共查询到20条相似文献,搜索用时 15 毫秒
1.
F. Carbonell K. J. Worsley L. Galan 《Annals of the Institute of Statistical Mathematics》2011,63(1):1-27
The statistical problem addressed in this paper is to approximate the P value of the maximum of a smooth random field of Wilks’s Λ statistics. So far results are only available for the usual univariate
statistics (Z, t, χ2, F) and a few multivariate statistics (Hotelling’s T
2, maximum canonical correlation, Roy’s maximum root). We derive results for any differentiable scalar function of two independent
Wishart random fields, such as Wilks’s Λ random field. We apply our results to a problem in brain shape analysis. 相似文献
2.
The ideas of variable sampling interval (VSI), variable sample size (VSS), variable sample size and sampling interval (VSSI), and variable parameters (VP) in the univariate case have been successfully applied to the multivariate case to improve the efficiency of Hotelling’s T2 chart with fixed sampling rate (FSR) in detecting small process shifts. However, the main disadvantage in using most of these control schemes is an increasing in the complexity due to the adaptive changes in sampling intervals. In this paper, retaining the lengths of sampling intervals constant, a variable sample size and control limit (VSSC) T2 chart is proposed and described. The statistical efficiency of the VSSC T2 chart in terms of the average time to signal a shift in process mean vector is compared with that of the VP, VSSI, VSS, VSI, and FSR T2 charts. From the results of comparison, it shows that the VSSC T2 chart for a (very) small shift in the process mean vector gives a better performance than the VSSI, VSS, VSI, and FSR T2 charts; meanwhile, it presents a similar performance to the VP T2 chart. Furthermore, from the viewpoint of practicability, it is more convenient for administrating the control chart than the VSI, VSSI, and VP T2 chart. Thus, it may provide a good option for quick response to small shifts in a multivariate process. 相似文献
3.
M. V. Koutras S. Bersimis P. E. Maravelakis 《Methodology and Computing in Applied Probability》2007,9(2):207-224
The aim of this paper is to present the basic principles and recent advances in the area of statistical process control charting
with the aid of runs rules. More specifically, we review the well known Shewhart type control charts supplemented with additional
rules based on the theory of runs and scans. The motivation for this article stems from the fact that during the last decades,
the performance improvement of the Shewhart charts by exploiting runs rules has attracted continuous research interest. Furthermore,
we briefly discuss the Markov chain approach which is the most popular technique for studying the run length distribution
of run based control charts.
相似文献
4.
Markos V. Koutras Sotirios Bersimis Demetrios L. Antzoulakos 《Methodology and Computing in Applied Probability》2006,8(3):409-426
The most popular multivariate process monitoring and control procedure used in the industry is the chi-square control chart.
As with most Shewhart-type control charts, the major disadvantage of the chi-square control chart, is that it only uses the
information contained in the most recently inspected sample; as a consequence, it is not very efficient in detecting gradual
or small shifts in the process mean vector. During the last decades, the performance improvement of the chi-square control
chart has attracted continuous research interest. In this paper we introduce a simple modification of the chi-square control
chart which makes use of the notion of runs to improve the sensitivity of the chart in the case of small and moderate process
mean vector shifts.
相似文献
5.
For several decades, much attention has been paid to the two-sample Behrens-Fisher (BF) problem which tests the equality of
the means or mean vectors of two normal populations with unequal variance/covariance structures. Little work, however, has
been done for the k-sample BF problem for high dimensional data which tests the equality of the mean vectors of several high-dimensional normal
populations with unequal covariance structures. In this paper we study this challenging problem via extending the famous Scheffe’s
transformation method, which reduces the k-sample BF problem to a one-sample problem. The induced one-sample problem can be easily tested by the classical Hotelling’s
T
2 test when the size of the resulting sample is very large relative to its dimensionality. For high dimensional data, however,
the dimensionality of the resulting sample is often very large, and even much larger than its sample size, which makes the
classical Hotelling’s T
2 test not powerful or not even well defined. To overcome this difficulty, we propose and study an L
2-norm based test. The asymptotic powers of the proposed L
2-norm based test and Hotelling’s T
2 test are derived and theoretically compared. Methods for implementing the L
2-norm based test are described. Simulation studies are conducted to compare the L
2-norm based test and Hotelling’s T
2 test when the latter can be well defined, and to compare the proposed implementation methods for the L
2-norm based test otherwise. The methodologies are motivated and illustrated by a real data example.
The work was supported by the National University of Singapore Academic Research Grant (Grant No. R-155-000-085-112) 相似文献
6.
Monitoring process variability using auxiliary information 总被引:2,自引:1,他引:1
Muhammad Riaz 《Computational Statistics》2008,23(2):253-276
In this study a Shewhart type control chart namely V
r
chart is proposed for improved monitoring of process variability (targeting large shifts) of a quality characteristic of
interest Y. The proposed control chart is based on regression type estimator of variance using a single auxiliary variable X. It is assumed that (Y, X) follow a bivariate normal distribution. The design structure of V
r
chart is developed and its comparison is made with the well-known Shewhart control chart namely S
2 chart used for the same purpose. Using power curves as a performance measure it is observed that V
r
chart outperforms the S
2 chart for detecting moderate to large shifts, which is main target of Shewhart type control charts, in process variability
under certain conditions on ρ
yx
. These efficiency conditions on ρ
yx
are also obtained for V
r
chart in this study. 相似文献
7.
Most industrial products and processes are characterized by several, typically correlated measurable variables, which jointly describe the product or process quality. Various control charts such as Hotelling’s T2, EWMA and CUSUM charts have been developed for multivariate quality control, where the values of the chart parameters, namely the sample size, sampling interval and the control limits are determined to satisfy given economic and/or statistical requirements. It is well known that this traditional non-Bayesian approach to a control chart design is not optimal, but very few results regarding the form of the optimal Bayesian control policy have appeared in the literature, all limited to a univariate chart design. In this paper, we consider a multivariate Bayesian process mean control problem for a finite production run under the assumption that the observations are values of independent, normally distributed vectors of random variables. The problem is formulated in the POMDP (partially observable Markov decision process) framework and the objective is to determine a control policy minimizing the total expected cost. It is proved that under standard operating and cost assumptions the control limit policy is optimal. Cost comparisons with the benchmark chi-squared chart and the MEWMA chart show that the Bayesian chart is highly cost effective, the savings are larger for smaller values of the critical Mahalanobis distance between the in-control and out-of-control process mean. 相似文献
8.
Abraham Zaks 《Israel Journal of Mathematics》1980,37(4):281-302
LetR be a commutative domain with 1. We termR an HFD (Half-Factorial-Domain) provided the equality Π
i=1
n
χi=Π{f=1/m}y
f impliesm=n, whenever thex’s and they’s are non-zero, non-unit and irreducible elements ofR. The purpose of this note is to study HFD’s, in particular, Krull domains that are HFD’s, and to provide examples of HFD’s,
that contradict a conjecture of Narkiewicz. 相似文献
9.
S. Simic 《Acta Mathematica Hungarica》2009,124(4):353-361
We prove a global assertion on logarithmic convexity of Csiszár’s ƒ-divergence. It follows that the relative s-information measure is log-convex for s ∈ ℝ, wherefrom some new inequalities connecting Kullback-Leibler divergence and χ2 and Hellinger distances arise. 相似文献
10.
A process variability control chart 总被引:1,自引:0,他引:1
In this study a Shewhart type control chart namely the V
t
chart, is proposed for improved monitoring of the process variability of a quality characteristic of interest Y. The proposed control chart is based on the ratio type estimator of the variance using a single auxiliary variable X. It is assumed that (Y, X) follows a bivariate normal distribution. The design structure of the V
t
chart is developed for Phase-I quality control and its comparison is made with those of the S
2 chart (a well-known Shewhart control chart) and the V
r
chart (a Shewhart type control chart proposed by Riaz (Comput Stat, 2008a) used for the same purpose. It is observed that
the proposed V
t
chart outperforms the S
2 and V
r
charts, in terms of discriminatory power, for detecting moderate to large shifts in the process variability. It is observed
that the performance of the V
t
chart keeps improving with an increase in |ρ
yx
| , where ρ
yx
is the correlation between Y and X. 相似文献
11.
Control charts are the most popular tool for monitoring production quality. In traditional control charts, it is usually supposed that the observations follow a multivariate normal distribution. Nevertheless, there are many practical applications where the normality assumption is not fulfilled. Furthermore, the performance of these charts in the presence of measurement errors (outliers) in the historical data has been improved using robust control charts when the observations follow a normal distribution. In this paper, we develop a new control chart for t‐Student data based on the trimmed T2 control chart () through the adaptation of the elements of this chart to the case of this distribution. Simulation studies show that a control chart performs better than T2 in t‐Student samples for individual observations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
12.
Allan Berele 《Israel Journal of Mathematics》2007,160(1):371-387
In this paper we study the cocharacter sequence of M
2,1 and obtain estimates for the multiplicities of the irreducible S
n
-characters χλ, where λ is any partition with at most 5 parts.
The author’s work was supported by both the Faculty Research Council of De Paul University and the National Security Agency,
under Grant MDA904-500270. The United States Government is authorized to reproduce and distribute reprints notwithstanding
any copyright notation herein. 相似文献
13.
Moritz Minzlaff 《Mathematics in Computer Science》2010,3(2):209-224
Following Gaudry and Gürel who extended Kedlaya’s algorithm to superelliptic curves, we introduce Harvey’s optimisation for
large characteristic p to the superelliptic case. As result, we state the most general algorithm to compute zeta functions that runs soft linear
in p
1/2. We demonstrate its effectiveness using a Magma implementation. 相似文献
14.
We generalize Weil’s converse theorem to Jacobi cusp forms of weight k, index m and Dirichlet character χ over the group Γ
0(N)⋉ℤ2. Then two applications of this result are given; we generalize a construction of Jacobi forms due to Skogman and present
a new proof for several known lifts of such Jacobi forms to half-integral weight modular forms. 相似文献
15.
Vivek V. Rane 《Proceedings Mathematical Sciences》2003,113(3):213-221
Euler-Maclaurin and Poisson analogues of the summations ε
a <n ≤b
χ(n)f(n), have been obtained in a unified manner, where (χ(n)) is a periodic complex sequence;d(n) is the divisor function andf(x) is a sufficiently smooth function on [a, b]. We also state a generalised Abel’s summation formula, generalised Euler’s summation formula and Euler’s summation formula
in several variables. 相似文献
16.
CHEN Zhuo & LIU Zhangju Department of Mathematics Capital Normal University Beijing China School of Mathematical Science Peking University Beijing China 《中国科学A辑(英文版)》2006,49(2):277-288
For a transitive Lie algebroid A on a connected manifold M and its representation on a vector bundle F, we define a morphism of cohomology groups rk: Hk(A,F) → Hk(Lx,Fx), called the localization map, where Lx is the adjoint algebra at x ∈ M. The main result in this paper is that if M is simply connected, or H (LX,FX) is trivial, then T is injective. This means that the Lie algebroid 1-cohomology is totally determined by the 1-cohomology of its adjoint Lie algebra in the above two cases. 相似文献
17.
Francisco-Javier Turiel 《manuscripta mathematica》2003,110(2):195-201
Consider an effective real analytic action of a connected Lie group G on a compact connected surface of Euler characteristic χ≠0. We show that if the action has no fixed point then χ≥1 and the
Lie algebra 𝒢 of G is isomorphic either to a subalgebra of the affine algebra of ℝ2, which is the extension of the ideal of constant vector fields by an irreducible linear subalgebra, or to sl(2,ℝ), o(3), sl(2,ℂ) and sl(3,ℝ).
Received: 7 August 2001 Published online: 24 January 2003 相似文献
18.
Rafael Bru Rafael Cantó Ricardo L. Soto Ana M. Urbano 《Central European Journal of Mathematics》2012,10(1):312-321
Given a square matrix A, a Brauer’s theorem [Brauer A., Limits for the characteristic roots of a matrix. IV. Applications to stochastic matrices,
Duke Math. J., 1952, 19(1), 75–91] shows how to modify one single eigenvalue of A via a rank-one perturbation without changing any of the remaining eigenvalues. Older and newer results can be considered
in the framework of the above theorem. In this paper, we present its application to stabilization of control systems, including
the case when the system is noncontrollable. Other applications presented are related to the Jordan form of A and Wielandt’s and Hotelling’s deflations. An extension of the aforementioned Brauer’s result, Rado’s theorem, shows how
to modify r eigenvalues of A at the same time via a rank-r perturbation without changing any of the remaining eigenvalues. The same results considered by blocks can be put into the
block version framework of the above theorem. 相似文献
19.
The Hadwiger number η(G) of a graph G is the largest integer n for which the complete graph K
n
on n vertices is a minor of G. Hadwiger conjectured that for every graph G, η(G) ≥ χ(G), where χ(G) is the chromatic number of G. In this paper, we study the Hadwiger number of the Cartesian product of graphs.
As the main result of this paper, we prove that for any two graphs G
1 and G
2 with η(G
1) = h and η(G
2) = l. We show that the above lower bound is asymptotically best possible when h ≥ l. This asymptotically settles a question of Z. Miller (1978).
As consequences of our main result, we show the following:
Alexandr Kostochka: Research of this author is supported in part by NSF grant DMS-0650784 and grant 06-01-00694 of the Russian
Foundation for Basic Research. 相似文献
1. | Let G be a connected graph. Let be the (unique) prime factorization of G. Then G satisfies Hadwiger’s conjecture if k ≥ 2 log log χ(G) + c′, where c′ is a constant. This improves the 2 log χ(G) + 3 bound in [2]. |
2. | Let G 1 and G 2 be two graphs such that χ(G 1) ≥ χ(G 2) ≥ c log1.5(χ(G 1)), where c is a constant. Then satisfies Hadwiger’s conjecture. |
3. | Hadwiger’s conjecture is true for G d (Cartesian product of G taken d times) for every graph G and every d ≥ 2. This settles a question by Chandran and Sivadasan [2]. (They had shown that the Hadiwger’s conjecture is true for G d if d ≥ 3). |
20.
Anish Sarkar Kanwar Sen Anuradha 《Annals of the Institute of Statistical Mathematics》2004,56(2):317-349
We consider a {0,1}-valuedm-th order stationary Markov chain. We study the occurrences of runs where two 1’s are separated byat most/exactly/at least k 0’s under the overlapping enumeration scheme wherek≥0 and occurrences of scans (at leastk
1 successes in a window of length at mostk, 1≤k
1≤k) under both non-overlapping and overlapping enumeration schemes. We derive the generating function of first two types of
runs. Under the conditions, (1) strong tendency towards success and (2) strong tendency towards reversing the state, we establish
the convergence of waiting times of ther-th occurrence of runs and scans to Poisson type distributions. We establish the central limit theorem and law of the iterated
logarithm for the number of runs and scans up to timen. 相似文献