共查询到20条相似文献,搜索用时 562 毫秒
1.
Virendra C. Bhavsar Uday G. Gujar Joseph D. Horton Lambros A. Lambrou 《BIT Numerical Mathematics》1990,30(2):257-267
The discrepancy of a pseudo-random number (PRN) sequence has been defined as a quantity which measures the deviation of the sequence's distribution from the ideal uniform distribution. In this paper, we give three algorithms for computer evaluation of the discrepancy of PRN sequences. The computational results for the discrepancy of PRN sequences generated by a linear congruential method are included.This research is partially funded by Natural Sciences and Engineering Research Council of Canada, Grant No. 0GP00089. A research grant from IBM Canada through the Supercomputer Center, University of New Brunswick, is gratefully acknowledged. 相似文献
2.
Paul Shaman 《Journal of multivariate analysis》2010,101(5):1263-1273
For a discrete time second-order stationary process, the Levinson-Durbin recursion is used to determine the coefficients of the best linear predictor of the observation at time k+1, given k previous observations, best in the sense of minimizing the mean square error. The coefficients determined by the recursion define a Levinson-Durbin sequence. We also define a generalized Levinson-Durbin sequence and note that binomial coefficients form a special case of a generalized Levinson-Durbin sequence. All generalized Levinson-Durbin sequences are shown to obey summation formulas which generalize formulas satisfied by binomial coefficients. Levinson-Durbin sequences arise in the construction of several autoregressive model coefficient estimators. The least squares autoregressive estimator does not give rise to a Levinson-Durbin sequence, but least squares fixed point processes, which yield least squares estimates of the coefficients unbiased to order 1/T, where T is the sample length, can be combined to construct a Levinson-Durbin sequence. By contrast, analogous fixed point processes arising from the Yule-Walker estimator do not combine to construct a Levinson-Durbin sequence, although the Yule-Walker estimator itself does determine a Levinson-Durbin sequence. The least squares and Yule-Walker fixed point processes are further studied when the mean of the process is a polynomial time trend that is estimated by least squares. 相似文献
3.
Summary Given a sequence of ϕ-mixing random variables not necessarily stationary, a Chernoff-Savage theorem for two-sample linear
rank statistics is proved using the Pyke-Shorack [5] approach based on weak convergence properties of empirical processes
in an extended metric. This result is a generalization of Fears and Mehra [4] in that the stationarity is not required and
that the condition imposed on the mixing numbers is substantially relaxed. A similar result is shown to hold for strong mixing
sequences under slightly stronger conditions on the mixing numbers.
Research partially supported by the National Research Council of Canada under Grant No. A-3954. 相似文献
4.
Micha Sharir 《Combinatorica》1987,7(1):131-143
Davenport—Schinzel sequences are sequences that do not contain forbidden subsequences of alternating symbols. They arise in
the computation of the envelope of a set of functions. We obtain almost linear upper bounds on the length λs(n) of Davenport—Schinzel sequences composed ofn symbols in which no alternating subsequence is of length greater thans+1. These bounds are of the formO(nα(n)O(α(n)5-3)), and they generalize and extend the tight bound Θ(nα(n)) obtained by Hart and Sharir for the special cases=3 (α(n) is the functional inverse of Ackermann’s function), and also improve the upper boundO(n log*n) due to Szemerédi.
Work on this paper has been supported in part by a grant from the U.S. — Israeli Binational Science Foundation. 相似文献
5.
The classical Gauss code problem asks to characterize which cyclic sequences arise as the vertex sequence of the straight-ahead path of a 4-regular graph embedded in the plane This problem is generalized to certain 4 regular graphs in arbitrary surfacesA characterization is given for the existence of a 4-regular graph in a specified surface yielding the specified sequence This characterization is obtained using a generalization of Shank's left-right paths 相似文献
6.
The skew of a binary string is the difference between the number of zeroes and the number of ones, while the length of the string is the sum of these two numbers. We consider certain suffixes of the lexicographically-least de Bruijn sequence at natural breakpoints of the binary string. We show that the skew and length of these suffixes are enumerated by sequences generalizing the Fibonacci and Lucas numbers, respectively. 相似文献
7.
Naoki Osada 《Numerical Algorithms》1992,3(1):335-344
A fixed point sequence is singular if the Jacobian matrix at the limit has 1 as an eigenvalue. The asymptotic behaviour of some singular fixed point sequences in one dimension are extended toN dimensions. Three algorithms extrapolating singular fixed point sequences inN dimensions are given. Using numerical examples three algorithms are tested and compared. 相似文献
8.
In this paper we use the Nash-Williams theory of fronts and barriers to study weakly null sequences in Banach spaces. Specifically, we show how barriers relate to the classical fact that C(K) with K a countable compactum is c0-saturated. Another result relates the notion of a barrier to the Maurey-Rosenthal example of a weakly null sequence with no unconditional subsequences. In particular, we construct examples of weakly-null sequences which are α-unconditional but not β-unconditional. 相似文献
9.
Richard C Bradley 《Journal of multivariate analysis》1981,11(1):1-16
This article is motivated by a central limit theorem of Ibragimov for strictly stationary random sequences satisfying a mixing condition based on maximal correlations. Here we show that the mixing condition can be weakened slightly, and construct a class of stationary random sequences covered by the new version of the theorem but not Ibragimov's original version. Ibragimov's theorem is also extended to triangular arrays of random variables, and this is applied to some kernel-type estimates of probability density. 相似文献
10.
Francisco J. Caro-LoperaVíctor Leiva N. Balakrishnan 《Journal of multivariate analysis》2012,104(1):126-139
In this paper, we establish a connection between the Hadamard product and the usual matrix multiplication. In addition, we study some new properties of the Hadamard product and explore the inverse problem associated with the established connection, which facilitates diverse applications. Furthermore, we propose a matrix-variate generalized Birnbaum-Saunders (GBS) distribution. Three representations of the matrix-variate GBS density are provided, one of them by using the mentioned connection. The main motivation of this article is based on the fact that the representation of the matrix-variate GBS density based on element-by-element specification does not allow matrix transformations. Consequently, some statistical procedures based on this representation, such as multivariate data analysis and statistical shape theory, cannot be performed. For this reason, the primary goal of this work is to obtain a matrix representation of the matrix-variate GBS density that is useful for some statistical applications. When the GBS density is expressed by means of a matrix representation based on the Hadamard product, such a density is defined in terms of the original matrices, as is common for many matrix-variate distributions, allowing matrix transformations to be handled in a natural way and then suitable statistical procedures to be developed. 相似文献
11.
Davenport—Schinzel sequences are sequences that do not contain forbidden subsequences of alternating symbols. They arise in
the computation of the envelope of a set of functions. We show that the maximal length of a Davenport—Schinzel sequence composed
ofn symbols is Θ (nα(n)), where α(n) is the functional inverse of Ackermann’s function, and is thus very slowly increasing to infinity. This is achieved by establishing
an equivalence between such sequences and generalized path compression schemes on rooted trees, and then by analyzing these
schemes.
Work on this paper by the second author has been supported in part by a grant from the U.S.-Israeli Binational Science Foundation. 相似文献
12.
Pavel Trojovský 《Discrete Applied Mathematics》2007,155(15):2017-2024
Some new identities for the Fibonomial coefficients are derived. These identities are related to the generating function of the kth powers of the Fibonacci numbers. Proofs are based on manipulation with the generating function of the sequence of “signed Fibonomial triangle”. 相似文献
13.
Pavel Valtr† 《Combinatorica》2003,23(1):151-184
In this paper we study labeled–tree analogues of
(generalized) Davenport–Schinzel sequences.We say that two sequences a
1 ...
a
k
, b
1 ...
b
k
of equal length
k are isomorphic, if
a
i
= a
j
i
b
i
= b
j
(for all
i, j). For example, the sequences 11232,
33141 are isomorphic. We investigate the maximum size of a
labeled (rooted) tree with each vertex labeled by one of
n labels in such a way that,
besides some technical conditions, the sequence of labels along
any path (starting from the root) contains no subsequence
isomorphic to a fixed forbidden sequence
u.We study two models of such labeled trees. Each of the
models is known to be essentially equivalent also to other
models. The labeled paths in a special case of one of our models
correspond to classical Davenport–Schinzel sequences.We investigate, in particular, for which sequences
u the labeled tree has at
most O(n) vertices. In both models, we answer
this question for any forbidden sequence u over a two-element alphabet and also
for a large class of other sequences u.* This research was partially supported by Charles
University grants No. 99/158 and 99/159 and by Czech Republic
Grant GAR 201/99/0242. Supported by project LN00A056 of The Ministry of
Education of the Czech Republic. 相似文献
14.
L. M. García. Raffi E. A. Sánchez. Pérez J. V. Sánchez. Pérez 《Integral Equations and Operator Theory》2006,54(4):495-510
Let λ be a countably additive vector measure with values in a separable real Hilbert space H. We define and study a pseudo metric on a Banach lattice of integrable functions related to λ that we call a λ-weighted distance.
We compute the best approximation with respect to this distance to elements of the function space by the use of sequences
with special geometric properties. The requirements on the sequence of functions are given in terms of a commutation relation
between these functions that involves integration with respect to λ. We also compare the approximation that is obtained in
this way with the corresponding projection on a particular Hilbert space. 相似文献
15.
By using chaos expansion into multiple stochastic integrals, we make a wavelet analysis of two self-similar stochastic processes: the fractional Brownian motion and the Rosenblatt process. We study the asymptotic behavior of the statistic based on the wavelet coefficients of these processes. Basically, when applied to a non-Gaussian process (such as the Rosenblatt process) this statistic satisfies a non-central limit theorem even when we increase the number of vanishing moments of the wavelet function. We apply our limit theorems to construct estimators for the self-similarity index and we illustrate our results by simulations. 相似文献
16.
The Jacobi–Stirling numbers of the first and second kinds were first introduced in Everitt et al. (2007) [8] and they are a generalization of the Legendre–Stirling numbers. Quite remarkably, they share many similar properties with the classical Stirling numbers. In this paper we study total positivity properties of these numbers. In particular, we prove that the matrix whose entries are the Jacobi–Stirling numbers is totally positive and that each row and each column is a Pólya frequency sequence, except for the columns with (unsigned) numbers of the first kind. 相似文献
17.
The censored linear regression model, also referred to as the accelerated failure time (AFT) model when the logarithm of the survival time is used as the response variable, is widely seen as an alternative to the popular Cox model when the assumption of proportional hazards is questionable. Buckley and James [Linear regression with censored data, Biometrika 66 (1979) 429-436] extended the least squares estimator to the semiparametric censored linear regression model in which the error distribution is completely unspecified. The Buckley-James estimator performs well in many simulation studies and examples. The direct interpretation of the AFT model is also more attractive than the Cox model, as Cox has pointed out, in practical situations. However, the application of the Buckley-James estimation was limited in practice mainly due to its illusive variance. In this paper, we use the empirical likelihood method to derive a new test and confidence interval based on the Buckley-James estimator of the regression coefficient. A standard chi-square distribution is used to calculate the P-value and the confidence interval. The proposed empirical likelihood method does not involve variance estimation. It also shows much better small sample performance than some existing methods in our simulation studies. 相似文献
18.
F.Rudolf Beyl 《Journal of Pure and Applied Algebra》1976,7(2):175-193
An abelian group A is called absolutely abelian, if in every central extension N ? G ? A the group G is also abelian. The abelian group A is absolutely abelian precisely when the Schur multiplicator H2A vanished. These groups, and more generally groups with HnA = 0 for some n, are characterized by elementary internal properties. (Here H1A denotes the integral homology of A.) The cases of even n and odd n behave strikingly different. There are 2?ο different isomorphism types of abelian groups A with reduced torsion subgroup satisfying H2nA = 0. The major tools are direct limit arguments and the Lyndon-Hochschild-Serre (L-H-S) spectral sequence, but the treatment of absolutely abelian groups does not use spectral sequences. All differentials dr for r ≥ 2 in the L-H-S spectral sequence of a pure abelian extension vanish. Included is a proof of the folklore theorem, that homology of groups commutes with direct limits also in the group variable, and a discussion of the L-H-S spectral sequence for direct limits. 相似文献
19.
Simeon M. Berman 《Annals of the Institute of Statistical Mathematics》1984,36(1):301-321
Summary Let {X
n,j,−∞<j<∞∼,n≧1, be a sequence of stationary sequences on some probability space, with nonnegative random variables. Under appropriate
mixing conditions, it is shown thatS
n=Xn,1+…+X
n,n has a limiting distribution of a general infinitely divisible form. The result is applied to sequences of functions {f
n(x)∼ defined on a stationary sequence {X
j∼, whereX
n.f=fn(Xj). The results are illustrated by applications to Gaussian processes, Markov processes and some autoregressive processes of
a general type.
This paper represents results obtained at the Courant Institute of Mathematical Sciences, New York University, under the sponsorship
of the National Sciences Foundation, Grant MCS 82-01119. 相似文献
20.
We prove a central limit theorem for strictly stationary random fields under a sharp projective condition. The assumption was introduced in the setting of random sequences by Maxwell and Woodroofe. Our approach is based on new results for triangular arrays of martingale differences, which have interest in themselves. We provide as applications new results for linear random fields and nonlinear random fields of Volterra-type. 相似文献