The F test for comparing two normal variances: correct and incorrect calculation of the two-sided p-value?

This article illustrates that not all statistical software packages are correctly calculating a p-value for the classical F test comparison of two independent Normal variances. This is illustrated with a simple example, and the reasons why are discussed. Eight different software packages are considered.

Small time two-sided LIL behavior for Lévy processes at zero

We wish to characterize when a Lévy process X t crosses boundaries b(t), in a two-sided sense, for small times t, where b(t) satisfies very mild conditions. An integral test is furnished for computing the value of sup t→0|X t |/b(t) = c. In some cases, we also specify a function b(t) in terms of the Lévy triplet, such that sup t→0 |X t |/b(t) = 1.

On the principal eigenvalue of a Robin problem with a large parameter

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

Extended factorizations of exponential functionals of Lévy processes

Pardo, Patie, and Savov derived, under mild conditions, a Wiener-Hopf type factorization for the exponential functional of proper Lévy processes. In this paper, we extend this factorization by relaxing a finite moment assumption as well as by considering the exponential functional for killed Lévy processes. As a by-product, we derive some interesting fine distributional properties enjoyed by a large class of this random variable, such as the absolute continuity of its distribution and the smoothness, boundedness or complete monotonicity of its density. This type of results is then used to derive similar properties for the law of maxima and first passage time of some stable Lévy processes. Thus, for example, we show that for any stable process with $\rho\in(0,\frac{1}{\alpha}-1]$, where $\rho\in[0,1]$ is the positivity parameter and $\alpha$ is the stable index, then the first passage time has a bounded and non-increasing density on $\mathbb{R}_+$. We also generate many instances of integral or power series representations for the law of the exponential functional of Lévy processes with one or two-sided jumps. The proof of our main results requires different devices from the one developed by Pardo, Patie, Savov. It relies in particular on a generalization of a transform recently introduced by Chazal et al together with some extensions to killed Lévy process of Wiener-Hopf techniques. The factorizations developed here also allow for further applications which we only indicate here also allow for further applications which we only indicate here.

Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere

The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjørtoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows.By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities.The case of moist adiabatic systems is also considered.

A Wiener-Hopf type factorization for the exponential functional of Levy processes

For a Lévy process ξ=(ξt)t≥0 drifting to −∞, we define the so-called exponential functional as follows: Formula Under mild conditions on ξ, we show that the following factorization of exponential functionals: Formula holds, where × stands for the product of independent random variables, H− is the descending ladder height process of ξ and Y is a spectrally positive Lévy process with a negative mean constructed from its ascending ladder height process. As a by-product, we generate an integral or power series representation for the law of Iξ for a large class of Lévy processes with two-sided jumps and also derive some new distributional properties. The proof of our main result relies on a fine Markovian study of a class of generalized Ornstein–Uhlenbeck processes, which is itself of independent interest. We use and refine an alternative approach of studying the stationary measure of a Markov process which avoids some technicalities and difficulties that appear in the classical method of employing the generator of the dual Markov process.

Estimating the hidden number of scrapie affected holdings in great Britain using a simple, truncated count model allowing for heterogeneity.

None of the current surveillance streams monitoring the presence of scrapie in Great Britain provide a comprehensive and unbiased estimate of the prevalence of the disease at the holding level. Previous work to estimate the under-ascertainment adjusted prevalence of scrapie in Great Britain applied multiple-list capture–recapture methods. The enforcement of new control measures on scrapie-affected holdings in 2004 has stopped the overlapping between surveillance sources and, hence, the application of multiple-list capture–recapture models. Alternative methods, still under the capture–recapture methodology, relying on repeated entries in one single list have been suggested in these situations. In this article, we apply one-list capture–recapture approaches to data held on the Scrapie Notifications Database to estimate the undetected population of scrapie-affected holdings with clinical disease in Great Britain for the years 2002, 2003, and 2004. For doing so, we develop a new diagnostic tool for indication of heterogeneity as well as a new understanding of the Zelterman and Chao’s lower bound estimators to account for potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a special, locally truncated Poisson likelihood equivalent to a binomial likelihood. This understanding allows the extension of the Zelterman approach by means of logistic regression to include observed heterogeneity in the form of covariates—in case studied here, the holding size and country of origin. Our results confirm the presence of substantial unobserved heterogeneity supporting the application of our two estimators. The total scrapie-affected holding population in Great Britain is around 300 holdings per year. None of the covariates appear to inform the model significantly.

Pesticides, preference heterogeneity and environmental taxes

In this paper we present results from two choice experiments (CE), designed to take account of the different negative externalities associated with pesticide use in agricultural production. For cereal production, the most probable impact of pesticide use is a reduction in environmental quality. For fruit and vegetable production, the negative externality is on consumer health. Using latent class models we find evidence of the presence of preference heterogeneity in addition to reasonably high willingness to pay (WTP) estimates for a reduction in the use of pesticides for both environmental quality and consumer health. To place our WTP estimates in a policy context we convert them into an equivalent pesticide tax by type of externality. Our tax estimates suggest that pesticide taxes based on the primary externality resulting from a particular mode of agricultural production are a credible policy option that warrants further consideration.

Estimating the hidden number of scrapie affected holdings in great Britain using a simple, truncated count model allowing for heterogeneity

None of the current surveillance streams monitoring the presence of scrapie in Great Britain provide a comprehensive and unbiased estimate of the prevalence of the disease at the holding level. Previous work to estimate the under-ascertainment adjusted prevalence of scrapie in Great Britain applied multiple-list capture-recapture methods. The enforcement of new control measures on scrapie-affected holdings in 2004 has stopped the overlapping between surveillance sources and, hence, the application of multiple-list capture-recapture models. Alternative methods, still under the capture-recapture methodology, relying on repeated entries in one single list have been suggested in these situations. In this article, we apply one-list capture-recapture approaches to data held on the Scrapie Notifications Database to estimate the undetected population of scrapie-affected holdings with clinical disease in Great Britain for the years 2002, 2003, and 2004. For doing so, we develop a new diagnostic tool for indication of heterogeneity as well as a new understanding of the Zelterman and Chao's lower bound estimators to account for potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a special, locally truncated Poisson likelihood equivalent to a binomial likelihood. This understanding allows the extension of the Zelterman approach by means of logistic regression to include observed heterogeneity in the form of covariates-in case studied here, the holding size and country of origin. Our results confirm the presence of substantial unobserved heterogeneity supporting the application of our two estimators. The total scrapie-affected holding population in Great Britain is around 300 holdings per year. None of the covariates appear to inform the model significantly.

A comparison of three different models for estimating relative risk in meta-analysis of clinical trials under unobserved heterogeneity

We focus on the comparison of three statistical models used to estimate the treatment effect in metaanalysis when individually pooled data are available. The models are two conventional models, namely a multi-level and a model based upon an approximate likelihood, and a newly developed model, the profile likelihood model which might be viewed as an extension of the Mantel-Haenszel approach. To exemplify these methods, we use results from a meta-analysis of 22 trials to prevent respiratory tract infections. We show that by using the multi-level approach, in the case of baseline heterogeneity, the number of clusters or components is considerably over-estimated. The approximate and profile likelihood method showed nearly the same pattern for the treatment effect distribution. To provide more evidence two simulation studies are accomplished. The profile likelihood can be considered as a clear alternative to the approximate likelihood model. In the case of strong baseline heterogeneity, the profile likelihood method shows superior behaviour when compared with the multi-level model. Copyright (C) 2006 John Wiley & Sons, Ltd.

A phylogenetic mixture model for detecting pattern-heterogeneity in gene sequence or character-state data

We describe a general likelihood-based 'mixture model' for inferring phylogenetic trees from gene-sequence or other character-state data. The model accommodates cases in which different sites in the alignment evolve in qualitatively distinct ways, but does not require prior knowledge of these patterns or partitioning of the data. We call this qualitative variability in the pattern of evolution across sites "pattern-heterogeneity" to distinguish it from both a homogenous process of evolution and from one characterized principally by differences in rates of evolution. We present studies to show that the model correctly retrieves the signals of pattern-heterogeneity from simulated gene-sequence data, and we apply the method to protein-coding genes and to a ribosomal 12S data set. The mixture model outperforms conventional partitioning in both these data sets. We implement the mixture model such that it can simultaneously detect rate- and pattern-heterogeneity. The model simplifies to a homogeneous model or a rate- variability model as special cases, and therefore always performs at least as well as these two approaches, and often considerably improves upon them. We make the model available within a Bayesian Markov-chain Monte Carlo framework for phylogenetic inference, as an easy-to-use computer program.

Modeling the effects of node heterogeneity on the performance of grid applications

The performance benefit when using grid systems comes from different strategies, among which partitioning the applications into parallel tasks is the most important. However, in most cases the enhancement coming from partitioning is smoothed by the effects of synchronization overheads, mainly due to the high variability in the execution times of the different tasks, which, in turn, is accentuated by the large heterogeneity of grid nodes. In this paper we design hierarchical, queuing network performance models able to accurately analyze grid architectures and applications. Thanks to the model results, we introduce a new allocation policy based on a combination between task partitioning and task replication. The models are used to study two real applications and to evaluate the performance benefits obtained with allocation policies based on task replication.

Energy exchange in a dense urban environment Part II: impact of spatial heterogeneity of the surface

The centre of cities, characterised by spatial and temporal complexity, are challenging environments for micrometeorological research. This paper considers the impact of sensor location and heterogeneity of the urban surface on flux observations in the dense city centre of London, UK. Data gathered at two sites in close vicinity, but with different measurement heights, were analysed to investigate the influence of source area characteristics on long-term radiation and turbulent heat fluxes. Combining consideration of diffuse radiation and effects of specular reflections, the non-Lambertian urban surface is found to impact the measurements of surface albedo. Comparisons of observations from the two sites reveal that turbulent heat fluxes are similar under some flow conditions. However, they mostly observe processes at different scales due to their differing measurement heights, highlighting the critical impact of siting sensors in urban areas. A detailed source area analysis is presented to investigate the surface controls influencing the energy exchanges at the different scales

Firms’ exporting and importing activities: is there a two-way relationship?

The literature on firm heterogeneity and trade has highlighted that most trading firms tend to engage in both importing and exporting activities. This paper provides some evidence that helps understanding to what extent this is the result of a two-way relationship. Using firm-level data for a group of 27 Eastern European and Central Asian countries from the World Bank Business Environment and Enterprise Performance Survey (BEEPS) over the period 2002–2008, we estimate a bivariate probit model of exporting and importing. After controlling for size (and other firm-level characteristics) we find that firms’ exporting activity does not increase the probability of importing, while the latter has a positive effect on foreign sales. This effect is mainly channeled through an increase in firm productivity and product innovation.