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1.
In the present paper families of truncated distributions with a Lebesgue density
forx=(x
1,...,x
n
) ε ℝ
n
are considered, wheref
0:ℝ → (0, ∞) is a known continuous function andC
n
(ϑ) denotes a normalization constant. The unknown truncation parameterϑ which is assumed to belong to a bounded parameter intervalΘ=[0,d] is to be estimated under a convex loss function. It is studied whether a two point prior and a corresponding Bayes estimator
form a saddle point when the parameter interval is sufficiently small. 相似文献
2.
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
3.
Summary Completeness of a family of probability distributions implies its bounded completeness but not conversely. An example of a
family which is boundedly complete but not complete was presented by Lehmann and Scheffe [5]. This appears to be the only
such example quoted in the statistical literature. The purpose of this note is to provide further examples of this type. It
is shown that any given family of power series distributions can be used to construct a class containing infinitely many boundedly
complete, but not complete, families. Furthermore, it is shown that the family of continuous distributions
, is boundedly complete, but not complete, whereU denotes the uniform distribution on [a, b] and {P
ϑ,ϑ ∈ IR}, is a translation family generated by a distributionP
0 with mean value zero, which is continuous with respect to the Lebesgue measure. 相似文献
4.
5.
6.
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
7.
8.
Herbert Vogt 《Metrika》1996,44(1):207-221
Let ζ
t
be the number of events which will be observed in the time interval [0;t] and define
as the average number of events per time unit if this limit exists. In the case of i.i.d. waiting-times between the events,E[ζ
t
] is the renewal function and it follows from well-known results of renewal theory thatA exists and is equal to 1/τ, if τ>0 is the expectation of the waiting-times.
This holds true also when τ = ∞.A may be estimate by ζ
t
/t or
where
is the mean of the firstn waiting-timesX
1,X
2, ...,X
n
. Both estimators converage with probability 1 to 1/τ if theX
i are i.i.d.; but the expectation of
may be infinite for alln and also if it is finite,
is in general a positively biased estimator ofA. For a stationary renewal process, ζ
t
/t is unbiased for eacht; if theX
i
are i.i.d. with densityf(x), then ζ
t
/t has this property only iff(x) is of the exponential type and only for this type the numbers of events in consecutive time intervals [0,t], [t, 2t], ... are i.i.d. random variables for arbitraryt > 0. 相似文献
9.
Prof. Dr. T. J. Terpstra 《Metrika》1989,36(1):63-90
We considerr ×c populations with failure ratesλ
ij(t) satisfying the condition
相似文献
10.
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
11.
12.
13.
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
14.
A mixture experiment is an experiment in which the k ingredients are nonnegative and subject to the simplex restriction on the (k − 1)-dimensional probability simplex S
k-1. In this work, an essentially complete class of designs under the Kiefer ordering for a linear log contrast model with a
mixture experiment is presented. Based on the completeness result, -optimal designs for all p,−∞ ≤ p ≤ 1 including D- and A-optimal are obtained, where the eigenvalues of the design moment matrix are used. By using the approach presented here, we
gain insight on how these -optimal designs behave.
Mong-Na Lo Huang was supported in part by the National Science Council of Taiwan, ROC under grant NSC 93-2118-M-110-001. 相似文献
15.
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
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