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1.
Holger Dette 《Metrika》1993,40(1):37-50
The optimal design problem for the estimation of several linear combinationsc′
l
ϑ (l=1, …,m) is considered in the usual linear regression modely=f′(x)ϑ (f(x) ∈ ℝ
k
,ϑ ∈ ℝ
k
). An optimal design minimizes a (weighted)p-norm of the variances of the least squares estimates for the different linear combinationsc′
l
ϑ. A generalized Elfving theorem is used to derive the relation of the new optimality criterion to theE-optimal design problem. It is shown that theE-optimal design for the parameterϑ minimizes such a (weighted)p-norm whenever the vectorc=(c′
1, …, c′k)′ is an inball vector of a symmetric convex and compact “Elfving set” in. 相似文献
2.
Prof. Dr. J. Pfanzagl 《Metrika》1970,15(1):141-148
Summary Let (X,A) be a measurable space andP
ϑη |A (ϑη) ∈ Θ x H, ∥A, (θ, η) ∈ Θ×H, a parametrized family of probability measures (for short:p-measures). This paper is concerned with the problem of consistently estimatingθ from realizations governed by
, where ηu ∈ H, v ∈ ℕ, are unknown. 相似文献
3.
LetP be a probability measure on ℝ andI
x be the set of alln-dimensional rectangles containingx. If for allx ∈ ℝn and θ ∈ ℝ the inequality
holds,P is a normal distributioin with mean 0 or the unit mass at 0. The result generalizes Teicher’s (1961) maximum likelihood characterization
of the normal density to a characterization ofN(0, σ2) amongall distributions (including those without density). The m.l. principle used is that of Scholz (1980). 相似文献
4.
The Baysian estimation of the mean vector θ of a p-variate normal distribution under linear exponential (LINEX) loss function is studied when as a special restricted model, it is suspected that for a p × r known matrix Z the hypothesis θ = Zβ, ${\beta\in\Re^r}The Baysian estimation of the mean vector θ of a p-variate normal distribution under linear exponential (LINEX) loss function is studied when as a special restricted
model, it is suspected that for a p × r known matrix Z the hypothesis θ = Zβ, b ? ?r{\beta\in\Re^r} may hold. In this area we show that the Bayes and empirical Bayes estimators dominate the unrestricted estimator (when nothing
is known about the mean vector θ). 相似文献
5.
A minimal characterization of the covariance matrix 总被引:1,自引:0,他引:1
Summary LetX be ak-dimensional random vector with mean vectorμ and non-singular covariance matrix Σ. We show that among all pairs (a, Δ),a ∈ IR
k
, Δ ∈ IR
k×k
positive definite and symmetric andE(X−a)′ Δ−1(X−a)=k, (μ, Σ) is the unique pair which minimizes det Δ. This motivates certain robust estimators of location and scale.
Research supported by the Nuffield Foundation. 相似文献
6.
In this paper we consider the case of the scale-contaminated normal (mixture of two normals with equal mean components but
different component variances: (1−p)N(μ,σ2)+pN(μ,τ2) with σ and τ being non-negative and 0≤p≤1). Here is the scale error and p denotes the amount with which this error occurs. It's maximum deviation to the best normal distribution is studied and shown
to be montone increasing with increasing scale error. A closed-form expression is derived for the proportion which maximizes
the maximum deviation of the mixture of normals to the best normal distribution. Implications to power studies of tests for
normality are pointed out.
Received May 2001 相似文献
7.
Draper and Guttman (1997) shows that for basic 2k−p designs, p≥0, k − p replicates of blocks designs of size two are needed to estimate all the usual (estimable) effects. In this work, we provide
an algebraic formal proof for the two-level blocks designs results and present results applicable to the general case; that
is, for the case of s
k factorial (p=0) or s
k−p fractional factorial (p >0) designs in s
b blocks, where 0<b<k− p, at least replicates are needed to clear up all possible effects. Through the theoretical development presented in this work, it can
provide a clearer view on why those results would hold. We will also discuss the estimation equations given in Draper and
Guttman (1997).
Research supported in part by the National Science Council of Taiwan, R.O.C., Grant No. NSC 89-2118-M110-010.
Acknowledgement. The authors would like to thank the referee for very helpful comments. 相似文献
8.
N. Shephard 《Journal of Applied Econometrics》1993,8(Z1):S135-S152
New strategies for the implementation of maximum likelihood estimation of nonlinear time series models are suggested. They make use of recent work on the EM algorithm and iterative simulation techniques. The estimation procedures are applied to the problem of fitting stochastic variance models to exchange rate data. 相似文献
9.
Ten empirical models of travel behavior are used to measure the variability of structural equation model goodness-of-fit as
a function of sample size, multivariate kurtosis, and estimation technique. The estimation techniques are maximum likelihood,
asymptotic distribution free, bootstrapping, and the Mplus approach. The results highlight the divergence of these techniques when sample sizes are small and/or multivariate kurtosis
high. Recommendations include using multiple estimation techniques and, when sample sizes are large, sampling the data and
reestimating the models to test both the robustness of the specifications and to quantify, to some extent, the large sample
bias inherent in the χ
2 test statistic. 相似文献
10.
Multi-stage point and interval estimation of the largest mean ofK normal populations and the associated second-order properties 总被引:1,自引:0,他引:1
Summary We havek independent normal populations with unknown meansμ
1, …,μ
k and a common unknown varianceσ
2. Both point and interval estimation procedures for the largest mean are proposed by means of sequential and three-stage procedures.
For the point estimation problem, we require that the maximal risk be at mostW, a preassigned positive number. For the other problem, we wish to construct a fixed-width confidence interval having the
confidence coefficient at least 1-α, a preassigned number between zero and one. Asymptotic second order expansions are provided for various characteristics,
such as average sample size, associated risks etc., for the suggested multi-stage estimation procedures. 相似文献
11.
Minimax estimators andΓ-minimax estimators for a bounded normal mean under the lossl
p (θ, d)=|θ-d|p
Summary Let the random variableX be normal distributed with known varianceσ
2>0. It is supposed that the unknown meanθ is an element of a bounded intervalΘ. The problem of estimatingθ under the loss functionl
p
(θ, d)=|θ-d|
p
p≥2 is considered. In case the length of the intervalθ is sufficiently small the minimax estimator and theΓ(β, τ)-minimax estimator, whereΓ(β, τ) represents special vague prior information, are given. 相似文献
12.
Massimiliano Amarante 《Decisions in Economics and Finance》2004,27(1):81-85
Abstract
In Marinacci (2000), the following theorem was proved.
Theorem 1. (Marinacci (2000) Let P and Q be two finitely additive probabilities on a λ -system Σ . Suppose that P is convex-ranged and that Q is countably additive. If there exists an A
+ ∈ Σ with 0<P(A
+ )<1 such that
whenever B∈ Σ , then P=Q.
Mathematics Subject Classification (2000): 28A10, 91B06
Journal of Economic Literature Classification: C60, D81 相似文献
13.
We consider the problem of component-wise estimation of ordered scale parameters of two gamma populations, when it is known
apriori which population corresponds to each ordered parameter. Under the scale equivariant squared error loss function, smooth
estimators that improve upon the best scale equivariant estimators are derived. These smooth estimators are shown to be generalized
Bayes with respect to a non-informative prior. Finally, using Monte Carlo simulations, these improved smooth estimators are
compared with the best scale equivariant estimators, their non-smooth improvements obtained in Vijayasree, Misra & Singh (1995),
and the restricted maximum likelihood estimators.
Acknowledgments. Authors are thankful to a referee for suggestions leading to improved presentation. 相似文献
14.
Summary For a linear modelY =ϑ + Z,ϑ ∈V,V ⊂ ℝ
n
a linear space, the following theorem is proved under simple conditions on the subspaceV: The projection onV (i.e. the least squares estimate forϑ) is a sufficient statistic iffZ is normally distributed. Further, this result is extended to the case of a multivariate linear model. 相似文献
15.
Prof. Dr. J. Pfanzagl 《Metrika》1969,14(1):249-272
Summary The concept of minimum contrast (m.c.) estimates used in this paper covers maximum likelihood (m.l.) estimates as a special
case. Section 1 contains sufficient conditions for the existence of measurable m.c. estimates and for their consistency.
The application of these results to m.l. estimates (section 2) yields the existence of m.l. estimates for families ofp-measures (probability measures) which are compact metric or locally compact with countable base, admitting upper semicontinuous
densities, whereas the classical results refer to continuous densities. This generalization is insofar of interest as upper
semicontinuous versions of the densities exist whenever the densities areμ-upper semicontinuous (whereasμ-continuity does not, in general, entail the existence of continuous versions).
Under appropriate regularity conditions, consistency of asymptotic maximum likelihood estimates is proven for compact (and
also locally compact) separable metric families ofp-measures with upper semicontinuous densities and for arbitrary families having uniformly continuous densities with respect
to the uniformity of vague convergence. The conditions sufficient for consistency are shown “indispensable” by counterexamples.
Section 3 contains auxiliary results. Besides their relevance for sections 1 and 2, some of them may also be of interest in
themselves, e.g. Theorem (3.4) on the selection of semicontinuous functions from semicontinuous equivalence classes. 相似文献
16.
Some properties of the minimum and the maximum of random variables with joint logconcave distributions 总被引:1,自引:1,他引:0
It is shown that if (X
1, X
2, . . . , X
n
) is a random vector with a logconcave (logconvex) joint reliability function, then X
P
= min
i∈P
X
i
has increasing (decreasing) hazard rate. Analogously, it is shown that if (X
1, X
2, . . . , X
n
) has a logconcave (logconvex) joint distribution function, then X
P
= max
i∈P
X
i
has decreasing (increasing) reversed hazard rate. If the random vector is absolutely continuous with a logconcave density
function, then it has a logconcave reliability and distribution functions and hence we obtain a result given by Hu and Li
(Metrika 65:325–330, 2007). It is also shown that if (X
1, X
2, . . . , X
n
) has an exchangeable logconcave density function then both X
P
and X
P
have increasing likelihood ratio. 相似文献
17.
We consider the sequential point estimation problem of the powers of a normal scale parameter σr with r≠ 0 when the loss function is squared error plus linear cost. It is shown that the regret due to using our fully sequential
procedure in ignorance of σ is asymptotically minimized for estimating σ−2. We also propose a bias-corrected procedure to reduce the risk and show that the larger the distance between r and −2 is, the more effective our bias-corrected procedure is.
Received August 2000 相似文献
18.
Pearn et al. (1999) considered a capability index C
′′
pmk, a new generalization of C
pmk, for processes with asymmetric tolerances. In this paper, we provide a comparison between C
′′
pmk and other existing generalizations of C
pmk on the accuracy of measuring process performance for processes with asymmetric tolerances. We show that the new generalization
C
′′
pmk is superior to other existing generalizations of C
pmk. Under the assumption of normality, we derive explicit forms of the cumulative distribution function and the probability
density function of the estimated index . We show that the cumulative distribution function and the probability density function of the estimated index can be expressed in terms of a mixture of the chi-square distribution and the normal distribution. The explicit forms of
the cumulative distribution function and the probability density function considerably simplify the complexity for analyzing
the statistical properties of the estimated index .
Received April 2000 相似文献
19.
Let X
1, X
2, ..., X
n
be independent exponential random variables such that X
i
has failure rate λ for i = 1, ..., p and X
j
has failure rate λ* for j = p + 1, ..., n, where p ≥ 1 and q = n − p ≥ 1. Denote by D
i:n
(p,q) = X
i:n
−X
i-1:n
the ith spacing of the order statistics X
1:n
≤ X
2:n
≤ ... ≤ X
n:n
, i = 1, ..., n, where X
0:n
≡ 0. The purpose of this paper is to investigate multivariate likelihood ratio orderings between spacings D
i:n
(p,q), generalizing univariate comparison results in Wen et al.(J Multivariate Anal 98:743–756, 2007). We also point out that
such multivariate likelihood ratio orderings do not hold for order statistics instead of spacings.
Supported by National Natural Science Foundation of China, the Program for New Century Excellent Talents in University (No.:
NCET-04-0569), and by the Knowledge Innovation Program of the Chinese Academy of Sciences (No.: KJCX3-SYW-S02). 相似文献
20.
The problem of estimating a linear combination,μ, of means ofp-independent, first-order autoregressive models is considered. Sequential procedures are derived (i) to estimateμ pointwise using the linear combination of sample means, subject to a loss function (squared error plus cost per observation),
and (ii) to arrive at a fixed-width confidence interval forμ. It is observed that in the case of point estimation we do not require a sampling scheme, where as in the case of interval
estimation we do require a sampling scheme and a scheme similar to the one given in Mukhopadhyay and Liberman (1989) is proposed.
All the first order efficiency properties of the sequential procedures involved here are derived. This paper is an extension
of results of Sriram (1987) involving one time series to multiple time series.
Research supported by AFOSR Grant number 89-0225. 相似文献