共查询到20条相似文献,搜索用时 31 毫秒
1.
Let X
1, X
2, ..., X
n
be a random sample from a normal distribution with unknown mean μ and known variance σ
2. In many practical situations, μ is known a priori to be restricted to a bounded interval, say [−m, m] for some m > 0. The sample mean , then, becomes an inadmissible estimator for μ. It is also not minimax with respect to the squared error loss function. Minimax and other estimators for this problem have
been studied by Casella and Strawderman (Ann Stat 9:870–878, 1981), Bickel (Ann Stat 9:1301–1309, 1981) and Gatsonis et al.
(Stat Prob Lett 6:21–30, 1987) etc. In this paper, we obtain some new estimators for μ. The case when the variance σ
2 is unknown is also studied and various estimators for μ are proposed. Risk performance of all estimators is numerically compared for both the cases when σ
2 may be known and unknown. 相似文献
2.
We consider the problem of constructing simultaneous fixed-width confidence intervals for all pairwise treatment differences
μ1−μ
J
, in the presence ofk(≥2) independent populationsN
p
(μ1,Σ), 1≤i≠j≤k. Appropriate purely sequential, accelerated sequential and three-stage sampling strategies have been developed and variousfirst-order asymptotic properties are then derived when Σ
pxp
is completely unknown, but positive definite (p.d.). In the two special cases when the largest component variance in Σ is
a known multiple of one of the variances or Σ=σ2
H where σ(>0) is unknown, butH
pxp is known and p.d., the original multistage sampling strategies are specialized. Under such special circumstances, associatedsecond-order characteristics are then developed. It is to be noted that our present formulation and the methodologies fill important voids
in the context of multivariate multiple comparisons which is a challenging area that has not yet been fully explored. Moderate
sample performances of the proposed techniques were very encouraging and detailed remarks on these were included in Mukhopadhyay
and Aoshima (1997). 相似文献
3.
Hagen Scherb 《Metrika》2001,53(1):71-84
Uniformly most powerful (UMP) tests are known to exist in one-parameter exponential families when the hypothesis H
0 and the alternative hypothesis H
1 are given by
(i) H
0 : θ≤θ0, H
1 : θ>θ0, and
(ii) H
0 : θ≤θ1 or θ≥θ2, H
1 : θ1<θ<θ2, where θ1<θ2.
Likewise, uniformly most powerful unbiased (UMPU) tests do exist when the hypotheses H
0 and H
1 take the form
(iii) H
0 : θ1≤θ≤θ2, H
1 : θ<θ1 or θ>θ2, where θ1<θ2, and
(iv) H
0 : θ=θ0, H
1:θ≠θ0.
To determine tests in case (i), only one critical value c and one randomization constant γ have to be computed. In cases (ii) through (iv) tests are determined by two critical values
c
1, c
2 and two randomization constants γ1, γ2. Unlike determination of tests in case (i), computation of critical values and randomization constants in the remaining cases
is rather difficult, unless distributions are symmetric. No straightforward method to determine two-sided UMP tests in discrete
sample spaces seems to be known. The purpose of this note is to disclose a distribution independent principle for the determination
of UMP tests in cases (ii) through (iv).
Received: March 1999 相似文献
4.
LetX
1,X
2,… be i.i.d. with finite meanμ>0,S
n
=X
1+…+X
n
. Forf(n)=n
β
,c>0 we consider the stopping timesT
c
=inf{n:S
n
>c+f(n)} with overshootR
c
=S
T
c
−(c+f(T
c
)). For 0<β<1 we give a bound for sup
c≥0 ER
c
in the spirit of Lorden’s well-known inequality forf=0. 相似文献
5.
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
6.
Some notions ofL
p
(μ)-completeness resp. totally L
p
(μ)-completeness (1≦p≦∞) are characterized for families of probability distributions dominated by aσ-finite measureμ and their conservation with respect to direct products is proved. Furthermore, it is shown that totallyL
∞(μ)-completeness does not implyL
1(μ)-completeness and that there are families of probability distributions in the i.i.d. case induced by the order statistic,
which are L1(μ)-complete but not totallyL
∞(μ)-complete. 相似文献
7.
The center of a univariate data set {x
1,…,x
n} can be defined as the point μ that minimizes the norm of the vector of distances y′=(|x
1−μ|,…,|x
n−μ|). As the median and the mean are the minimizers of respectively the L
1- and the L
2-norm of y, they are two alternatives to describe the center of a univariate data set. The center μ of a multivariate data set {x
1,…,x
n} can also be defined as minimizer of the norm of a vector of distances. In multivariate situations however, there are several
kinds of distances. In this note, we consider the vector of L
1-distances y′1=(∥x
1- μ∥1,…,∥x
n- μ∥1) and the vector of L
2-distances y′2=(∥x
1- μ∥2,…,∥x
n-μ∥2). We define the L
1-median and the L
1-mean as the minimizers of respectively the L
1- and the L
2-norm of y
1; and then the L
2-median and the L
2-mean as the minimizers of respectively the L
1- and the L
2-norm of y
2. In doing so, we obtain four alternatives to describe the center of a multivariate data set. While three of them have been
already investigated in the statistical literature, the L
1-mean appears to be a new concept.
Received January 1999 相似文献
8.
Rainer Göb 《Metrika》1997,45(1):131-169
Consider lots of discrete items 1, 2, …,N with quality characteristicsx
1,x
2, …,x
N
. Leta be a target value for item quality. Lot quality is identified with the average square deviation
from target per item in the lot (lot average square deviation from target). Under economic considerations this is an appropriate
lot quality indicator if the loss respectively the profit incurred from an item is a quadratic function ofx
i
−a. The present paper investigates tests of significance on the lot average square deviationz under the following assumptions: The lot is a subsequence of a process of production, storage, transport; the random quality
characteristics of items resulting from this process are i.i.d. with normal distributionN(μ, σ
2); the target valuea coincides with the process meanμ. 相似文献
9.
We consider the problem of comparison of one test treatment (τ0) with a set of v control treatments (τ1, τ2, …, τv) using distance optimality [DS-optimality] criterion introduced by Sinha (1970) in some treatment-connected design settings.
It turns out that the nature of DS-optimal designs is quite similar to that for the usual A−, D− and E− optimality criteria. However, the optimality problem is quite complicated in most situations. First we deal with the CRD
model and derive DS-optimal allocations for a given set of treatments. The results are almost identical to the A-optimal allocations
for such problems. Then we consider a block design set-up and examine the nature of DS-optimal designs. In the process, we
introduce the method of weighted coverage probability and maximize the resulting expression to obtain an optimal design.
Received: December 1999 相似文献
10.
LetX
1,X
2, ...,X
n
(n≥3) be a random sample on a random variableX with distribution functionF having a unique continuous inverseF
−1 over (a,b), −∞≤a<b≤∞ the support ofF. LetX
1:n
<X
2:n
<...<X
n:n
be the corresponding order statistics. Letg be a nonconstant continuous function over (a,b). Then for some functionG over (a, b) and for some positive integersr ands, 1<r+1<s≤n
相似文献
11.
Nigm et al. (2003, statistics 37: 527–536) proposed Bayesian method to obtain predictive interval of future ordered observation Y
(j) (r < j≤ n ) based on the right type II censored samples Y
(1) < Y
(2) < ... < Y
(r) from the Pareto distribution. If some of Y
(1) < ... < Y
(r-1) are missing or false due to artificial negligence of typist or recorder, then Nigm et al.’s method may not be an appropriate
choice. Moreover, the conditional probability density function (p.d.f.) of the ordered observation Y
(j) (r < j ≤ n ) given Y
(1) <Y
(2) < ... < Y
(r) is equivalent to the conditional p.d.f. of Y
(j) (r < j ≤ n ) given Y
(r). Therefore, we propose another Bayesian method to obtain predictive interval of future ordered observations based on the
only ordered observation Y
(r), then compares the length of the predictive intervals when using the method of Nigm et al. (2003, statistics 37: 527–536) and our proposed method. Numerical examples are provided to illustrate these results. 相似文献
12.
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
13.
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
14.
Summary Dynamic exponential family regression provides a framework for nonlinear regression analysis with time dependent parametersβ
0,β
1, …,β
t, …, dimβ
t=p. In addition to the familiar conditionally Gaussian model, it covers e.g. models for categorical or counted responses. Parameters
can be estimated by extended Kalman filtering and smoothing. In this paper, further algorithms are presented. They are derived
from posterior mode estimation of the whole parameter vector (β′0, …,β′t) by Gauss-Newton resp. Fisher scoring iterations. Factorizing the information matrix into block-bidiagonal matrices, algorithms
can be given in a forward-backward recursive form where only inverses of “small”p×p-matrices occur. Approximate error covariance matrices are obtained by an inversion formula for the information matrix, which
is explicit up top×p-matrices.
Heinz Leo Kaufmann, my friend and coauthor for many years, died in a tragical rock climbing accident in August 1989. This
paper is dedicated to his memory. 相似文献
15.
Summary LetX=(X
ij
)=(X
1, ...,X
n
)’,X’
i
=(X
i1, ...,X
ip
)’,i=1,2, ...,n be a matrix having a multivariate elliptical distribution depending on a convex functionq with parameters, 0,σ. Let ϱ2=ϱ
2
-2
be the squared multiple correlation coefficient between the first and the remainingp
2+p
3=p−1 components of eachX
i
. We have considered here the problem of testingH
0:ϱ2=0 against the alternativesH
1:ϱ
1
-2
=0, ϱ
2
-2
>0 on the basis ofX andn
1 additional observationsY
1 (n
1×1) on the first component,n
2 observationsY
2(n
2×p
2) on the followingp
2 components andn
3 additional observationsY
3(n
3×p
3) on the lastp
3 components and we have derived here the locally minimax test ofH
0 againstH
1 when ϱ
2
-2
→0 for a givenq. This test, in general, depends on the choice ofq of the familyQ of elliptically symmetrical distributions and it is not optimality robust forQ. 相似文献
16.
Let {v
n(θ)} be a sequence of statistics such that whenθ =θ
0,v
n(θ
0)
N
p(0,Σ), whereΣ is of rankp andθ εR
d. Suppose that underθ =θ
0, {Σ
n} is a sequence of consistent estimators ofΣ. Wald (1943) shows thatv
n
T
(θ
0)Σ
n
−1
v
n(θ
0)
x
2(p). It often happens thatv
n(θ
0)
N
p(0,Σ) holds butΣ is singular. Moore (1977) states that under certain assumptionsv
n
T
(θ
0)Σ
n
−
v
n(θ
0)
x
2(k), wherek = rank (Σ) andΣ
n
−
is a generalized inverse ofΣ
n. However, Moore’s result as stated is incorrect. It needs the additional assumption that rank (Σ
n) =k forn sufficiently large. In this article, we show that Moore’s result (as corrected) holds under somewhat different, but easier
to verify, assumptions.
Research partly supported by the U.S. Army Research Office through the Mathematical Sciences Institute at Cornell University. 相似文献
17.
Summary A new multivariate kernel probability density estimator is introduced and its strong uniform consistency is proved under certain
regularity conditions. This result is then applied particularly to a kernel estimator whose mean vector and covariance matrix
areμ
n andV
n, respectively, whereμ
n is an unspecified estimator of the mean vector andV
n, up to a multiplicative constant, the sample covariance matrix of the probability density to be estimated, respectively.
Work supported by the Natural Sciences and Engineering Research Council of Canada and by the Fonds F.C.A.R. of the Province
of Quebec. 相似文献
18.
Min-Hsiao Tsai 《Metrika》2009,70(3):355-367
Consider the problem of discriminating between two rival response surface models and estimating parameters in the identified
model. To construct designs serving for both model discrimination and parameter estimation, the M
γ-optimality criterion, which puts weight γ (0≤γ≤1) for model discrimination and 1 − γ for parameter estimation, is adopted.
The corresponding M
γ-optimal product design is explicitly derived in terms of canonical moments. With the application of the maximin principle
on the M
γ-efficiency of any M
γ'-optimal product design, a criterion-robust optimal product design is proposed. 相似文献
19.
A distributionF is said to be “more IFR” than another distributionG ifG
−1
F is convex. WhenF(0) =G(0) = 0, the problem of testingH
0 :F(x) =G (θx) for someθ > 0 andx ⩾ 0, against the alternativeH
A:F is more IFR thanG, is considered in this paper. Both cases, whenG is completely specified (one-sample case) and when it is not specified but a random sample form it is available (two-sample
case) are considered. The proposed tests are based onU-statistics. The asymptotic relative efficiency of the tests are compared with several other tests and the test statistics
remain asymptotically normal under certain dependency assumptions.
Research supported in part by a grant from the US Air Force Office of Scientific Research. 相似文献
20.
This paper deals with the estimation of survivor function
using optimally selected order statistics when the sample sizen is large. We use the estimates (μ*,σ*) based on the optimum set of order statistics
for largen and fixedk (≤n) such that the estimate
has optimum variance property. The asymptotic relative efficiency of such an estimator is compared with the one based on
the complete sample. The general theory of the problem and specific details with respect to a two-parameter Normal, Logistic,
Exponential and Pareto distributions is considered as an example. 相似文献
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