the lebesgue measure, or the loss functions are sufficiently smooth. 相似文献
7.
Haruhiko Ogasawara 《Annals of the Institute of Statistical Mathematics》2009,61(4):995-1017
Asymptotic cumulants of the distributions of the sample singular vectors and values of cross covariance and correlation matrices
are obtained under nonnormality. The asymptotic cumulants are used to have the approximations of the distributions of the
estimators by the Edgeworth expansions up to order O(1/n) and Hall’s method with variable transformation. The cases of Studentized estimators are also considered. As an application
of the method, the distributions of the parameter estimators in the model of inter-battery factor analysis are expanded. Interpreting
the singular vectors and values in the context of the factor model with distributional conditions, the asymptotic robustness
of some lower-order normal-theory cumulants of the distributions of the sample singular vectors and values under nonnormality
is shown. 相似文献
8.
9.
J. Dippon 《Mathematical Methods of Statistics》2008,17(2):138-145
Assume that the function values f(x) of an unknown regression function f: ℝ → ℝ can be observed with some random error V. To estimate the zero ϑ of f, Robbins and Monro suggested to run the recursion X
n+1 = X
n
− a/n
Y
n
with Y
n
= f(X
n
) − V
n
. Under regularity assumptions, the normalized Robbins-Monro process, given by (X
n+1 − ϑ)/√Var(X
n+1, is asymptotically standard normal. In this paper Edgeworth expansions are presented which provide approximations of the
distribution function up to an error of order o(1/√n) or even o(1/n). As corollaries asymptotic confidence intervals for the unknown parameter ϑ are obtained with coverage probability errors of order O(1/n). Further results concern Cornish-Fisher expansions of the quantile function, an Edgeworth correction of the distribution
function and a stochastic expansion in terms of a bivariate polynomial in 1/√n and a standard normal random variable. The proofs of this paper heavily rely on recently published results on Edgeworth expansions
for approximations of the Robbins-Monro process.
相似文献
10.
Haruhiko Ogasawara 《Journal of multivariate analysis》2010,101(4):936-948
Accurate distributions of the estimator of the tetrachoric correlation coefficient and, more generally, functions of sample proportions for the 2 by 2 contingency table are derived. The results are obtained given the definitions of the estimators even when some marginal cell(s) are empty. Then, asymptotic expansions of the distributions of the parameter estimators standardized by the population asymptotic standard errors up to order O(1/n) and those of the studentized ones up to the order next beyond the conventional normal approximation are derived. The asymptotic results can be obtained in a much shorter computation time than the accurate ones. Numerical examples were used to illustrate advantages of the studentized estimator of Fisher’s z transformation of the tetrachoric correlation coefficient. 相似文献
11.
F. Gtze 《Journal of multivariate analysis》1987,22(2)
Edgeworth approximations for multivariate U-statistics hold up to the order o(n−1/2) under moment conditions and the assumption that the projection of the U-statistic to sums of i.i.d. random vectors is strongly nonlattice. 相似文献
12.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(9):1135-1140
Let X,V1,…,Vn−1 be n random vectors in ℝp with joint density of the form ƒ((X - θ)′ Σ−1(X - θ) + Σj=1n−1 Vji Σ−1Vj), where both θ and Σ are unknown. We consider the problem of estimating θ under the invariant loss (δ - θ)′ Σ−1 (δ - θ) and propose estimators which dominate the usual estimator δ0(X) = X simultaneously for the entire class of such distributions. The proof involves the development of expressions which are analogous to unbiased estimators of risk and which in fact reduce to unbiased estimators of risk in the Gaussian case. The method is applicable to the case where Σ is structured. 相似文献
13.
Gutti Jogesh Babu 《Probability Theory and Related Fields》1991,90(2):275-290
Summary The product limit estimator
of an unknown distributionF is represented as aU-statistic plus an error of the ordero(1/n). Using this, the maximum likelihood estimator of the specific risk rate in the time interval [0,M], is shown to admit a two term Edgeworth expansion. This risk rate for a specific cause of death is defined as the ratio of the probability of death, due to that particular cause, in the time interval [0,M], to the mean life time of an individual up to that time pointM. Similar expansions for the bootstrapped statistics are used to show that the bootstrap distribution, of the studentized estimator of the risk rate, approximates the sampling distribution better than the corresponding normal distribution.Research supported in part by NSA Grant MDA 904-90-H-1001 and by NSF Grant DMS-9007717 相似文献
14.
It is already known that the uniformly minimum variance unbiased (UMVU) estimator of the generalized variance always exists
for any natural exponential family. However, in practice, this estimator is often difficult to obtain. This paper provides
explicit forms of the UMVU estimators for the bivariate and symmetric multivariate gamma models, which are diagonal quadratic
exponential families. For the non-independent multivariate gamma models, it is shown that the UMVU and the maximum likelihood
estimators are not proportional.
相似文献
15.
对于平衡线性混合模型,本文提出了一组易验证的条件,在此条件下,方差分量的谱分解估计、方 差分析估计和最小范数二次无偏估计都相等且为一致最小方差无偏估计.同时证明了在此条件下,似然 方程和限制似然方程都有显式解,还给出了许多满足这组条件的平衡线性混合模型的例子. 相似文献
16.
Using the Markowitz mean–variance portfolio optimization theory, researchers have shown that the traditional estimated return greatly overestimates the theoretical optimal return, especially when the dimension to sample size ratio p/n is large. Bai et al. (2009) propose a bootstrap-corrected estimator to correct the overestimation, but there is no closed form for their estimator. To circumvent this limitation, this paper derives explicit formulas for the estimator of the optimal portfolio return. We also prove that our proposed closed-form return estimator is consistent when n → ∞ and p/n → y ∈ (0, 1). Our simulation results show that our proposed estimators dramatically outperform traditional estimators for both the optimal return and its corresponding allocation under different values of p/n ratios and different inter-asset correlations ρ, especially when p/n is close to 1. We also find that our proposed estimators perform better than the bootstrap-corrected estimators for both the optimal return and its corresponding allocation. Another advantage of our improved estimation of returns is that we can also obtain an explicit formula for the standard deviation of the improved return estimate and it is smaller than that of the traditional estimate, especially when p/n is large. In addition, we illustrate the applicability of our proposed estimate on the US stock market investment. 相似文献
17.
We consider estimation after a group sequential test about a multivariate normal mean, such as a χ2 test or a sequential version of the Bonferroni procedure. We derive the density function of the sufficient statistics and show that the sample mean remains to be the maximum likelihood estimator but is no longer unbiased. We propose an alternative Rao-Blackwell type unbiased estimator. We show that the family of distributions of the sufficient statistic is not complete, and there exist infinitely many unbiased estimators of the mean vector and none has uniformly minimum variance. However, when restricted to truncation-adaptable statistics, completeness holds and the Rao-Blackwell estimator has uniformly minimum variance. 相似文献
18.
Qihua Wang 《中国科学A辑(英文版)》1997,40(11):1136-1147
LetS(s,t) be the bivariate survival function. LetS π(s,t) be the bivariate product limit estimator proposed by Campbell and Földes. The one-term Edgeworth expansion forS π(s,t) is established by expressing logS π(s,t)-logS(s,t) as U-statistics, which admits one-term Edgeworth expansion plus some remainders with sufficient accuracy. 相似文献
19.
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
20.
Consider p independent distributions each belonging to the one parameter exponential family with distribution functions absolutely continuous with respect to Lebesgue measure. For estimating the natural parameter vector with p ≥ p0 (p0 is typically 2 or 3), a general class of estimators dominating the minimum variance unbiased estimator (MVUE) or an estimator which is a known constant multiple of the MVUE is produced under different weighted squared error losses. Included as special cases are some results of Hudson [13] and Berger [5]. Also, for a subfamily of the general exponential family, a class of estimators dominating the MVUE of the mean vector or an estimator which is a known constant multiple of the MVUE is produced. The major tool is to obtain a general solution to a basic differential inequality. 相似文献