共查询到20条相似文献,搜索用时 15 毫秒
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Ajit Chaturvedi 《Annals of the Institute of Statistical Mathematics》1988,40(4):769-783
The sequential procedures developed by Starr (1966, Ann. Math. Statist., 37, 1173–1185) for estimating the mean of a normal population are further analyzed. Asymptotic properties of the regret and first two moments of the stopping rules are studied and second-order approximations are derived. 相似文献
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This paper is concerned with the problem of estimating a matrix of means in multivariate normal distributions with an unknown covariance matrix under invariant quadratic loss. It is first shown that the modified Efron-Morris estimator is characterized as a certain empirical Bayes estimator. This estimator modifies the crude Efron-Morris estimator by adding a scalar shrinkage term. It is next shown that the idea of this modification provides a general method for improvement of estimators, which results in the further improvement on several minimax estimators. As a new method for improvement, an adaptive combination of the modified Stein and the James-Stein estimators is also proposed and is shown to be minimax. Through Monte Carlo studies of the risk behaviors, it is numerically shown that the proposed, combined estimator inherits the nice risk properties of both individual estimators and thus it has a very favorable risk behavior in a small sample case. Finally, the application to a two-way layout MANOVA model with interactions is discussed. 相似文献
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James O. Berger 《Journal of multivariate analysis》1978,8(2):173-180
Let X be an observation from a p-variate (p ≥ 3) normal random vector with unknown mean vector θ and known covariance matrix . The problem of improving upon the usual estimator of θ, δ0(X) = X, is considered. An approach is developed which can lead to improved estimators, δ, for loss functions which are polynomials in the coordinates of (δ ? θ). As an example of this approach, the loss L(δ, θ) = |δ ? θ|4 is considered, and estimators are developed which are significantly better than δ0. When is the identity matrix, these estimators are of the form . 相似文献
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Satoshi Kuriki 《Annals of the Institute of Statistical Mathematics》1993,45(4):731-739
The unbiased estimator of risk of the orthogonally invariant estimator of the skew-symmetric normal mean matrix is obtained, and a class of minimax estimators and their order-preserving modification are proposed. The estimators have applications in paired comparisons model. A Monte Carlo study to compare the risks of the estimators is given. 相似文献
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A.S Holevo 《Journal of multivariate analysis》1973,3(3):262-275
Mean estimation for a random function is considered in its most general context, including both the case of infinite dimensional mean and exact estimation. The existence theorem for the best linear unbiased estimates is established. The general definition of the pseudobest estimate is given; necessary and sufficient conditions for the efficiency of the pseudobest estimates are obtained. As an application the problem of the periodic trend estimation is considered. 相似文献
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James Berger 《Journal of multivariate analysis》1976,6(2):256-264
Let X be a p-variate (p ≥ 3) vector normally distributed with mean θ and known covariance matrix . It is desired to estimate θ under the quadratic loss (δ ? θ)tQ(δ ? θ), where Q is a known positive definite matrix. A broad class of minimax estimators for θ is developed. 相似文献
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Yuzo Maruyama 《Journal of multivariate analysis》2004,88(2):320-334
We consider estimation of a multivariate normal mean vector under sum of squared error loss.We propose a new class of minimax admissible estimator which are generalized Bayes with respect to a prior distribution which is a mixture of a point prior at the origin and a continuous hierarchical type prior. We also study conditions under which these generalized Bayes minimax estimators improve on the James–Stein estimator and on the positive-part James–Stein estimator. 相似文献
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Yuzo Maruyama Katsunori Iwasaki 《Annals of the Institute of Statistical Mathematics》2005,57(1):145-156
On the problem of estimating a positive normal mean with known variance, it is well known that one minimax admissible estimator
is the generalized Bayes one with respect to the non-informative prior measure, the Lebesgue measure, restricted on the positive
half-line. When the true variance is misspecified, however, it is shown that this estimator does not always retain minimaxity
and admisssibility. In particular, it is almost surely inadmissible in the misspecification case. 相似文献
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We consider the problem of making statistical inference about the mean of a normal distribution based on a random sample of
quantized (digitized) observations. This problem arises, for example, in a measurement process with errors drawn from a normal
distribution and with a measurement device or process with a known resolution, such as the resolution of an analog-to-digital
converter or another digital instrument. In this paper we investigate the effect of quantization on subsequent statistical
inference about the true mean. If the standard deviation of the measurement error is large with respect to the resolution
of the indicating measurement device, the effect of quantization (digitization) diminishes and standard statistical inference
is still valid. Hence, in this paper we consider situations where the standard deviation of the measurement error is relatively
small. By Monte Carlo simulations we compare small sample properties of the interval estimators of the mean based on standard
approach (i.e. by ignoring the fact that the measurements have been quantized) with some recently suggested methods, including
the interval estimators based on maximum likelihood approach and the fiducial approach. The paper extends the original study
by Hannig et al. (2007). 相似文献
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It is shown that bootstrap methods for estimating the distribution of the Studentized mean produce consistent estimators in quite general contexts, demanding not a lot more than existence of finite mean. In particular, neither the sample mean (suitably normalized) nor the Studentized mean need converge in distribution. It is unnecessary to assume that the sampling distribution is in the domain of attraction of any limit law.Now at Michigan State University 相似文献
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Rasul A. Khan 《Journal of multivariate analysis》1978,8(4):550-558
Let X1, X2,… be idd random vectors with a multivariate normal distribution N(μ, Σ). A sequence of subsets {Rn(a1, a2,…, an), n ≥ m} of the space of μ is said to be a (1 − α)-level sequence of confidence sets for μ if P(μ Rn(X1, X2,…, Xn) for every n ≥ m) ≥ 1 − α. In this note we use the ideas of Robbins Ann. Math. Statist. 41 (1970) to construct confidence sequences for the mean vector μ when Σ is either known or unknown. The constructed sequence Rn(X1, X2, …, Xn) depends on Mahalanobis'
or Hotelling's
according as Σ is known or unknown. Confidence sequences for the vector-valued parameter in the general linear model are also given. 相似文献
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This paper addresses the problem of estimating the normal mean matrix in the case of unknown covariance matrix. This problem is solved by considering generalized Bayesian hierarchical models. The resulting generalized Bayes estimators with respect to an invariant quadratic loss function are shown to be matricial shrinkage equivariant estimators and the conditions for their minimaxity are given. 相似文献
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O. M. Uryas'eva 《Journal of Mathematical Sciences》1993,66(3):2327-2330
We consider prediction and estimation of the unknown mean of a homogeneous and isotropic random field from observations of the field and the normal derivative on a sphere in Rn. The solution is represented as a linear functional dependent on some parameters. The equations for the unknown parameters are given.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 112–116, 1988. 相似文献