Models for circular data from time series spectra

Circular data are those for which the natural support is the unit circle and its toroidal extensions. Numerous constructions have been proposed which can be used to generate models for such data. We propose a new, very general, one based on the normalization of the spectra of complex-valued stationary processes. As illustrations of the new construction's application, we study models for univariate circular data obtained from the spectra of autoregressive moving average models and relate them to existing models in the literature. We also propose and investigate multivariate circular models obtained from the high-order spectra of stationary stochastic processes generated using linear filtering with an autoregressive moving average response function. A new family of distributions for a Markov process on the circle is also introduced. Results for asymptotically optimal inference for dependent observations on the circle are presented which provide a new paradigm for inference with circular models. The application of one of the new families of spectra-generated models is illustrated in an analysis of wind direction data.     

An improved analysis of experimental data from 125 I hot-line autoradiographs: allowing for the effects of background grains

In this paper we suggest a new statistical method of correcting the results of hot-line experiments for the effects of background sources and we use the new method to reassess the adequacy of three probability distributions proposed in the literature for image spread from line sources. The data are from sources labelled with ¹²⁵I in semi-thin resin sections 0·4-0·8 μm in thickness. The new method reveals that two of the models describe the empirical distributions more closely than earlier analysis had suggested, and it confirms an increasing relationship between half distance of image spread and the thickness of the source. However, it also confirms that considerable ‘inter hot-line’ experimental variation remains, even after background correction. This suggests that multiple experiments are needed to produce reliable estimates of half distance.     

对称非线性系统的无交互控制

本文讨论了具有对称性的非线性系统的无交互控制问题。通过定义对称系统的导出分布族的新概念,我们得出了问题可解的条件。我们取得的结果较不具对称性的情况要简单一些。从而说明,对称性不仅使得系统具有较好的结构,而且使得它的其它一些问题的研究得到简化。     

VaR and ES for linear portfolios with mixture of elliptic distributions risk factors

In this paper, we generalize the Linear VaR method from portfolios with normally distributed risk factors to portfolios with mixture of elliptically distributed ones. We treat both the Expected Shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a mixture of multivariate t-distributions. This is a part of J. SADEFO-KAMDEM PhD Thesis[12] of the Université de Reims, France . It has been presented at the workshop on modelling and computation in Financial Engineering at Bad Herrenalb, Germany May 6-8, 2003. The author is an associate professor at the Department of mathematics, université d’Evry Val d’Essonne.     

On the recent papers by Nagode et al.

The recent work Professor Nagode and colleagues is discussed with respect to the use of mixture Weibull models.     

Block noninteracting control with stability via static state feedback

Necessary and sufficient conditions for the existence of a static state feedback that achieves noninteraction and internal stability are obtained. This is accomplished by first characterizing the set of all controllability subspaces (distributions) that can arise as solutions to the noninteracting control problem. This characterization is then used to identify a fixed internal dynamics that is common to every noninteractive closed loop. The stability properties of this dynamics is shown to be the key factor in the problem of achieving noninteracting control with internal stability.     

Inference for pth‐order random coefficient integer‐valued autoregressive processes

Abstract. A pth‐order random coefficient integer‐valued autoregressive [RCINAR(p)] model is proposed for count data. Stationarity and ergodicity properties are established. Maximum likelihood, conditional least squares, modified quasi‐likelihood and generalized method of moments are used to estimate the model parameters. Asymptotic properties of the estimators are derived. Simulation results on the comparison of the estimators are reported. The models are applied to two real data sets.     

Almost k-wise independence versus k-wise independence

We say that a distribution over {0,1}ⁿ is (ε,k)-wise independent if its restriction to every k coordinates results in a distribution that is ε-close to the uniform distribution. A natural question regarding (ε,k)-wise independent distributions is how close they are to some k-wise independent distribution. We show that there exist (ε,k)-wise independent distributions whose statistical distance is at least n^O(k)·ε from any k-wise independent distribution. In addition, we show that for any (ε,k)-wise independent distribution there exists some k-wise independent distribution, whose statistical distance is n^O(k)·ε.     

Synthesis and characterization of acidic properties of Al-SBA-15 materials with varying Si/Al ratios

Al-SBA-15 of varying Si/Al ratios in the range 11.4–78.4 was synthesized using tri-block copolymer P123. The calcined materials were examined by XRD, pore size distribution, surface area, ²⁷Al NMR spectroscopy. The acidity and acid strength distribution were studied using microcalorimetric adsorption of NH₃. The acidic properties were also examined by cumene cracking reaction as a function of Si/Al ratios. Systematic variation of acidity and activity was observed as a function of Si/Al ratio. The initial heats of NH₃ adsorption correlated well with activity indicate that acid sites with ΔH > 100 kJ/mole is responsible for cumene cracking activity. Linear correlations were obtained with total acidity and cumene cracking activities. The tetrahedral aluminum was found to be responsible for the observed acidities and catalytic activities.     

Parametric and nonparametric Bayesian model specification: A case study involving models for count data

In this paper we present the results of a simulation study to explore the ability of Bayesian parametric and nonparametric models to provide an adequate fit to count data of the type that would routinely be analyzed parametrically either through fixed-effects or random-effects Poisson models. The context of the study is a randomized controlled trial with two groups (treatment and control). Our nonparametric approach uses several modeling formulations based on Dirichlet process priors. We find that the nonparametric models are able to flexibly adapt to the data, to offer rich posterior inference, and to provide, in a variety of settings, more accurate predictive inference than parametric models.