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1.
Given a prior distribution for a model
, the prior information specified on a nested submodel
by means of a conditioning procedure crucially depends on the parameterisation used to describe the model. Regression coefficients represent the most common parameterisation of Gaussian DAG models. Nevertheless, in the specification of prior distributions, invariance considerations lead to the use of different parameterisations of the model, depending on the required invariance class. In this paper we consider the problem of prior specification by conditioning on zero regression coefficients and show that also such a procedure satisfies the property of invariance with respect to a class of parameterisations and characterise such a class. 相似文献
2.
Thomas Nittner 《Statistical Methods and Applications》2003,12(2):195-210
The additive model
is considered when some observations on x are missing at random but corresponding observations on y are available. Especially for this model, missing at random is an interesting case because the complete case analysis is expected to be no more suitable. A simulation experiment is reported and the different methods are compared based on their superiority with respect to the sample mean squared error. Some focus is also given on the sample variance and the estimated bias. In detail, the complete case analysis, a kind of stochastic mean imputation, a single imputation and the nearest neighbor imputation are discussed. 相似文献
3.
This paper is devoted to the problem of estimating the square of population mean (μ2) in normal distribution when a prior estimate or guessed value σ0
2 of the population variance σ2 is available. We have suggested a family of shrinkage estimators , say, for μ2 with its mean squared error formula. A condition is obtained in which the suggested estimator is more efficient than Srivastava et al’s (1980) estimator Tmin. Numerical illustrations have been carried out to demonstrate the merits of the constructed estimator over Tmin. It is observed that some of these estimators offer improvements over Tmin particularly when the population is heterogeneous and σ2 is in the vicinity of σ0
2. 相似文献
4.
In this paper we consider the inferential aspect of the nonparametric estimation of a conditional function , where X
t,m
represents the vector containing the m conditioning lagged values of the series. Here is an arbitrary measurable function. The local polynomial estimator of order p is used for the estimation of the function g, and of its partial derivatives up to a total order p. We consider α-mixing processes, and we propose the use of a particular resampling method, the local polynomial bootstrap, for the approximation
of the sampling distribution of the estimator. After analyzing the consistency of the proposed method, we present a simulation
study which gives evidence of its finite sample behaviour. 相似文献
5.
Martin Bachmaier 《Statistical Papers》2000,41(1):53-64
Using Fisher's information fort-distributions, the absolute asymptotic efficiency of some M-estimates for scale with known location parameter is calculated
and graphically illustrated. The compared estimators are the standard deviationS
*, the mean absolute deviation, called mean deviationD
*, the median absolute deviation, called MAD*, and some M-estimates for scale, one, which is very robust, and another one with high asymptotic efficiency fort-distributions close to the normal. The last one is considered with monotone (in the positive field) and with very late redescending
χ-function too. Also the
, an alternative and generalized excess measure defined as the double relative asymptotic variance of the underlying scale
estimator
in the previous paper, is calculated fort-distributions and graphically illustrated, because there is the relation that the higher the asymptotic efficiency of
is, the lower is the corresponding
. 相似文献
6.
Milan Merkle 《Statistical Methods and Applications》1996,5(3):323-334
Summary Let
, whereX
i are i.i.d. random variables with a finite variance σ2 and
is the usual estimate of the mean ofX
i. We consider the problem of finding optimal α with respect to the minimization of the expected value of |S
2(σ)−σ2|k for variousk and with respect to Pitman's nearness criterion. For the Gaussian case analytical results are obtained and for some non-Gaussian
cases we present Monte Carlo results regarding Pitman's criteron.
This research was supported by Science Fund of Serbia, grant number 04M03, through Mathematical Institute, Belgrade. 相似文献
7.
When constructing uniform random numbers in [0, 1] from the output of a physical device, usually n independent and unbiased bits B
j
are extracted and combined into the machine number
. In order to reduce the number of data used to build one real number, we observe that for independent and exponentially distributed random variables X
n
(which arise for example as waiting times between two consecutive impulses of a Geiger counter) the variable U
n : = X
2n – 1/(X
2n – 1 + X
2n
) is uniform in [0, 1]. In the practical application X
n
can only be measured up to a given precision (in terms of the expectation of the X
n
); it is shown that the distribution function obtained by calculating U
n
from these measurements differs from the uniform by less than /2.We compare this deviation with the error resulting from the use of biased bits B
j
with P
{B
j
= 1{ =
(where ] –
[) in the construction of Y above. The influence of a bias is given by the estimate that in the p-total variation norm Q
TV
p
= (
|Q()|
p
)1/p
(p 1) we have P
Y
– P
0
Y
TV
p
(c
n
· )1/p
with c
n
p
for n . For the distribution function F
Y
– F
0
Y
2(1 – 2–n
)|| holds. 相似文献
8.
Essential graphs and largest chain graphs are well-established graphical representations of equivalence classes of directed acyclic graphs and chain graphs respectively,
especially useful in the context of model selection. Recently, the notion of a labelled block ordering of vertices
was introduced as a flexible tool for specifying subfamilies of chain graphs. In particular, both the family of directed
acyclic graphs and the family of “unconstrained” chain graphs can be specified in this way, for the appropriate choice of
. The family of chain graphs identified by a labelled block ordering of vertices is partitioned into equivalence classes each represented by means of a -essential graph. In this paper, we introduce a topological ordering of meta-arrows and use this concept to devise an efficient procedure for the construction of -essential graphs. In this way we also provide an efficient procedure for the construction of both largest chain graphs and
essential graphs. The key feature of the proposed procedure is that every meta-arrow needs to be processed only once. 相似文献
9.
Summary The Zenga index,
, is shown to be a concentration index, in the sense that, ifX andY are non negative random variables with 0<E(X), E(Y)<+∞, then
(X)⩾
(Y) whenever the Lorenz curves satisfyL
x(p)≤L
y(p) for all p.
Research partially supported by: M.U.R.S.T. 40% ?Inferenza statistica: basi probabilistiche e sviluppi metodologici?. 相似文献
10.
11.
Olivier Cappé Randal Douc Arnaud Guillin Jean-Michel Marin Christian P. Robert 《Statistics and Computing》2008,18(4):447-459
In this paper, we propose an adaptive algorithm that iteratively updates both the weights and component parameters of a mixture
importance sampling density so as to optimise the performance of importance sampling, as measured by an entropy criterion.
The method, called M-PMC, is shown to be applicable to a wide class of importance sampling densities, which includes in particular
mixtures of multivariate Student t distributions. The performance of the proposed scheme is studied on both artificial and real examples, highlighting in particular
the benefit of a novel Rao-Blackwellisation device which can be easily incorporated in the updating scheme.
This work has been supported by the Agence Nationale de la Recherche (ANR) through the 2006–2008 project
’
. Both last authors are grateful to the participants to the BIRS
meeting on “Bioinformatics, Genetics and Stochastic Computation: Bridging the Gap”, Banff, for their comments on an earlier
version of this paper. The last author also acknowledges an helpful discussion with Geoff McLachlan. The authors wish to thank
both referees for their encouraging comments. 相似文献
12.
13.
Estimation of a normal mean relative to balanced loss functions 总被引:3,自引:0,他引:3
LetX
1,…,X
nbe a random sample from a normal distribution with mean θ and variance σ2. The problem is to estimate θ with Zellner's (1994) balanced loss function,
% MathType!End!2!1!, where 0<ω<1. It is shown that the sample mean
% MathType!End!2!1!, is admissible. More generally, we investigate the admissibility of estimators of the form
% MathType!End!2!1! under
% MathType!End!2!1!. We also consider the weighted balanced loss function,
% MathType!End!2!1!, whereq(θ) is any positive function of θ, and the class of admissible linear estimators is obtained under such loss withq(θ) =e
θ
. 相似文献
14.
Crude oil and natural gas depletion may be modelled by a diffusion process based upon a constrained life-cycle. Here we consider
the Generalized Bass Model. The choice is motivated by the realistic assumption that there is a self-evident link between
oil and gas extraction and the spreading of the modern technologies in wide areas such as transport, heating, cooling, chemistry
and hydrocarbon fuels consumption. Such a model may include deterministic or semi-deterministic regulatory interventions.
Statistical analysis is based upon nonlinear methodologies and more flexible autoregressive structure of residuals. The technical
aim of this paper is to outline the meaningful hierarchy existing among the components of such diffusion models. Statistical
effort in residual component analysis may be read as a significant confirmation of a well-founded diffusion process under
rare but strong deterministic shocks. Applications of such ideas are proposed with reference to world oil and gas production
data and to particular regions such as mainland U.S.A., U.K., Norway and Alaska. The main results give new evidence in time-peaks
location and in residual
times to depletion. 相似文献
15.
The objective of this paper is to construct an unbiased estimator (up to order 0(1/n)) of the population mean
of the study variatey which is more efficient than the sample mean
of the ‘n’ obsrvedy-values. In particular, the unbiased estimators are discussed for the cases of positive and negative correlations of the study
variatey and the auxiliary variatex. 相似文献
16.
This paper considers estimation of a exponential mean time to failure using a loss function that reflects both goodness of
fit and precision of estimation. The admissibility and inadmissibility of a class of linear estimators of the form
are studied. 相似文献
17.
Perfect simulation of positive Gaussian distributions 总被引:1,自引:0,他引:1
We provide an exact simulation algorithm that produces variables from truncated Gaussian distributions on (
+)
p
via a perfect sampling scheme, based on stochastic ordering and slice sampling, since accept-reject algorithms like the one of Geweke (1991) and Robert (1995) are difficult to extend to higher dimensions. 相似文献
18.
Summary In this paper likelihood is characterized as an index which measures how much a model fits a sample. Some properties required
to an index of fit are introduced and discussed, while stressing how they describe aspects inner to idea of fit. Finally we
prove that, if an index of fit is maximal when the model reaches the distribution of the sample, then such an index is an
increasing continuous transform of
, where thep
i's are the theoretical relative frequencies provided by the model and theq
i's are the actual relative frequencies of the sample. 相似文献
19.
Janusz Wywiał 《Statistical Papers》2004,45(3):413-431
LetF(x,y) be a distribution function of a two dimensional random variable (X,Y). We assume that a distribution functionF
x(x) of the random variableX is known. The variableX will be called an auxiliary variable. Our purpose is estimation of the expected valuem=E(Y) on the basis of two-dimensional simple sample denoted by:U=[(X
1, Y1)…(Xn, Yn)]=[X Y]. LetX=[X
1…X
n]andY=[Y
1…Y
n].This sample is drawn from a distribution determined by the functionF(x,y). LetX
(k)be the k-th (k=1, …,n) order statistic determined on the basis of the sampleX. The sampleU is truncated by means of this order statistic into two sub-samples:
% MathType!End!2!1! and
% MathType!End!2!1!.Let
% MathType!End!2!1! and
% MathType!End!2!1! be the sample means from the sub-samplesU
k,1 andU
k,2, respectively. The linear combination
% MathType!End!2!1! of these means is the conditional estimator of the expected valuem. The coefficients of this linear combination depend on the distribution function of auxiliary variable in the pointx
(k).We can show that this statistic is conditionally as well as unconditionally unbiased estimator of the averagem. The variance of this estimator is derived.
The variance of the statistic
% MathType!End!2!1! is compared with the variance of the order sample mean. The generalization of the conditional estimation
of the mean is considered, too. 相似文献
20.
The pooled variance of p samples presumed to have been obtained from p populations having common variance σ2, has invariably been adopted as the default estimator for σ2. In this paper, alternative estimators of the common population variance are developed. These estimators are biased and have
lower mean-squared error values than . The comparative merit of these estimators over the unbiased estimator is explored using relative efficiency (a ratio of
mean-squared error values). 相似文献