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1.
Chris Field John Robinson Elvezio Ronchetti 《Annals of the Institute of Statistical Mathematics》2008,60(1):225-227
We obtain marginal tail area approximations for the one-dimensional test statistic based on the appropriate component of the
M-estimate for both standardized and Studentized versions which are needed for tests and confidence intervals. The result is
proved under conditions which allow the application to finite sample situations such as the bootstrap and involves a careful
discretization with saddlepoints being used for each neighbourhood. These results are used to obtain second-order relative
error results on the accuracy of the Studentized and the tilted bootstrap. The tail area approximations are applied to a Poisson
regression model and shown to have very good accuracy.
An erratum to this article can be found at 相似文献
2.
The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact intervals, only. This method, which is based on an approximate partition of unity, was introduced by Maz’ya in 1991 and has mainly been used for functions defined on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed.In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly. 相似文献
3.
Abstract We study multiple Riemann-Stieltjes integral approximations to multiple Stratonovich fractional integrals. Two standard approximations (Wong-Zakai and Mollifier approximations) are considered and we show the convergence in the mean square sense and uniformly on compact time intervals of these approximations to the multiple Stratonovich fractional integral. 相似文献
4.
An iterative method, combining bisections and successive approximations, is proposed for computing intervals containing the Gittins indices. The intervals could be of a specified maximum length, or be merely disjoint. The first option gives approximations of the Gittins indices. The second option gives a ranking of indices, which in many applications is sufficient.Supported by the Royal Norwegian Council for Industrial and Scientific Research and by the National Science Foundation. 相似文献
5.
Sonia Mazzucchi Valter Moretti Ivan Remizov Oleg Smolyanov 《Mathematische Nachrichten》2023,296(3):1244-1284
Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks. 相似文献
6.
Prof. Dr. Hans-Peter Blatt 《Numerische Mathematik》1977,27(2):191-202
Summary In this paper, we study the continuity of the dependence of best rational. approximations to functions real-valued and continuous on unbounded intervals. We give sufficient conditions for continuity which seem to be also necessary. 相似文献
7.
The M/G/K queueing system is one of the oldest models for multiserver systems and has been the topic of performance papers for almost
half a century. However, even now, only coarse approximations exist for its mean waiting time. All the closed-form (nonnumerical)
approximations in the literature are based on (at most) the first two moments of the job size distribution. In this paper
we prove that no approximation based on only the first two moments can be accurate for all job size distributions, and we
provide a lower bound on the inapproximability ratio, which we refer to as “the gap.” This is the first such result in the
literature to address “the gap.” The proof technique behind this result is novel as well and combines mean value analysis,
sample path techniques, scheduling, regenerative arguments, and asymptotic estimates. Finally, our work provides insight into
the effect of higher moments of the job size distribution on the mean waiting time. 相似文献
8.
G. W. Riley 《Israel Journal of Mathematics》1979,33(1):9-31
This paper presents some extensions and applications of the method of approximations of ergodic theory (see [6]). Two notions
of approximation are defined which are applicable to arbitrary σ-finite-measure-preserving group actions (see §1). Building
upon results of [2], [13] and [6], the speeds of such approximations are related to the questions of spectral multiplicity,
spectral type and ergodicity (see §3). For the result on spectral multiplicity, there is first established a general result
concerning the spectral decomposition of unitary representations (see §2). The last section is devoted to applications—chiefly
to certain classes of cylinder transformations which arise in connection with irregularity of distribution (see [12]). These
transformations provide examples (on infinite measure spaces) of approximations of all finite multiplicities. The method of
approximations is shown to be a natural tool for the study of their spectral properties. 相似文献
9.
Christopher S. Withers Saralees Nadarajah 《Bulletin of the Brazilian Mathematical Society》2011,42(2):213-242
Cornish-Fisher expansions about the normal distribution provide accurate approximations for distributions of estimates and
also for the level in the nominal error of confidence intervals. However, there is an advantage is expanding about a skew distribution like the chi-square, since the first order approximations become second order if the skewness is matched. Higher
order approximations are also simplified. We demonstrate the method by approximating the distribution of standardized and
Studentized linear combinations of means. 相似文献
10.
A new algorithm is proposed for computing the intersection of two plane curves given in rational parametric form. It relies
on the Ehrlich–Aberth iteration complemented with some computational tools like the properties of Sylvester and Bézout matrices,
a stopping criterion based on the concept of pseudo-zero, an inclusion result and the choice of initial approximations based
on the Newton polygon. The algorithm is implemented as a Fortran 95 module. From the numerical experiments performed with
a wide set of test problems it shows a better robustness and stability with respect to the Manocha–Demmel approach based on
eigenvalue computation. In fact, the algorithm provides better approximations in terms of the relative error and performs
successfully in many critical cases where the eigenvalue computation fails. 相似文献
11.
H.J Kushner 《Journal of Mathematical Analysis and Applications》1976,53(2):251-265
The paper treats the problem of obtaining numerical solutions to the Fokker-Plank equation for the density of a diffusion, and for the conditional density, given certain “white noise” corrupted observations. These equations generally have a meaning only in the weak sense; the basic assumptions on the diffusion are that the coefficients are bounded, and uniformly continuous, and that the diffusion has a unique solution in the sense of multivariate distributions. It is shown that, if the finite difference approximations are carefully (but naturally) chosen, then the finite difference solutions to the formal adjoints yield immediately a sequence of approximations that converge weakly to the weak sense solution to the Fokker-Plank equation (conditional or not), as the difference intervals go to zero.The approximations seem very natural for this type of problem. They are related to the transition functions of a sequence of Markov chains, the measures of whose continuous time interpolations converge weakly to the (measure of) diffusion, as the difference intervals go to zero, and, hence, seem to have more physical significance than the usual (formal or not) approximations. The method is purely probabilistic and relies heavily on results of the weak convergence of measures on abstract spaces. 相似文献
12.
To solve one-dimensional linear weakly singular integral equations on bounded intervals, with input functions which may be smooth or not, we propose to introduce first a simple smoothing change of variable, and then to apply classical numerical methods such as product-integration and collocation based on global polynomial approximations. The advantage of this approach is that the order of the methods can be arbitrarily high and that the associated linear systems one has to solve are very well-conditioned.
13.
M. A. Sukhorol’skii 《Ukrainian Mathematical Journal》1997,49(5):787-797
We study the order of polynomial approximations of periodic functions on intervals which are internal with respect to the
main interval of periodicity and on which these functions are sufficiently smooth. The estimates obtained contain parameters
which characterize the smoothness and alternation of signs of nuclear functions and parameters that determine classes of approximated
functions.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp.706–714, May, 1997. 相似文献
14.
Many approximations of queueing performance measures are based on moment matching. Empirical and theoretical results show
that although approximations based on two moments are often accurate, two-moment approximations can be arbitrarily bad and
sometimes three-moment approximations are far better. In this paper, we investigate graphically error bounds for two- and
three-moment approximations of three performance measures forGI/M/ · type models. Our graphical analysis provides insight into the adequacy of two- and three-moment approximations as a function
of standardized moments of the interarrival-time distribution. We also discuss how the behavior of these approximations varies
with other model parameters and with the performance measure being approximated. 相似文献
15.
《European Journal of Operational Research》1998,105(1):216-223
Lagrangean relaxation produces bounds on the optimal value of (mixed) integer programming problems. These bounds, together with integer feasible solution values, provide intervals bracketing the optimal value of the original problem. When the residual gap, i.e., the relative size of the interval, is too large for the approximations to be deemed satisfactory, it is desirable to ‘strengthen’ the Lagrangean bounds. One possible strengthening technique consists of identifying cuts which are violated by the current Lagrangean solution, and dualizing them. Unfortunately not every valid inequality that is currently violated will improve the Lagrangean relaxation bound when dualized. This paper investigates what makes a violated cut ‘efficient’ in improving bounds. It also provides examples of efficient cuts for several (mixed) integer programming problems. 相似文献
16.
A new approach to the approximation of operators in the Hilbert space of functions on a locally compact Abelian (LCA) group is developed. This approach is based on sampling the symbols of such operators. To choose the points for sampling, we use the approximations of LCA groups by finite groups, which were introduced and investigated by Gordon. In the case of the group R
n
, the constructed approximations include the finite-dimensional approximations of the coordinate and linear momentum operators, suggested by Schwinger. The finite-dimensional approximations of the Schrödinger operator based on Schwinger's approximations were considered by Digernes, Varadarajan, and Varadhan in Rev. Math. Phys. 6 (4) (1994), 621–648 where the convergence of eigenvectors and eigenvalues of the approximating operators to those of the Schrödinger operator was proved in the case of a positive potential increasing at infinity. Here this result is extended to the case of Schrödinger-type operators in the Hilbert space of functions on LCA groups. We consider the approximations of p-adic Schrödinger operators as an example. For the investigation of the constructed approximations, the methods of nonstandard analysis are used. 相似文献
17.
This paper proposes a new methodology to schedule activities in projects with stochastic activity durations. The main idea
is to determine for each activity an interval in which the activity is allowed to start its processing. Deviations from these intervals result in penalty costs. We employ
the Cross-Entropy methodology to set the intervals so as to minimize the sum of the expected penalty costs. The paper describes
the implementation of the method, compares its results to other heuristic methods and provides some insights towards actual
applications. 相似文献
18.
Direct numerical solutions of scattering problems based on boundary-integral equations are computationally costly at high frequencies. A numerical method is presented that efficiently computes accurate approximations to unknown surface quantities given known surface data (an approximate Dirichlet-to-Neumann map). The method is based on a pseudo-differential impedance operator (PIO) numerically implemented using rational approximations. An example of a PIO is the so-called on-surface radiation condition (OSRC) method. For a convex obstacle, the method can be viewed as applying a parabolic equation directly on the surface of a scatterer. In contrast to past OSRCs, the use of rational approximations provides accuracy for wide scattering angles which is needed for grazing angles of incidence. Generalization to impedance operators for two-dimensional acoustic scatterers with concave parts is presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
M. Celia Rodríguez-Campos 《Journal of multivariate analysis》1999,69(2):218
Local confidence intervals for regression function with binary response variable are constructed. These intervals are based on both theoretical and “plug-in” normal asymptotic distribution of a usual statistic. In the plug-in approach, two ways of estimating bias are proposed; for them we obtain the mean squared error and deduce an expression of an optimal bandwidth. The rate of convergence of theoretical distributions to their limits is obtained by means of Edgeworth expansions. Likewise, these expansions allow us to deduce properties about the coverage probability of the confidence intervals. Theoretic approximations to that probability are compared in a simulation study with the corresponding coverage rates. 相似文献
20.
Toshikazu Kimura 《Queueing Systems》1994,17(3-4):347-382
This paper provides a unifying method of generating and/or evaluating approximations for the principal congestion measures in aGI/G/s queueing system. The main focus is on the mean waiting time, but approximations are also developed for the queue-length distribution, the waiting-time distribution and the delay probability for the Poisson arrival case. The approximations have closed forms that combine analytical solutions of simpler systems, and hence they are referred to as system-interpolation approximations or, simply, system interpolations. The method in this paper is consistent with and generalizes system interpolations previously presented for the mean waiting time in theGI/G/s queue. 相似文献