Pierre Lafaye de Micheaux

Short communication: Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods

Liu, Tang and Zhang [Liu, H. Tang, Y., Zhang H.H. 2009. A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. Computational Statistics & Data Analysis 53, 853-856] proposed a chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. To approximate the distribution of interest, they used a non-central chi-square distribution, where the degrees of freedom and the non-centrality parameter were calculated using the first four cumulants of the quadratic form. Numerical examples were encouraging, suggesting that the approximation was particularly accurate in the upper tail of the distribution. We present here additional empirical evidence, comparing Liu-Tang-Zhangs four-moment non-central chi-square approximation with exact methods. While the moment-based method is interesting because of its simplicity, we demonstrate that it should be used with care in practical work, since numerical examples suggest that significant differences may occur between that method and exact methods, even in the upper tail of the distribution.

Odor vapor pressure and quality modulate local field potential oscillatory patterns in the olfactory bulb of the anesthetized rat.

A central question in chemical senses is the way that odorant molecules are represented in the brain. To date, many studies, when taken together, suggest that structural features of the molecules are represented through a spatio‐temporal pattern of activation in the olfactory bulb (OB), in both glomerular and mitral cell layers. Mitral/tufted cells interact with a large population of inhibitory interneurons resulting in a temporal patterning of bulbar local field potential (LFP) activity. We investigated the possibility that molecular features could determine the temporal pattern of LFP oscillatory activity in the OB. For this purpose, we recorded the LFPs in the OB of urethane‐anesthetized, freely breathing rats in response to series of aliphatic odorants varying subtly in carbon‐chain length or functional group. In concordance with our previous reports, we found that odors evoked oscillatory activity in the LFP signal in both the beta and gamma frequency bands. Analysis of LFP oscillations revealed that, although molecular features have almost no influence on the intrinsic characteristics of LFP oscillations, they influence the temporal patterning of bulbar oscillations. Alcohol family odors rarely evoke gamma oscillations, whereas ester family odors rather induce oscillatory patterns showing beta/gamma alternation. Moreover, for molecules with the same functional group, the probability of gamma occurrence is correlated to the vapor pressure of the odor. The significance of the relation between odorant features and oscillatory regimes along with their functional relevance are discussed.

Preorthographical constraints on visual word recognition: Evidence from a case study of developmental surface dyslexia

We investigated the visual word recognition ability of M.T., a young boy with surface dyslexia, by means of a paradigm that measures performance as a function of the eye fixation position within the word, known as the “viewing-position effect” paradigm. In well-achieving readers, the viewing-position effect is mainly determined by factors affecting letter visibility and by lexical constraints on word recognition. We further quantified M.T.s sensory limitations on letter visibility by computing visual-span profiles—that is, the number of letters recognizable at a glance. Finally, in an ideal-observers perspective, M.T.s performance was compared with a parameter-free model combining M.T.s letter visibility data with a simple lexical matching rule. The results showed that M.T. did not use the whole visual information available on letter identities to recognize words and that preorthographical factors constrained his word recognition performance. The results can be best accounted for by a reduction of the number of letters processed in parallel.

Image analysis and statistical inference in neuroimaging with R

R is a language and environment for statistical computing and graphics. It can be considered an alternative implementation of the S language developed in the 1970s and 1980s for data analysis and graphics (Becker and Chambers, 1984; Becker et al., 1988). The R language is part of the GNU project and offers versions that compile and run on almost every major operating system currently available. We highlight several R packages built specifically for the analysis of neuroimaging data in the context of functional MRI, diffusion tensor imaging, and dynamic contrast-enhanced MRI. We review their methodology and give an overview of their capabilities for neuroimaging. In addition we summarize some of the current activities in the area of neuroimaging software development in R.

Understanding Convergence Concepts: A Visual-Minded and Graphical Simulation-Based Approach

This article describes the difficult concepts of convergence in probability, convergence almost surely, convergence in law, and convergence in rth mean using a visual-minded and graphical simulation-based approach. For this purpose, each probability of events is approximated by a frequency. An R package that reproduces all of the experiments cited in this article is available in CRAN. See the online Supplement for details.

Multivariate nonparametric test of independence

The problem of testing mutual independence of p random vectors in a general setting where the dimensions of the vectors can be different and the distributions can be discrete, continuous or both is of great importance. We propose such a test which utilizes multivariate characteristic functions and is a generalization of known results. We characterize the limiting distribution of the test statistic under the null hypothesis. The limiting null distribution is approximated and the method is validated. Numerical results based on simulations are investigated and our methodology is implemented in the R package IndependenceTests. Power comparisons are also presented for some partial cases of our general test, where some competitive procedures exist.

Confidence Intervals and Hypothesis Testing

This chapter is a catalogue of R functions commonly used to get confidence intervals for usual parameters: mean, proportion, variance, median and correlation. We also present a catalogue of R functions to perform standard hypothesis testing. Furthermore, a few practical worksheets will help the reader understand how to interpret confidence intervals, as well as the various errors related to hypothesis testing.

POWER AND SAMPLE SIZE DETERMINATION IN CLINICAL TRIALS WITH MULTIPLE PRIMARY CONTINUOUS CORRELATED ENDPOINTS

The use of two or more primary correlated endpoints is becoming increasingly common. A mandatory approach when analyzing data from such clinical trials is to control the family-wise error rate (FWER). In this context, we provide formulas for computation of sample size and for data analysis. Two approaches are discussed: an individual method based on a union–intersection procedure and a global procedure, based on a multivariate model that can take into account adjustment variables. These methods are illustrated with simulation studies and applications. An R package known as rPowerSampleSize is also available.

Programming in R

The strength of the R system is that it includes a real programming language. We shall see that it offers very original programming concepts. The concept of objects is very present in R. Object-oriented programming as used in R is transparent for the user, in the sense that you do not need to understand the theory in order to use it. The same cannot be said for the developer who wishes to respect the spirit of R.

Test of Normality Against Generalized Exponential Power Alternatives

The family of symmetric generalized exponential power (GEP) densities offers a wide range of tail behaviors, which may be exponential, polynomial, and/or logarithmic. In this article, a test of normality based on Raos score statistic and this family of GEP alternatives is proposed. This test is tailored to detect departures from normality in the tails of the distribution. The main interest of this approach is that it provides a test with a large family of symmetric alternatives having non-normal tails. In addition, the tests statistic consists of a combination of three quantities that can be interpreted as new measures of tail thickness. In a Monte-Carlo simulation study, the proposed test is shown to perform well in terms of power when compared to its competitors.