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1.
Summary Let
be a sequence of independent identically distributed random variables withθ
1∼G and the conditional distribution ofx
1 givenθ
1=θ given by
. HereG is unknown andF
θ(·) is known. This paper provides estimators
ofG based onx
1, …,x
n such that the random variable sup
has an asymptotic distribution asn→∞ under certain on conditionsG and for certain choices ofF
θ. A simulation model has been discussed involving the uniform distribution on (0, θ) forF
θ and an exponential distribution forG.
Research supported by the National Science Foundation under Grant #MCS77-26809. 相似文献
2.
Y. L. Tong 《Annals of the Institute of Statistical Mathematics》1987,39(1):289-297
Summary This paper concerns interval estimation of the critical value θ which satisfies
under the general linear model,Y
i
=μ(x
i
)+ε
i
(i=1,2,···), where
for
and the functional forms off
j
′
s are known. From an asymptotic expansion it is shown that, under reasonable conditions, the limiting distribution of
is normal. Thus in the large-sample case a confidence interval for θ can be obtained. Such a result is useful when one is
interested in carrying out a retrospective analysis rather than designing the experiment (as in the Kiefer-Wolfowitz procedure).
In Section 3 a sequential procedure is considered for confidence intervals with fixed width 2d. It is shown that, for a given stopping variableN,
is also asymptotically normal asd→0. Thus the coverage probability converges to 1−α (preassigned) asd→0. An example of application in estimating the phase parameter in circadian rhythms is given for the purpose of illustration.
Research partially supported by the NSF Grant DMS-8502346. 相似文献
3.
Yasunori Fujikoshi Yoshimichi Ochi 《Annals of the Institute of Statistical Mathematics》1984,36(1):119-128
Summary In this paper we obtain an asymptotic expansion of the distribution of the maximum likelihood estimate (MLE)
based onT observations from the first order Gaussian process up to the term of orderT
−1. The expansion is used to compare
with a generalized estimate
including the least square estimate (LSE)
, based on the asymptotic probabilities around the true value of the estimates up to the terms of orderT
−1. It is shown that
(or the modified MLE
) is better than
(or the modified estimate
). Further, we note that
does not attain the bound for third order asymptotic median unbiased estimates. 相似文献
4.
Consider the parameter space Θ which is an open subset of ℝ
k
,k≧1, and for each θ∈Θ, let the r.v.′sY
n
,n=0, 1, ... be defined on the probability space (X,A,P
θ) and take values in a Borel setS of a Euclidean space. It is assumed that the process {Y
n
},n≧0, is Markovian satisfying certain suitable regularity conditions. For eachn≧1, let υ
n
be a stopping time defined on this process and have some desirable properties. For 0 < τ
n
→ ∞ asn→∞, set
h
n
→h ∈R
k
, and consider the log-likelihood function
of the probability measure
with respect to the probability measure
. Here
is the restriction ofP
θ to the σ-field induced by the r.v.′sY
0,Y
1, ...,
. The main purpose of this paper is to obtain an asymptotic expansion of
in the probability sense. The asymptotic distribution of
, as well as that of another r.v. closely related to it, is obtained under both
and
.
This research was supported by the National Science Foundation, Grant MCS77-09574.
Research supported by the National Science Foundation, Grant MCS76-11620. 相似文献
5.
Let
and
be a perturbed eigenpair of a diagonalisable matrixA. The problem is to bound the error in
and
. We present one absolute perturbation bound and two relative perturbation bounds.
The absolute perturbation bound is an extension of Davis and Kahan's sin θ Theorem from Hermitian to diagonalisable matrices.
The two relative perturbation bounds assume that
and
are an exact eigenpair of a perturbed matrixD
1
AD
2
, whereD
1 andD
2 are non-singular, butD
1
AD
2 is not necessarily diagonalisable. We derive a bound on the relative error in
and a sin θ theorem based on a relative eigenvalue separation. The perturbation bounds contain both the deviation ofD
1 andD
2 from similarity and the deviation ofD
2 from identity.
This work was partially supported by NSF grant CCR-9400921. 相似文献
6.
Ryoichi Shimizu 《Annals of the Institute of Statistical Mathematics》1986,38(1):195-204
Summary LetX be a positive random variable with the survival function
and the densityf. LetX have the moments μ=E(X) and μ2=E(X
2) and put ε=|1-μ2/2μ2|. Put
and
. It is proved that the following inequalities hold:
, for allx>0, ifq(x) is monotone and that
, ifq
1
(x) is monotone. It is also shown that Brown's inequality
which holds wheneverq
1
(x) is increasing is not valid in general whenq
1 is decreasing.
The Institute of Statistical Mathematics 相似文献
7.
Ivan Č. Jovanović Eberhard Malkowsky Vladimir Rakočević 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):308-314
LetF be aBK space withAK and
denote the set of all formal power series
with
such that
ε F for the sequence of coefficients of
. We give a necessary and sufficient condition for a point to be a bounded point evaluation on
, and for a polynomial to be cyclic in
. As special cases, we obtain the results for the space ℓ
p
(β) in [7].
Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and,
in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8. 相似文献
8.
J. Pfanzagl 《Annals of the Institute of Statistical Mathematics》2003,55(1):95-110
Let
be a general family of probability measures,κ :
a functional, and
the optimal limit distribution for regular estimator sequences of κ. On intervals symmetric about 0, the concentration of
this optimal limit distribution can be surpassed by the asymptotic concentration of an arbitrary estimator sequence only forP in a “small” subset of
. For asymptotically median unbiased estimator sequences the same is true for arbitrary intervals containing 0. The emphasis
of the paper is on “pointwise” conditions for
, as opposed to conditions on shrinking neighbourhoods, and on “general” rather than parametric families. 相似文献
9.
K. I. Beidar M. Bre@scaron;ar M. A. Chebotar 《Journal of Mathematical Sciences》2000,102(6):4557-4565
Let
, be the algebra of upper triangular r×r matrices over field aF. We describe multilinear maps
, where n≤r, such that [f(A,...,A), A]=0 for all
, provided that |F| >n + 1. As an application of the results obtained, we describe linear automorphisms θ of
such that [θ(A2), θ(A)]=0 for all
.
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 74, Algebra-15,
2000. 相似文献
10.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2002,51(3):403-410
Let
be a sequence of positive numbers and 1≤p<∞. We consider the spaceH
p(β) of all power series
such that Σ|
(n)|p β(n
p<∞. We investigate regions on which our formal power series represent bounded analytic functions.
Research partially supported by the Shiraz University Research Council Grant No. 79-SC-1311-675. 相似文献