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1.
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
2.
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
3.
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
4.
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
5.
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
6.
7.
Summary Letg(x) andf(x) be continuous density function on (a, b) and let {ϕj} be a complete orthonormal sequence of functions onL
2(g), which is the set of squared integrable functions weighted byg on (a, b). Suppose that
over (a, b). Given a grouped sample of sizen fromf(x), the paper investigates the asymptotic properties of the restricted maximum likelihood estimator of density, obtained by
setting all but the firstm of the ϑj’s equal to0. Practical suggestions are given for performing estimation via the use of Fourier and Legendre polynomial series.
Research partially supported by: CNR grant, n. 93. 00837. CT10. 相似文献
8.
We consider the situation where one wants to maximise a functionf(θ,x) with respect tox, with θ unknown and estimated from observationsy
k
. This may correspond to the case of a regression model, where one observesy
k
=f(θ,x
k
)+ε
k
, with ε
k
some random error, or to the Bernoulli case wherey
k
∈{0, 1}, with Pr[y
k
=1|θ,x
k
|=f(θ,x
k
). Special attention is given to sequences given by
, with
an estimated value of θ obtained from (x1, y1),...,(x
k
,y
k
) andd
k
(x) a penalty for poor estimation. Approximately optimal rules are suggested in the linear regression case with a finite horizon,
where one wants to maximize ∑
i=1
N
w
i
f(θ, x
i
) with {w
i
} a weighting sequence. Various examples are presented, with a comparison with a Polya urn design and an up-and-down method
for a binary response problem. 相似文献
9.
Improvement of the Liu estimator in linear regression model 总被引:2,自引:0,他引:2
In the presence of stochastic prior information, in addition to the sample, Theil and Goldberger (1961) introduced a Mixed
Estimator
for the parameter vector β in the standard multiple linear regression model (T,Xβ,σ2
I). Recently, the Liu estimator which is an alternative biased estimator for β has been proposed by Liu (1993).
In this paper we introduce another new Liu type biased estimator called Stochastic restricted Liu estimator
for β, and discuss its efficiency. The necessary and sufficient conditions for mean squared error matrix of the Stochastic restricted Liu estimator
to exceed the mean squared error matrix of the mixed estimator
will be derived for the two cases in which the parametric restrictions are correct and are not correct. In particular we
show that this new biased estimator is superior in the mean squared error matrix sense to both the Mixed estimator
and to the biased estimator introduced by Liu (1993). 相似文献
10.
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
11.
M. Ishaq Bhatti 《Statistical Papers》1995,36(1):299-312
Recently, Knautz and Trenkler (1993) considered Christensen’s (1987) equicorrelated linear regression model as an example
to show that S2 and
are independent even though the disturbances are equicorrelated. This paper addresses the issue of testing for the equicorrelation
coefficient in the linear regression model based on survey data. It computes exact and approximate critical values using Point
optimal and F-test statistics, respectively. An empirical comparison of these critical values at five percent nominal level
are presented to demonstrate the performance of the new tests. 相似文献
12.
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
13.
The value for which the mean square error of a biased estimatoraT for the mean μ is less than the variance of an unbiased estimatorT is derived by minimizingMSE(aT). The resulting optimal value is 1/[1+c(n)v
2], wherev=σ/μ, is the coefficient of variation. WhenT is the UMVUE
, thenc(n)=1/n, and the optimal value becomes 1/(n+v
2) (Searls, 1964). Whenever prior information about the size ofv is available the shrinkage procedure is useful. In fact for some members of the one-parameter exponential families it is
known that the variance is at most a quadratic function of the mean. If we identify the pertinent coefficients in the quadratic
function, it becomes easy to determinev. 相似文献
14.
In this paper we consider the problem of estimating the expected value of a fuzzy-valued random element in random samplings
from finite populations. To this purpose, we quantify the associated sampling error by means of a parameterized measure we
have introduced in a previous paper.
Keywords: Aumann's integral, expected value of a fuzzy random variable, fuzzy random variable,
-mean squared dispersion, random samplings, random set. 相似文献
15.
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
16.
Summary We consider a lotL formed byN apparently similar unitsW
1,…,W
N, where each of theW
i may come from one of two different populationsP
1 andP
2;T
1,…,T
N denote the corresponding lifetimes. The units fromP
i
undergo a failure of kindi and their survival function isS
i
(t).
We assume that the failure rate function
are known and that the units fromP
1 are ?substandard?: λ
1
(t)≥λ
2
(t), ∀t≥0.
We want to putW
1,…,W
N under a pre-operational test (burn-in test) in order to eliminate at least a great part of the substandard units and we face
the problem of obtaining a rule for stopping the test under the assumption that, with the failure of a unit, it is possible
to recognize the population from which the unit comes.
Such a problem will be formalized as an optimal stopping problem for a suitably defined Markov process. Our study shall evidentiate
some fundamental aspects of the problem and the role of the prior distribution of the (random) numberM
0 of those units inL coming fromP
1 (substandard). The latter distribution has a great influence on the form of the solution.
This research was supported by the C.N.R. Project ?Statistica Bayesiana e Simulazione in Affidalità e Modellistica Biologica?. 相似文献
17.
This paper deals with the construction of optimum partitions
of
for a clustering criterion which is based on a convex function of the class centroids
as a generalization of the classical SSQ clustering criterion for n data points. We formulate a dual optimality problem involving two sets of variables and derive a maximum-support-plane (MSP) algorithm for constructing a (sub-)optimum partition as a generalized k-means algorithm. We present various modifications of the basic criterion and describe the corresponding MSP algorithm. It is shown that the method can also be used for solving optimality problems in classical statistics (maximizing Csiszárs
-divergence) and for simultaneous classification of the rows and columns of a contingency table. 相似文献
18.
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
19.
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
20.
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