Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

Summary.  We propose a general bootstrap procedure to approximate the null distribution of non-parametric frequency domain tests about the spectral density matrix of a multivariate time series. Under a set of easy-to-verify conditions, we establish asymptotic validity of the bootstrap procedure proposed. We apply a version of this procedure together with a new statistic to test the hypothesis that the spectral densities of not necessarily independent time series are equal. The test statistic proposed is based on an L ₂-distance between the non-parametrically estimated individual spectral densities and an overall, 'pooled' spectral density, the latter being obtained by using the whole set of m time series considered. The effects of the dependence between the time series on the power behaviour of the test are investigated. Some simulations are presented and a real life data example is discussed.     

一类M-矩阵阿达玛积最小特征根的下界

讨论一个 M- 矩阵与另一个 M- 矩阵的逆的阿达玛积的最小特征根,证明了对任一矩阵B,如果 B- 1 的主对角线元素的值相等,则q( A‘B- 1) > 1n ·q( A)q( B) .     

Semiparametric estimation of spatial long-range dependence

Estimation of the long-range dependence parameter in spatial processes using a semiparametric approach is studied. An extended formulation of the averaged periodogram method proposed in Robinson [1994. Semiparametric analysis of long memory time series. Ann. Statist. 22, 515–539] is derived, considering a certain homogeneous and isotropic behaviour of the spectral distribution in the low frequencies. The weak consistency of the estimator proposed is proved.     

附着滴在粗糙多孔介质表面铺展渗透的数值研究

为了探究附着滴在粗糙多孔介质表面的动力学行为,课题组通过ANSYS FLUENT对液滴在多孔介质上的铺展渗透进行了研究。首先用凹凸槽来代替表面粗糙度的方法,然后使用VOF模型追踪液滴形态变化,最后利用PISO 算法进行数值模拟计算。定量分析了邦德数、平衡接触角、达西数和多孔介质表面粗糙度对液滴铺展半径和渗透深度的影响。结果表明：随着液滴邦德数的增大,液滴更易变形,铺展和渗透深度增加;随着平衡接触角的增大,液滴越难铺展和渗透,但液滴后期阶段渗透深度增加;随着达西数增大,多孔介质的渗透率增大,所以渗透深度增加,而铺展半径相对减小;随着多孔介质表面粗糙度的增大,铺展半径减小,渗透深度增大。该研究的成果有利于提高生产质量和减少环境污染。     

Computational analysis of the queue with working breakdowns and delaying repair under a Bernoulli-schedule-controlled policy

This paper considers a single server queueing system with working breakdowns and delaying repair under a Bernoulli-schedule-controlled policy. At a breakdown instant, the system either goes to repair period immediately with probability p, or continues to provide auxiliary service for the current customers with probability q = 1 ? p. While the system resides in the auxiliary service period, it may go to repair period if there is no customer at the epoch of service completion or the occurrence of breakdown. By using the matrix analytic method and the spectral expansion method, we respectively obtain the steady state distribution to make the straightforward computation of performance measures and the Laplace-Stieltjes transform of the stationary sojourn time of an arbitrary customer. In addition, some numerical examples are presented to show the impact of parameters on the performance measures.     

Approximation of IMSE-optimal Designs via Quadrature Rules and Spectral Decomposition

We address the problem of computing integrated mean-squared error (IMSE) optimal designs for interpolation of random fields with known mean and covariance. We assume that the mean squared error is integrated through a discrete measure and restrict the design space to its support. We show that the IMSE and its approximation by spectral truncation can be easily evaluated, which makes their global minimization affordable. Numerical experiments are carried out that illustrate the effectiveness of the approach.     

Linex discrepancy for bandwidth selection

A bandwidth selection based on Linex discrepancy is proposed for kernel smoothing of periodogram. The selection minimizes Linex discrepancy between the smoothed and true spectrums. Two estimators are introduced for Linex discrepancy. The bandwidth choice outperforms some common bandwidth choices.     

A Unified View of Nonparametric Trend-Cycle Predictors Via Reproducing Kernel Hilbert Spaces

We provide a common approach for studying several nonparametric estimators used for smoothing functional time series data. Linear filters based on different building assumptions are transformed into kernel functions via reproducing kernel Hilbert spaces. For each estimator, we identify a density function or second order kernel, from which a hierarchy of higher order estimators is derived. These are shown to give excellent representations for the currently applied symmetric filters. In particular, we derive equivalent kernels of smoothing splines in Sobolev and polynomial spaces. The asymmetric weights are obtained by adapting the kernel functions to the length of the various filters, and a theoretical and empirical comparison is made with the classical estimators used in real time analysis. The former are shown to be superior in terms of signal passing, noise suppression and speed of convergence to the symmetric filter.     

稠油油藏水平井热采吞吐产能预测新模型

针对普通稠油油藏水平井热采吞吐产能预测缺少合适计算模型的现状,通过建立加热区和未加热区的复合流动模型,考虑加热区和未加热区原油黏度的差异,研究了水平井单井热采吞吐产能预测的解析模型,推导了水平井热采吞吐相对于冷采的产能增产倍数计算公式。研究表明,增产倍数主要受加热半径、油层厚度和水平段长度等因素影响。以渤海N油田热采水平井典型数据为基础建立机理模型,通过数值模拟得到不同吞吐轮次的加热半径,在此基础上,利用新模型计算了不同吞吐轮次的产能增产倍数,预测第一轮吞吐的增产倍数为1.6倍,该值与渤海N油田10口热采吞吐水平井第一轮吞吐效果评价结果吻合程度较高。     

A basic lemma and the analysis of block and Kronecker product designs

In this paper the analysis of the class of block designs whose C matrix can be expressed in terms of the Kronecker product of some elementary matrices is considered. The analysis utilizes a basic result concerning the spectral decomposition of the Kronecker product of symmetric matrices in terms of the spectral decomposition of the component matrices involved in the Kronecker product. The property (A) of Kurkjian and Zelen (1963) is generalised and the analysis of generalised property (A) designs is given. It is proved that a design is balanced factorially if and only if it is a generalised property (A) design. A method of analysis of Kronecker product block designs whose component designs are equi-replicate and proper is also suggested.