Nonparametric Resampling for Homogeneous Strong Mixing Random Fields

Künsch (1989, Ann. Statist.17 1217-1241) and Liu ane Singh (1992, in Exploring Limits of Bootstrap (R. Le Page and L. Billard, Eds.), pp. 225-248, Wiley, New York) have recently introduced a block resampling method that is successful in deriving consistent bootstrap estimates of distribution and variance for the sample mean of a strong mixing sequence. Raïs and Moore (1990, in Interface ′90) and Raïs (1992, Ph.D. Thesis, University of Montreal) extended the results of Künsch and Liu and Singh in the case of the sample mean of a homogeneous strong mixing random field in two dimensions (n = 2). In this paper, the general case (n Z⁺) is considered, and a resampling technique for strong mixing random fields is formulated, which is an extension of the "blocks of blocks" resampling scheme for sequences in Politis and Romano (1992, Ann. Statist.20 (4) 1985-2007). The "blocks of blocks" method can be used to construct asymptotically correct confidence intervals for parameters of the whole (infinite-dimensional) joint distribution of the random field, for example, the spectral density at a point. A variation of the "blocks of blocks" resampling scheme that involves "wrapping" the data around on a torus will also be studied, in view of its property to yield an unbiased bootstrap distribution.     

A Markov Chain Monte Carlo Convergence Diagnostic Using Subsampling

Abstract

A new diagnostic procedure for assessing convergence of a Markov chain Monte Carlo (MCMC) simulation is proposed. The method is based on the use of subsampling for the construction of confidence regions from asymptotically stationary time series as developed in Politis, Romano, and Wolf. The MCMC subsampling diagnostic is capable of gauging at what point the chain has “forgotten” its starting points, as well as to indicate how many points are needed to estimate the parameters of interest according to the desired accuracy. Simulation examples are also presented showing that the diagnostic performs favorably in interesting cases.     

Absolute charge transfer and fragmentation cross sections in He2+-C60 collisions

We have determined absolute charge transfer and fragmentation cross sections in He2++C60 collisions in the impact-energy range 0.1-250 keV by using a combined experimental and theoretical approach. We have found that the cross sections for the formation of He+ and He0 are comparable in magnitude, which cannot be explained by the sole contribution of pure single and double electron capture but also by contribution of transfer-ionization processes that are important even at low impact energies. The results show that multifragmentation is important only at impact energies larger than 40 keV; at lower energies, sequential C2 evaporation is the dominant process.     

A PRESSURE-BASED ALGORITHM FOR HIGH-SPEED TURBOMACHINERY FLOWS

The steady state Navier–Stokes equations are solved in transonic flows using an elliptic formulation. A segregated solution algorithm is established in which the pressure correction equation is utilized to enforce the divergence-free mass flux constraint. The momentum equations are solved in terms of the primitive variables, while the pressure correction field is used to update both the convecting mass flux components and the pressure itself. The velocity components are deduced from the corrected mass fluxes on the basis of an upwind-biased density, which is a mechanism capable of overcoming the ellipticity of the system of equations, in the transonic flow regime. An incomplete LU decomposition is used for the solution of the transport-type equations and a globally minimized residual method resolves the pressure correction equation. Turbulence is resolved through the k–ε model. Dealing with turbomachinery applications, results are presented in two-dimensional compressor and turbine cascades under design and off-design conditions. © 1997 John Wiley & Sons, Ltd.     

Time-dependent density functional theory molecular dynamics simulation of doubly charged uracil in gas phase

We use time-dependent density functional theory and Born-Oppenheimer molecular dynamics methods to investigate the fragmentation of doubly ionized uracil in gas phase. Different initial electronic excited states of the dication are obtained by removing electrons from different inner-shell orbitals of the neutral species. We show that shape-equivalent orbitals lead to very different fragmentation patterns revealing the importance of the intramolecular chemical environment. The results are in good agreement with ionion coincidence measurements of uracil collision with 100 keV protons.     

Robust Autocorrelation Estimation

In this article, we introduce a new class of robust autocorrelation estimators based on interpreting the sample autocorrelation function as a linear regression. We investigate the efficiency and robustness properties of the estimators that result from employing three common robust regression techniques. We discuss the construction of robust autocovariance and positive definite autocorrelation estimates, and their application to AR model fitting. We perform simulation studies with various outlier configurations to compare the different estimators.     

Higher-order accurate polyspectral estimation with flat-top lag-windows

Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical estimators with second-order kernels. A simple, data-dependent algorithm for selecting the bandwidth is introduced and is shown to be consistent with estimating the optimal bandwidth. The combination of the specialized family of kernels with the new bandwidth selection algorithm yields a considerably improved polyspectral estimator surpassing the performances of existing estimators using second-order kernels. Bispectral simulations with several standard models are used to demonstrate the enhanced performance with the proposed methodology.     

Truncated Estimation of Ratio Statistics with Application to Heavy Tail Distributions

The problem of estimation of the heavy tail index is revisited from the point of view of truncated estimation. A class of novel estimators is introduced having guaranteed accuracy based on a sample of fixed size. The performance of these estimators is quantified both theoretically and in simulations over a host of relevant examples. It is also shown that in several cases the proposed estimators attain — within a logarithmic factor — the optimal parametric rate of convergence. The property of uniform asymptotic normality of the proposed estimators is established.     

Superconductivity fluctuations in Bi(Pb) based granular ceramics superconductors: evidence for fractal behavior

We report precise measurements of the electrical resistivity in three different Bi(Pb) based granular ceramics superconductors. We show that a single critical exponent (5/6) describes the superconductivity fluctuations. Such a critical exponent indicates a fractal behavior of the superconducting path. Our results thus indicate a strict two dimensional fluctuation percolation set (below the superconductivity onset temperature 195 K down toT _c), and provide some proof for Tarascon et al. shell conductivity path hypothesis. We estimate the shell thickness to be of the order of 10 Å.