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1.
Point process diagnostics based on weighted second-order statistics and their asymptotic properties 总被引:2,自引:0,他引:2
Giada Adelfio Frederic Paik Schoenberg 《Annals of the Institute of Statistical Mathematics》2009,61(4):929-948
A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point
processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result
is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex point process model with an arbitrary conditional intensity function,
rather than a stationary Poisson model. Asymptotic properties of these generalized second-order statistics are derived, using
an approach based on martingale theory. 相似文献
2.
A simple analytic formula for the spectral radius of matrix continuous refinement operators is established. On the space
L2m(\mathbb Rs)L_2^m({{\mathbb R}}^s), m ≥ 1 and s ≥ 1, their spectral radius is equal to the maximal eigenvalue in magnitude of a number matrix, obtained from the dilation
matrix M and the matrix function c defining the corresponding refinement operator. A similar representation is valid for the continuous refinement operators
considered on spaces L
p
for p ∈ [1, ∞ ), p ≠ 2. However, additional restrictions on the kernel c are imposed in this case. 相似文献
3.
E. Alper Yıldırım 《Mathematical Methods of Operations Research》2010,71(2):267-281
Given a simple, undirected graph G, Budinich (Discret Appl Math 127:535–543, 2003) proposed a lower bound on the clique number of G by combining the quadratic programming formulation of the clique number due to Motzkin and Straus (Can J Math 17:533–540,
1965) with the spectral decomposition of the adjacency matrix of G. This lower bound improves the previously known spectral lower bounds on the clique number that rely on the Motzkin–Straus
formulation. In this paper, we give a simpler, alternative characterization of this lower bound. For regular graphs, this
simpler characterization allows us to obtain a simple, closed-form expression of this lower bound as a function of the positive
eigenvalues of the adjacency matrix. Our computational results shed light on the quality of this lower bound in comparison
with the other spectral lower bounds on the clique number. 相似文献
4.
Pierre Duchesne 《Annals of the Institute of Statistical Mathematics》2005,57(3):575-595
Portmanteau test statistics are useful for checking the adequacy of many time series models. Here we generalized the omnibus
procedure proposed by Duchesne and Roy (2004,Journal of Multivariate Analysis,89, 148–180) for multivariate stationary autoregressive models with exogenous variables (VARX) to the case of cointegrated (or
partially nonstationary) VARX models. We show that for cointegrated VARX time series, the test statistic obtained by comparing
the spectral density of the errors under the null hypothesis of non-correlation with a kernel-based spectral density estimator,
is asymptotically standard normal. The parameters of the model can be estimated by conditional maximum likelihood or by asymptotically
equivalent estimation procedures. The procedure relies on a truncation point or a smoothing parameter. We state conditions
under which the asymptotic distribution of the test statistic is unaffected by a data-dependent method. The finite sample
properties of the test statistics are studied via a small simulation study. 相似文献
5.
M. S. Sgibnev 《Siberian Mathematical Journal》2010,51(1):168-173
We study the uniqueness of a solution to a renewal type system of integral equations z=g+F * z on the line ℝ; here z is the unknown vector function, g is a known vector function, and F is a nonlattice matrix of finite measures on ℝ such that the matrix F(ℝ) is of spectral radius 1 and indecomposable. We show that in a certain class of functions each solution to the corresponding
homogeneous system coincides almost everywhere with a right eigenvector of F(ℝ) with eigenvalue 1. 相似文献
6.
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
7.
A. G. Bytsko 《Journal of Mathematical Sciences》2007,143(1):2754-2764
We study spectral decomposition of regular sl
2-invariant R-matrices R(λ) by the method of reduction of the Yang-Baxter equation to subspaces of a given spin. Restrictions
on the possible structure of several leading coefficients in the spectral decomposition are derived. The origin and structure
of the exceptional solution for spin s = 3 are explained. A similar analysis is performed for constant R-matrices. In particular,
it is shown that the permutation matrix ℙ is a “rigid” solution. Bibliography: 6 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 335, 2006, pp. 100–118. 相似文献
8.
V. N. Kublanovskaya 《Journal of Mathematical Sciences》2006,137(3):4835-4843
For a q-parameter polynomial m × n matrix F of rank ρ, solutions of the equation Fx = 0 at points of the spectrum of the matrix
F determined by the (q −1)-dimensional solutions of the system Z[F] = 0 are considered. Here, Z[F] is the polynomial vector
whose components are all possible minors of order ρ of the matrix F. A classification of spectral pairs in terms of the matrix
A[F], with which the vector Z[F] is associated, is suggested. For matrices F of full rank, a classification and properties
of spectral pairs in terms of the so-called levels of heredity of points of the spectrum of F are also presented. Bibliography:
4 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 132–149. 相似文献
9.
The paper presents a new monotonicity property of the Perron root of a nonnegative matrix. It is shown that this new property
implies known monotonicity properties and also the Chistyakov two-sided bounds for the Perron root of a block-partitioned
nonnegative matrix. Moreover, based on the monotonicity property suggested, the equality cases in Chistyakov’s theorem are
analyzed. Applications to bounding above the spectral radius of a complex matrix are presented. Bibliography: 9 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 13–29. 相似文献
10.
We give the spectral representation for a class of selfadjoint discrete graph Laplacians Δ, with Δ depending on a chosen graph
G and a conductance function c defined on the edges of G. We show that the spectral representations for Δ fall in two model classes, (1) tree-graphs with N-adic branching laws, and (2) lattice graphs. We show that the spectral theory of the first class may be computed with the
use of rank-one perturbations of the real part of the unilateral shift, while the second is analogously built up with the
use of the bilateral shift. We further analyze the effect on spectra of the conductance function c: How the spectral representation of Δ depends on c. 相似文献
11.
Evgenij Kritchevski 《Annales Henri Poincare》2008,9(4):685-709
We study the eigenvalue statistics for the hieracharchial Anderson model of Molchanov [21–23,27,28]. We prove Poisson fluctuations
at arbitrary disorder, when the the model has a spectral dimension d < 1. The proof is based on Minami’s technique [25] and
we give an elementary exposition of the probabilistic arguments.
Submitted: October 8, 2007. Accepted: December 17, 2007. 相似文献
12.
G. S. Lingappaiah 《Annals of the Institute of Statistical Mathematics》1985,37(1):151-163
Summary This paper analyses the shift in parameter of a life test model. This analysis depends on the prediction of order statistics
in future samples based on order statistics in a series of earlier samples in life tests having a general exponential model.
While a series ofk samples are being drawn, model itself undergoes a change. Firstly, a single shift is considered and the effect of this shift
on the variance is discussed. Generalisation withs shifts (s≦k) ink samples in also taken up and the semi-or-used priors (SOUPS) have been used to get predictive distributions. Finally, shift
afteri (i≦k) stages, from exponential to gamma model is considered and for this case effect of the shift on the variance as well as on
the Bayesian prediction region (BPR) is analysed along with set of tables. 相似文献
13.
Lubomir Gavrilov 《Mathematische Zeitschrift》1999,230(3):487-508
Consider an ordinary differential equation which has a Lax pair representation , where A(x) is a matrix polynomial with a fixed regular leading coefficient and the matrix B(x) depends only on A(x). Such an equation can be considered as a completely integrable complex Hamiltonian system. We show that the generic complex
invariant manifold of this Lax pair is an affine part of a non-compact commutative algebraic group – the generalized Jacobian of the spectral
curve with its points at “infinity” identified. Moreover, for suitable B(x), the Hamiltonian vector field defined by the Lax pair on the generalized Jacobian is translation-invariant.
Received April 29, 1997; in final form September 22, 1997 相似文献
14.
Michael A. Jones 《International Journal of Game Theory》1999,28(4):533-546
Limiting inspection to publicly correlated strategies linearizes the problem of finding subgame perfect equilibria for indefinitely
repeated Prisoners' Dilemmas. Equilibrium strategies satisfy a matrix inequality; the matrix depends on the duration of the
punishment mechanism. The existence of subgame perfect equilibria is determined by comparing a parameter of the stage game
to the spectral radius of the matrix. The spectral radii are found for the matrices associated with every possible duration
of punishment.
Quasifinite continuation probabilities are defined to be the set of continuation probabilities where the sole subgame perfect
equilibrium is noncooperative for any Prisoners' Dilemma stage game. The defining property of quasifinite continuation probabilities is determined by a common
factor of the different spectral radii. Additional properties of quasifinite continuation probabilities are examined.
Received: January 1996/final version: January 1999 相似文献
15.
In statistics of extremes, inference is often based on the excesses over a high random threshold. Those excesses are approximately
distributed as the set of order statistics associated to a sample from a generalized Pareto model. We then get the so-called
“maximum likelihood” estimators of the tail index γ. In this paper, we are interested in the derivation of the asymptotic distributional properties of a similar “maximum likelihood”
estimator of a positive tail index γ, based also on the excesses over a high random threshold, but with a trial of accommodation of bias in the Pareto model underlying
those excesses. We next proceed to an asymptotic comparison of the two estimators at their optimal levels. An illustration
of the finite sample behaviour of the estimators is provided through a small-scale Monte Carlo simulation study.
Research partially supported by FCT/POCTI and POCI/FEDER. 相似文献
16.
V. N. Kublanovskaya 《Journal of Mathematical Sciences》2011,176(1):93-101
The method of hereditary pencils, originally suggested by the author for solving spectral problems for two-parameter matrices
(pencils of matrices), is extended to the case of q-parameter, q ≥ 2, polynomial matrices. Algorithms for computing points of the finite regular and singular spectra of a q-parameter polynomial matrix and their theoretical justification are presented. Bibliography: 2 titles. 相似文献
17.
We continue the study of quantum matrix algebras of the GL(m|n) type. We find three alternative forms of the Cayley-Hamilton identity; most importantly, this identity can be represented
in a factored form. The factorization allows naturally dividing the spectrum of a quantum supermatrix into subsets of “even”
and “odd” eigenvalues. This division leads to a parameterization of the characteristic subalgebra (the subalgebra of spectral
invariants) in terms of supersymmetric polynomials in the eigenvalues of the quantum matrix. Our construction is based on
two auxiliary results, which are independently interesting. First, we derive the multiplication rule for Schur functions s
λ
(M) that form a linear basis of the characteristic subalgebra of a Hecke-type quantum matrix algebra; the structure constants
in this basis coincide with the Littlewood-Richardson coefficients. Second, we prove a number of bilinear relations in the
graded ring Λ of symmetric functions of countably many variables.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 14–46, April, 2006. 相似文献
18.
Yu E. Karpeshina 《Proceedings Mathematical Sciences》2002,112(1):117-130
We consider a matrix operatorH = (-Δ)l +V inR
n, wheren ≥ 2,l ≥ 1, 4l > n + 1, andV is the operator of multiplication by a periodic inx matrixV(x). We study spectral properties ofH in the high energy region. Asymptotic formulae for Bloch eigenvalues and the corresponding spectral projections are constructed.
The Bethe-Sommerfeld conjecture, stating that the spectrum ofH can have only a finite number of gaps, is proved. 相似文献
19.
V. N. Kublanovskaya 《Journal of Mathematical Sciences》1998,89(6):1715-1749
An approach to solving the following multiparameter algebraic problems is suggested: (1) spectral problems for singular matrices
polynomially dependent on q≥2 spectral parameters, namely: the separation of the regular and singular parts of the spectrum,
the computation of the discrete spectrum, and the construction of a basis that is free of a finite regular spectrum of the
null-space of polynomial solutions of a multiparameter polynomial matrix; (2) the execution of certain operations over scalar
and matrix multiparameter polynomials, including the computation of the GCD of a sequence of polynomials, the division of
polynomials by their common divisor, and the computation of relative factorizations of polynomials; (3) the solution of systems
of linear algebraic equations with multiparameter polynomial matrices and the construction of inverse and pseudoinverse matrices.
This approach is based on the so-called ΔW-q factorizations of polynomial q-parameter matrices and extends the method for
solving problems for one- and two-parameter polynomial matrices considered in [1–3] to an arbitrary q≥2. Bibliography: 12
titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 229, 1995, pp. 191–246.
Translated by V. N. Kublanovskaya. 相似文献
20.
Yu. A. Al’pin L. Yu. Kolotilina N. N. Korneeva 《Journal of Mathematical Sciences》2007,141(6):1586-1600
Given a finite set {Ax}x ∈ X of nonnegative matrices, we derive joint upper and lower bounds for the row sums of the matrices D−1 A(x) D, x ∈ X, where D is a specially chosen nonsingular diagonal matrix. These bounds, depending only on the sparsity patterns
of the matrices A(x) and their row sums, are used to obtain joint two-sided bounds for the Perron roots of given nonnegative matrices, joint upper
bounds for the spectral radii of given complex matrices, bounds for the joint and lower spectral radii of a matrix set, and
conditions sufficient for all convex combinations of given matrices to be Schur stable. Bibliography: 20 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 334, 2006, pp. 30–56. 相似文献