共查询到20条相似文献,搜索用时 31 毫秒
1.
Harry Joe 《Annals of the Institute of Statistical Mathematics》1985,37(1):165-172
Summary An α-percentile residual life function does not uniquely determine a life distribution; however, a continuous life distribution
can be uniquely determined by its α-percentile and β-percentile residual life functions if α and β satisfy a certain condition.
Two characterizations in terms of percentle residual lifetimes are given for the Beta (1, θ,K), Exponential (λ) and Pareto (θ,K) family of distributions. 相似文献
2.
Masafumi Akahira 《Annals of the Institute of Statistical Mathematics》1976,28(1):35-48
Summary Let {X
t
} be defined recursively byX
t
=θX
t−1+U
t
(t=1,2, ...), whereX
0=0 and {U
t
} is a sequence of independent identically distributed real random variables having a density functionf with mean 0 and varianceσ
2. We assume that |θ|<1. In the present paper we obtain the bound of the asymptotic distributions of asymptotically median
unbiased (AMU) estimators of θ and the sufficient condition that an AMU estimator be asymptotically efficient in the sense
that its distribution attains the above bound. It is also shown that the least squares estimator of θ is asymptotically efficient
if and only iff is a normal density function.
University of Electro-Communications 相似文献
3.
Éric Marchand François Perron 《Annals of the Institute of Statistical Mathematics》2009,61(1):215-234
For the problem of estimating under squared error loss the parameter of a symmetric distribution which is subject to an interval
constraint, we develop general theory which provides improvements on various types of inadmissible procedures, such as maximum
likelihood procedures. The applications and further developments given include: (i) symmetric location families such as the
exponential power family including double-exponential and normal, Student and Cauchy, a Logistic type family, and scale mixture
of normals in cases where the variance is lower bounded; (ii) symmetric exponential families such as those related to a Binomial(n,p) model with bounded |p−1/2| and to a Beta(α + θ, α −θ) model; and (iii) symmetric location distributions truncated to an interval (−c,c). Finally, several of the dominance results are studied with respect to model departures yielding robustness results, and
specific findings are given for scale mixture of normals and truncated distributions.
Research supported by NSERC of Canada. 相似文献
4.
Summary Let (Ω,A) be a measurable space, let Θ be an open set inR
k
, and let {P
θ; θ∈Θ} be a family of probability measures defined onA. Let μ be a σ-finite measure onA, and assume thatP
θ≪μ for each θ∈Θ. Let us denote a specified version ofdP
θ
/d
μ
byf(ω; θ).
In many large sample problems in statistics, where a study of the log-likelihood is important, it has been convenient to impose
conditions onf(ω; θ) similar to those used by Cramér [2] to establish the consistency and asymptotic normality of maximum likelihood estimates.
These are of a purely analytical nature, involving two or three pointwise derivatives of lnf(ω; θ) with respect to θ. Assumptions of this nature do not have any clear probabilistic or statistical interpretation.
In [10], LeCam introduced the concept of differentially asymptotically normal (DAN) families of distributions. One of the
basic properties of such a family is the form of the asymptotic expansion, in the probability sense, of the log-likelihoods.
Roussas [14] and LeCam [11] give conditions under which certain Markov Processes, and sequences of independent identically
distributed random variables, respectively, form DAN families of distributions. In both of these papers one of the basic assumptions
is the differentiability in quadratic mean of a certain random function. This seems to be a more appealing type of assumption
because of its probabilistic nature.
In this paper, we shall prove a theorem involving differentiability in quadratic mean of random functions. This is done in
Section 2. Then, by confining attention to the special case when the random function is that considered by LeCam and Roussas,
we will be able to show that the standard conditions of Cramér type are actually stronger than the conditions of LeCam and
Roussas in that they imply the existence of the necessary quadratic mean derivative. The relevant discussion is found in Section
3.
This research was supported by the National Science Foundation, Grant GP-20036. 相似文献
5.
6.
Consider a regular parametric family of distributions F(·, θ). The classical change point problem deals with observations corresponding to θ = 0 before a point of change, and θ = μ after that. We substitute the latter constant μ by a set of random variables θ
i,n
called a random environment assuming that E[θ
i,n
] = μ
n
→ 0. The random environment can be independent or obtained by random permutations of a given set. We define the rates of
convergence and give the conditions under which the classical parametric change point algorithms apply. 相似文献
7.
N. Balakrishnan G. Iliopoulos 《Annals of the Institute of Statistical Mathematics》2009,61(3):753-772
In this paper, we present a general method which can be used in order to show that the maximum likelihood estimator (MLE)
of an exponential mean θ is stochastically increasing with respect to θ under different censored sampling schemes. This propery is essential for the construction of exact confidence intervals for
θ via “pivoting the cdf” as well as for the tests of hypotheses about θ. The method is shown for Type-I censoring, hybrid censoring and generalized hybrid censoring schemes. We also establish the
result for the exponential competing risks model with censoring. 相似文献
8.
A. Childs B. Chandrasekar N. Balakrishnan D. Kundu 《Annals of the Institute of Statistical Mathematics》2003,55(2):319-330
Chen and Bhattacharyya (1988,Comm. Statist. Theory Methods,17, 1857–1870) derived the exact distribution of the maximum likelihood estimator of the mean of an exponential distribution
and an exact lower confidence bound for the mean based on a hybrid censored sample. In this paper, an alternative simple form
for the distribution is obtained and is shown to be equivalent to that of Chen and Bhattacharyya (1988). Noting that this
scheme, which would guarantee the experiment to terminate by a fixed timeT, may result in few failures, we propose a new hybrid censoring scheme which guarantees at least a fixed number of failures
in a life testing experiment. The exact distribution of the MLE as well as an exact lower confidence bound for the mean is
also obtained for this case. Finally, three examples are presented to illustrate all the results developed here. 相似文献
9.
Tomohito Naito Kohei Asai Tomoyuki Amano Masanobu Taniguchi 《Statistical Inference for Stochastic Processes》2010,13(3):163-174
In this paper, we propose a local Whittle likelihood estimator for spectral densities of non-Gaussian processes and a local
Whittle likelihood ratio test statistic for the problem of testing whether the spectral density of a non-Gaussian stationary
process belongs to a parametric family or not. Introducing a local Whittle likelihood of a spectral density f
θ
(λ) around λ, we propose a local estimator [^(q)] = [^(q)] (l){\hat{\theta } = \hat{\theta } (\lambda ) } of θ which maximizes the local Whittle likelihood around λ, and use f[^(q)] (l) (l){f_{\hat{\theta } (\lambda )} (\lambda )} as an estimator of the true spectral density. For the testing problem, we use a local Whittle likelihood ratio test statistic
based on the local Whittle likelihood estimator. The asymptotics of these statistics are elucidated. It is shown that their
asymptotic distributions do not depend on non-Gaussianity of the processes. Because our models include nonlinear stationary
time series models, we can apply the results to stationary GARCH processes. Advantage of the proposed estimator is demonstrated
by a few simulated numerical examples. 相似文献
10.
Shaul K. Bar-Lev 《Annals of the Institute of Statistical Mathematics》1984,36(1):217-222
Summary Consider a truncated exponential family of absolutely continuous distributions with natural parameter θ and truncation parameter
γ. Strong consistency and asymptotic normality are shown to hold for the maximum likelihood and maximum conditional likelihood
estimates of θ with γ unknown. Moreover, these two estimates are also shown to have the same limiting distribution, coinciding
with that of the maximum likelihood estimate for θ when γ is assumed to be known. 相似文献
11.
This paper describes the cutting sequences of geodesic flow on the modular surface with respect to the standard fundamental domain of . The cutting sequence for a vertical geodesic is related to a one-dimensional continued fraction expansion for θ, called the one-dimensional Minkowski geodesic continued
fraction (MGCF) expansion, which is associated to a parametrized family of reduced bases of a family of 2-dimensional lattices.
The set of cutting sequences for all geodesics forms a two-sided shift in a symbol space which has the same set of forbidden blocks as for vertical geodesics. We show that this shift is not a sofic shift, and that
it characterizes the fundamental domain ℱ up to an isometry of the hyperbolic plane . We give conversion methods between the cutting sequence for the vertical geodesic , the MGCF expansion of θ and the additive ordinary continued fraction (ACF) expansion of θ. We show that the cutting sequence
and MGCF expansions can each be computed from the other by a finite automaton, and the ACF expansion of θ can be computed
from the cutting sequence for the vertical geodesic θ + it by a finite automaton. However, the cutting sequence for a vertical geodesic cannot be computed from the ACF expansion by
any finite automaton, but there is an algorithm to compute its first symbols when given as input the first symbols of the ACF expansion, which takes time and space .
(Received 11 August 2000; in revised form 18 April 2001) 相似文献
12.
This paper describes the cutting sequences of geodesic flow on the modular surface with respect to the standard fundamental domain of . The cutting sequence for a vertical geodesic is related to a one-dimensional continued fraction expansion for θ, called the one-dimensional Minkowski geodesic continued fraction (MGCF) expansion, which is associated to a parametrized family of reduced bases of a family of 2-dimensional lattices. The set of cutting sequences for all geodesics forms a two-sided shift in a symbol space which has the same set of forbidden blocks as for vertical geodesics. We show that this shift is not a sofic shift, and that it characterizes the fundamental domain ℱ up to an isometry of the hyperbolic plane . We give conversion methods between the cutting sequence for the vertical geodesic , the MGCF expansion of θ and the additive ordinary continued fraction (ACF) expansion of θ. We show that the cutting sequence and MGCF expansions can each be computed from the other by a finite automaton, and the ACF expansion of θ can be computed from the cutting sequence for the vertical geodesic θ + it by a finite automaton. However, the cutting sequence for a vertical geodesic cannot be computed from the ACF expansion by any finite automaton, but there is an algorithm to compute its first symbols when given as input the first symbols of the ACF expansion, which takes time and space . 相似文献
13.
Yu. G. Shondin 《Journal of Mathematical Sciences》1997,87(5):3941-3970
The spectral aspect of the problem of perturbations supported on thin sets of codimension θ≥2m in ℝn is considered for elliptic operators of order m. The problem of realization of such perturbations is formulated as a problem
of self-adjoint extension of a linear symmetric relation in a space with indefinite metric. It is shown how to construct such
a relation for a given elliptic operator and a family of distributions. Its functional model is obtained in terms of Q-functions.
Self-adjoint extensions and their resolvents are described. The theory developed is applied to quantum models of point interactions
in high dimensions and high moments. Bibliography: 35 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 222, 1900, pp. 246–292. 相似文献
14.
Joseph and Kwack [9] introduced the notion of (θ,s)-continuous functions in order to investigateS-closed spaces due to Thompson [32]. In [26], the present authors investigated further properties of (θ,s)-continuous functions. In this paper, we introduce a new class of functions called α-quasi-irresolute functions which is
weaker than (θ,s)-continuous and improve some results established in [26]. 相似文献
15.
Twisted identities in Coxeter groups 总被引:1,自引:1,他引:0
Axel Hultman 《Journal of Algebraic Combinatorics》2008,28(2):313-332
Given a Coxeter system (W,S) equipped with an involutive automorphism θ, the set of twisted identities is
We point out how ι(θ) shows up in several contexts and prove that if there is no s∈S such that s
θ(s) is of odd order greater than 1, then the Bruhat order on ι(θ) is a graded poset with rank function ρ given by halving the Coxeter length. Under the same condition, it is shown that the order complexes of the open intervals
either are PL spheres or ℤ-acyclic. In the general case, contractibility is shown for certain classes of intervals. Furthermore,
we demonstrate that sometimes these posets are not graded.
For the Poincaré series of ι(θ), i.e. its generating function with respect to ρ, a factorisation phenomenon is discussed. 相似文献
16.
LetG denote either of the groupsGL 2(q) or SL2(q). Then θ :G →G given by θ(A) = (A t)t, whereA t denotes the transpose of the matrixA, is an automorphism ofG. Therefore we may form the groupG.θ> which is the split extension of the groupG by the cyclic group θ of order 2. Our aim in this paper is to find the complex irreducible character table ofG. θ. 相似文献
17.
L. A. Petrov 《Functional Analysis and Its Applications》2009,43(4):279-296
We construct a two-parameter family of diffusion processes X
α,θ
on the Kingman simplex, which consists of all nonincreasing infinite sequences of nonnegative numbers with sum less than
or equal to one. The processes on this simplex arise as limits of finite Markov chains on partitions of positive integers.
For α = 0, our process coincides with the infinitely-many-neutral-alleles diffusion model constructed by Ethier and Kurtz (1981)
in population genetics. The general two-parameter case apparently lacks population-genetic interpretation. In the present
paper, we extend Ethier and Kurtz’s main results to the two-parameter case. Namely, we show that the (two-parameter) Poisson-Dirichlet
distribution PD(α,θ) is the unique stationary distribution for the process X
α,θ
and that the process is ergodic and reversible with respect to PD(α, θ). We also compute the spectrum of the generator of X
α,θ
. The Wright-Fisher diffusions on finite-dimensional simplices turn out to be special cases of X
α,θ
for certain degenerate parameter values. 相似文献
18.
A rate of convergence for the set compound estimation in a family of certain retracted distributions
Yoshiko Nogami 《Annals of the Institute of Statistical Mathematics》1982,34(1):241-257
Summary This paper is concerned with the set compound squared-error loss estimation problem. Here, the author obtains Lévy consistent
estimate
of the empiric distributionG
n of the parameters θ1,...,θn for a more general family of retracted distributions on the interval [θ, θ+1) than the uniform on [θ, θ+1) as in R. Fox (1970,Ann. Math. Statist.,41, 1845–1852; 1978,Ann. Statist.,6, 846–853) and exhibits a decision procedure based on
with a convergence rateO((n
−1 logn)1/4) for the mofified regret uniformly in (θ1, θ2, ..., θn ∈ Ωn with bounded Ω. The author also gives a counterexample to the convergence of the modified regret for Ω=(−∞, ∞).
This is part of the author's Ph. D. Thesis at Michigan State University. 相似文献
19.
Improving on the minimum risk equivariant estimator of a location parameter which is constrained to an interval or a half-interval 总被引:3,自引:0,他引:3
Éric Marchand William E. Strawderman 《Annals of the Institute of Statistical Mathematics》2005,57(1):129-143
For location families with densitiesf
0(x−θ), we study the problem of estimating θ for location invariant lossL(θ,d)=ρ(d−θ), and under a lower-bound constraint of the form θ≥a. We show, that for quite general (f
0, ρ), the Bayes estimator δ
U
with respect to a uniform prior on (a, ∞) is a minimax estimator which dominates the benchmark minimum risk equivariant (MRE) estimator. In extending some previous
dominance results due to Katz and Farrell, we make use of Kubokawa'sIERD (Integral Expression of Risk Difference) method, and actually obtain classes of dominating estimators which include, and
are characterized in terms of δ
U
. Implications are also given and, finally, the above dominance phenomenon is studied and extended to an interval constraint
of the form θ∈[a, b].
Research supported by NSERC of Canada. 相似文献
20.
The analytic behaviour of θ-vacuum energy is related to the existence of phase transitions in QCD and ℂP
N
sigma models. The absence of singularities different from Lee-Yang zeros only permits ∧ cusp singularities in the vacuum
energy density and never ∨ cusps. This fact, together with the Vafa-Witten diamagnetic inequality, provides a key missing
link in the Vafa-Witten proof of parity symmetry conservation in vector-like gauge theories and ℂP
N
sigma models. However, this property does not exclude the existence of a first phase transition at θ = π or a second order phase transition at θ = 0, which might be very relevant for interpretation of the anomalous behaviour of the topological susceptibility in the
ℂP1 sigma model. 相似文献