Test to compare two population logspectra

Summary  The objective of this paper is to compare time series patterns generated over two populations. A random sample of objects is chosen from each population. On each object, a stationary process with an absolutely continuous spectral distribution is observed at the same times. We assume that the logarithm of the periodogram from each time series follows a model which involves the pattern of each population. A statistical test is proposed which will compare these patterns. The probability distribution of the test under the null hypothesis is approximated by the bootstrap. The consistency of the method is analyzed using the Mallows metric. A simulation study is also carried out. This paper has been partially funded by I+D research program ref. BFM2000-0517     

Analytic smoothing of geometric maps with applications to KAM theory

We show that finitely differentiable diffeomorphisms which are either symplectic, volume-preserving, or contact can be approximated with analytic diffeomorphisms that are, respectively, symplectic, volume-preserving or contact. We prove that the approximating functions are uniformly bounded on some complex domains and that the rate of convergence, in Cr-norms, of the approximation can be estimated in terms of the size of such complex domains and the order of differentiability of the approximated function. As an application to this result, we give a proof of the existence, the local uniqueness and the bootstrap of regularity of KAM tori for finitely differentiable symplectic maps. The symplectic maps considered here are not assumed either to be written in action-angle variables or to be perturbations of integrable systems. Our main assumption is the existence of a finitely differentiable parameterization of a maximal dimensional torus that satisfies a non-degeneracy condition and that is approximately invariant. The symplectic, volume-preserving and contact forms are assumed to be analytic.     

Saddlepoint approximations to studentized bootstrap distributions based onM-estimates

Summary  Saddlepoint methods can provide extremely accurate approximations to resampling distributions. This article applies them to distributions of studentized bootstrap statistics based on robustM-estimates. As examples we consider the studentized versions of Huber’sM-estimate of location, of its initially MAD scaled version, and of Huber’s proposal 2. The studentized version of Huber’s proposal 2 seems to be a preferable measure of location. Remarks on implementation and related problems are given.     

Bandwidth choice for local polynomial estimation of smooth boundaries

Local polynomial methods hold considerable promise for boundary estimation, where they offer unmatched flexibility and adaptivity. Most rival techniques provide only a single order of approximation; local polynomial approaches allow any order desired. Their more conventional rivals, for example high-order kernel methods in the context of regression, do not have attractive versions in the case of boundary estimation. However, the adoption of local polynomial methods for boundary estimation is inhibited by lack of knowledge about their properties, in particular about the manner in which they are influenced by bandwidth; and by the absence of techniques for empirical bandwidth choice. In the present paper we detail the way in which bandwidth selection determines mean squared error of local polynomial boundary estimators, showing that it is substantially more complex than in regression settings. For example, asymptotic formulae for bias and variance contributions to mean squared error no longer decompose into monotone functions of bandwidth. Nevertheless, once these properties are understood, relatively simple empirical bandwidth selection methods can be developed. We suggest a new approach to both local and global bandwidth choice, and describe its properties.     

Approximation for bootstrapped empirical processes

We obtain an approximation for the bootstrapped empirical process with the rate of the Komlós, Major and Tusnády approximation for empirical processes. The proof of the new approximation is based on the Poisson approximation for the uniform empirical distribution function and the Gaussian approximation for randomly stopped sums.

     

Bootstrap Approximation to the Distribution of M-estimates in a Linear Model

The authors establish the approximations to the distribution of M-estimates in a linear model by the bootstrap and the linear representation of bootstrap M-estimation,and prove that the approximation is valid in probability 1.A simulation is made to show the effects of bootstrap approximation,randomly weighted approximation and normal approximation.     

(Un)Conditional Sample Generation Based on Distribution Element Trees

Recently, distribution element trees (DETs) were introduced as an accurate and computationally efficient method for density estimation. In this work, we demonstrate that the DET formulation promotes an easy and inexpensive way to generate random samples similar to a smooth bootstrap. These samples can be generated unconditionally, but also, without further complications, conditionally using available information about certain probability-space components. This article is accompanied by the R codes that were used to produce all simulation results. Supplementary material for this article is available online.     

Effect of high pressure on the reaction between bovine myofibrils and cathepsin D

This study deals with the effect of high pressure [50-500 MPa] and time of treatment [20-900 s] on the reaction between myofibrils and cathepsin D from bovine post mortem meat, using Surface Response Methodology. We shown that every high pressure treatment enhanced activity of cathepsin D as evaluated on haemoglobin as a substrate or on control meat myofibrils. We also put in evidence that cathepsin D could carry out the hydrolysis of high pressure treated myofibrils. At last we studied the action of pressurised cathepsin D on pressurised myofibrils, and proved that the hydrolysis was increasing up to 170 MPa and then decreased; above 300 MPa the activity was lower than with control cathepsin D and control myofibrils. Thus above 300 MPa recognition of natural substrate is affected by high pressure induced modifications. These results may help to explain why high pressure treatment of post rigor meat is not able to increase tenderness.     

Optimal operation of hydrothermal systems with Hydrological Scenario Generation through Bootstrap and Periodic Autoregressive Models

In electrical power systems with strong hydro generation, the use of adequate techniques to generate synthetic hydrological scenarios is extremely important for the evaluation of the ways the system behaves in order to meet the forecast energy demand. This paper proposes a new model to generate natural inflow energy scenarios in the long-term operation planning of large-sized hydrothermal systems. This model is based on the Periodic Autoregressive Model, PAR (p), where the identification of the p orders is based on the significance of the Partial Autocorrelation Function (PACF) estimated via Bootstrap, an intensive computational technique. The scenarios generated through this new technique were applied to the operation planning of the Brazilian Electrical System (BES), using the previously developed methodology of Stochastic Dynamic Programming based on Convex Hull algorithm (SDP-CHull). The results show that identification via Bootstrap is considerably more parsimonious, leading to the identification of lower orders models in most cases which retains the statistical characteristics of the original series. Additionally it presents a closer total mean operation cost when compared to the cost obtained via historic series.     

Benzophenone-3 ultrasound degradation in a multifrequency reactor: Response surface methodology approach

Response Surface Methodology was used for optimizing operating variables for a multi-frequency ultrasound reactor using BP-3 as a model compound. The response variable was the Triclosan degradation percent after 10 sonication min. Frequency at levels from 574, 856 and 1134 kHz were used. Power density, pulse time (PT), silent time (ST) and PT/ST ratio effects were also analyzed. 2² and 2³ experimental designs were used for screening purposes and a central composite design was used for optimization. An optimum value of 79.2% was obtained for a frequency of 574 kHz, a power density of 200 W/L, and a PT/ST ratio of 10. Significant variables were frequency and power level, the first having an optimum value after which degradation decreases while power density level had a strong positive effect on the whole operational range. PT, ST, and PT/ST ratio were not significant variables although it was shown that pulsed mode ultrasound has better degradation rates than continuous mode ultrasound; the effect less significant at higher power levels.