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1.
Marilyn Breen 《Monatshefte für Mathematik》2003,139(2):105-109
Let S be a nonempty closed, simply connected set in the plane. For α > 0, let ℳ denote the family of all maximal subsets of S which are starshaped via paths of length at most α. Then ⋂{M : M in ℳ} is either starshaped via α-paths or empty. The result fails without the simple connectedness condition. However, even
with a simple connectedness requirement, there is no Helly theorem for intersections of sets which are starshaped via α-paths.
Received November 19, 2001; in revised form April 25, 2002
Published online November 18, 2002 相似文献
2.
Baran Sándor Pap Gyula Van Zuijlen Martien C. A. 《Statistical Inference for Stochastic Processes》2004,7(3):279-304
A shifted Wiener sheet is observed above a decreasing curve Γ. By the help of a direct discrete approach and under weaker
assumptions than in the paper of Arató [Comput. Math. Appl.
33 (1997), 13–25], an explicit formula is derived for the maximum likelihood estimator of the shift parameter. This estimator
is a weighted linear combination of the values at the endpoints of the curve Γ and weighted integrals of the observed process
and its normal derivative along the curve Γ.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
3.
Shinto Eguchi 《Annals of the Institute of Statistical Mathematics》1986,38(1):385-398
Summary This paper is concerned with estimation for a subfamily of exponential-type, which is a parametric model with sufficient statistics.
The family is associated with a surface in the domain of a sufficient statistic. A new estimator, termed a projection estimator,
is introduced. The key idea of its derivation is to look for a one-to-one transformation of the sufficient statistic so that
the subfamily can be associated with a flat subset in the transformed domain. The estimator is defined by the orthogonal projection
of the transformed statistic onto the flat surface. Here the orthogonality is introduced by the inverse of the estimated variance
matrix of the statistic on the analogy of Mahalanobis's notion (1936,Proc. Nat. Inst. Sci. Ind.,2, 49–55). Thus the projection estimator has an explicit representation with no iterations. On the other hand, the MLE and
classical estimators have to be sought as numerical solutions by some algorithm with a choice of an initial value and a stopping
rule. It is shown that the projection estimator is first-order efficient. The second-order property is also discussed. Some
examples are presented to show the utility of the estimator. 相似文献
4.
Maria Chudnovsky Jim Geelen Bert Gerards Luis Goddyn Michael Lohman Paul Seymour 《Combinatorica》2006,26(5):521-532
Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint
A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem.
These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research
was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow. 相似文献
5.
Francisco Cribari-Neto Maria da Glória A. Lima 《Annals of the Institute of Statistical Mathematics》2010,62(6):1053-1082
The linear regression model is commonly used by practitioners to model the relationship between the variable of interest and
a set of explanatory variables. The assumption that all error variances are the same, known as homoskedasticity, is oftentimes
violated when cross sectional data are used. Consistent standard errors for the ordinary least squares estimators of the regression
parameters can be computed following the approach proposed by White (Econometrica 48:817–838, 1980). Such standard errors,
however, are considerably biased in samples of typical sizes. An improved covariance matrix estimator was proposed by Qian
and Wang (J Stat Comput Simul 70:161–174, 2001). In this paper, we improve upon the Qian–Wang estimator by defining a sequence
of bias-adjusted estimators with increasing accuracy. The numerical results show that the Qian–Wang estimator is typically
much less biased than the estimator proposed by Halbert White and that our correction to the former can be quite effective
in small samples. Finally, we show that the Qian–Wang estimator can be generalized into a broad class of heteroskedasticity-consistent
covariance matrix estimators, and our results can be easily extended to such a class of estimators. 相似文献
6.
Pao-sheng Shen 《Annals of the Institute of Statistical Mathematics》2011,63(6):1207-1219
Patilea and Rolin (Ann Stat 34(2):925–938, 2006) proposed a product-limit estimator of the survival function for twice censored data. In this article,
based on a modified self-consistent (MSC) approach, we propose an alternative estimator, the MSC estimator. The asymptotic
properties of the MSC estimator are derived. A simulation study is conducted to compare the performance between the two estimators.
Simulation results indicate that the MSC estimator outperforms the product-limit estimator and its advantage over the product-limit
estimator can be very significant when right censoring is heavy. 相似文献
7.
This paper is a continuation of Math. Res. Lett. 12 (2005), 493–512. We first construct special Lagrangian submanifolds of the Ricci-flat Stenzel metric (of holonomy SU(n)) on the cotangent bundle of Sn by looking at the conormal bundle of appropriate submanifolds of Sn. We find that the condition for the conormal bundle to be special Lagrangian is the same as that discovered by Harvey–Lawson
for submanifolds in Rn in their pioneering paper, Acta Math. 148 (1982), 47–157. We also construct calibrated submanifolds in complete metrics with special holonomy G2 and Spin(7) discovered by Bryant and Salamon (Duke Math. J. 58 (1989), 829–850) on the total spaces of appropriate bundles over self-dual Einstein four manifolds. The submanifolds are
constructed as certain subbundles over immersed surfaces. We show that this construction requires the surface to be minimal
in the associative and Cayley cases, and to be (properly oriented) real isotropic in the coassociative case. We also make
some remarks about using these constructions as a possible local model for the intersection of compact calibrated submanifolds
in a compact manifold with special holonomy.
Mathematics Subject Classification (2000): 53-XX, 58-XX. 相似文献
8.
In the paper we consider a changed segment model for sample distributions. We generalize Dümbgen’s [Ann. Stat. 19(3), 1471–1495, 1991] change point estimator and obtain optimal rates of convergence of estimators of the beginning and the
length of the changed segment.
This work was supported by cooperation agreement Lille-Vilnius EGIDE Gillibert. 相似文献
9.
Marilyn Breen 《Journal of Geometry》2009,94(1-2):1-6
Let S be a simply connected orthogonal polygon in the plane. A family of examples will establish the following result. For every n ≥ 2, there exists no Krasnosel’skii number h(n) which satisfies this property: If every h(n) points of S are visible via staircase n-paths from a common point, then S is starshaped via staircase n-paths. 相似文献
10.
Jin Ho KWAK Ju Mok OH 《数学学报(英文版)》2006,22(5):1305-1320
A graph G is one-regular if its automorphism group Aut(G) acts transitively and semiregularly on the arc set. A Cayley graph Cay(Г, S) is normal if Г is a normal subgroup of the full automorphism group of Cay(Г, S). Xu, M. Y., Xu, J. (Southeast Asian Bulletin of Math., 25, 355-363 (2001)) classified one-regular Cayley graphs of valency at most 4 on finite abelian groups. Marusic, D., Pisanski, T. (Croat. Chemica Acta, 73, 969-981 (2000)) classified cubic one-regular Cayley graphs on a dihedral group, and all of such graphs turn out to be normal. In this paper, we classify the 4-valent one-regular normal Cayley graphs G on a dihedral group whose vertex stabilizers in Aut(G) are cyclic. A classification of the same kind of graphs of valency 6 is also discussed. 相似文献
11.
Abstract. If u(z) is harmonic in with and we set
A result is obtained which shows, in particular that if and then a bound for can be obtained in terms of for a suitable constant , so that the logarithm of the oscillation has an approximate convexity property.
The proof uses classical inequalities of Hadamard and Borel–Carathéodory and this suggests a generalization to quasiregular
mappings in . Such results are obtained, though necessarily in a less precise form because of the lack of good explicit estimates for
-harmonic measures in spherical ring domains.
Received: 9 November 2000 / Published online: 18 January 2002 相似文献
12.
Summary In the problem of estimating the covariance matrix of a multivariate normal population, James and Stein (Proc. Fourth Berkeley Symp. Math. Statist. Prob.,1, 361–380, Univ. of California Press) obtained a minimax estimator under a scale invariant loss. In this paper we propose
an orthogonally invariant trimmed estimator by solving certain differential inequality involving the eigenvalues of the sample
covariance matrix. The estimator obtained, truncates the extreme eigenvalues first and then shrinks the larger and expands
the smaller sample eigenvalues. Adaptive version of the trimmed estimator is also discussed. Finally some numerical studies
are performed using Monte Carlo simulation method and it is observed that the trimmed estimate shows a substantial improvement
over the minimax estimator.
The second author's research was supported by NSF Grant Number MCS 82-12968. 相似文献
13.
M. O. Smolyanova 《Mathematical Notes》1995,58(3):970-982
A random variablef taking values in a Banach spaceE is estimated from another Banach-valued variableg. The best (with respect to theL
p-metrix) estimator is proved to exist in the case of Bochnerp-integrable variables. For a Hilbert spaceE andp=2, the best estimator is expressed in terms of the conditional expectation and, in the case of jointly Gaussian variables,
in terms of the orthoprojection on a certain subspace ofE. More explicit expressions in terms of surface measures are given for the case in which the underlying probability space
is a Hilbert space with a smooth probability measure. The results are applied to the Wiener process to improve earlier estimates
given by K. Ritter [4].
Translated fromMatematicheskie Zametki, Vol. 58, No. 3, pp. 425–444, September, 1995.
The author is grateful to B. S. Kashin for posing the problem and helping to write the article, and to the reviewer for a
number of useful remarks. 相似文献
14.
We construct an on-line estimator with equidistant design for tracking a smooth function from Stone–Ibragimov–Khasminskii’s
class. This estimator has the optimal convergence rate of risk to zero in sample size. The procedure for setting coefficients
of the estimator is controlled by a single parameter and has a simple numerical solution. The off-line version of this estimator
allows to eliminate a boundary layer. Simulation results are given.
This work is partially supported by a fellowship from the Yitzhak and Chaya Weinstein Research Institute for Signal Processing
at Tel Aviv University. 相似文献
15.
In this paper dynamic and stationary measures of importance of a component in a binary system are considered. To arrive at
explicit results we assume the performance processes of the components to be independent and the system to be coherent. Especially,
the Barlow–Proschan and the Natvig measures are treated in detail and a series of new results and approaches are given. For
the case of components not undergoing repair it is shown that both measures are sensible. Reasonable measures of component
importance for repairable systems represent a challenge. A basic idea here is also to take a so-called dual term into account.
According to the extended Barlow–Proschan measure a component is important if there are high probabilities both that its failure
is the cause of system failure and that its repair is the cause of system repair. Even with this extension results for the
stationary Barlow–Proschan measure are not satisfactory. According to the extended Natvig measure a component is important
if both by failing it strongly reduces the expected system uptime and by being repaired it strongly reduces the expected system
downtime. With this extension the results for the stationary Natvig measure seem very sensible. 相似文献
16.
Kai Diethelm 《Numerische Mathematik》1996,73(1):53-63
Summary.
We show that, if
(),
the error term of
every modified positive interpolatory quadrature rule for
Cauchy principal value integrals of the type
,
, fulfills
uniformly for all
, and hence it is
of optimal
order of magnitude in the classes
().
Here, is a weight function with the property
.
We give explicit upper bounds for the Peano-type error
constants of such rules.
This improves and completes earlier results by
Criscuolo and Mastroianni
(Calcolo 22 (1985), 391–441 and Numer. Math.
54 (1989), 445–461)
and Ioakimidis (Math. Comp. 44 (1985), 191–198).
For the special case of the Gaussian rule, we
show that the restriction
can be dropped.
The results are based on a new representation of the
Peano kernels of these formulae via the Peano kernels of the underlying
classical quadrature formulae. This representation may also be
useful in connection with some different problems.
Received November 21, 1994 相似文献
17.
18.
The aim of this paper is to present a general method to construct projective resolutions of globally defined Mackey functors
over a field of characteristic zero and apply it to obtain explicit resolutions for inflation functors. Our method is a special
case of Bouc’s method in (Proc. Symp. Pure Math. 63 (1998), 31–84) and uses global Mackey functors to construct the projective resolutions. 相似文献
19.
The construction of analogues of the Cauchy kernel is crucial for the solution of Riemann–Hilbert problems on compact Riemann
surfaces. A formula for the Cauchy kernel can be given as an infinite sum over the elements of a Schottky group, and this
sum is often used for the explicit evaluation of the kernel. In this paper a new formula for a quasi-automorphic analogue
of the Cauchy kernel in terms of the Schottky–Klein prime function of the associated Schottky double is derived. This formula
opens the door to finding new ways to evaluate the analogue of the Cauchy kernel in cases where the infinite sum over a Schottky
group is not absolutely convergent. Application of this result to the solution of the Riemann–Hilbert problem with a discontinuous
coefficient for symmetric automorphic functions is discussed.
Received: March 10, 2007. Accepted: April 11, 2007. 相似文献
20.
Consider a long term study, where a series of possibly censored failure times is observed. Suppose the failure times have a common marginal distribution functionF, but they exhibit a mode of dependence characterized by positive or negative association. Under suitable regularity conditions, it is shown that the Kaplan–Meier estimatorFnofFis uniformly strongly consistent; rates for the convergence are also provided. Similar results are established for the empirical cumulative hazard rate function involved. Furthermore, a stochastic process generated byFnis shown to be weakly convergent to an appropriate Gaussian process. Finally, an estimator of the limiting variance of the Kaplan–Meier estimator is proposed and it is shown to be weakly convergent. 相似文献