Asymptotics for testing hypothesis in some multivariate variance components model under non-normality

AbstractWe consider the problem of deriving the asymptotic distribution of the three commonly used multivariate test statistics, namely likelihood ratio, Lawley–Hotelling and Bartlett–Nanda–Pillai statistics, for testing hypotheses on the various effects (main, nested or interaction) in multivariate mixed models. We derive the distributions of these statistics, both in the null as well as non-null cases, as the number of levels of one of the main effects (random or fixed) goes to infinity. The robustness of these statistics against departure from normality will be assessed.Essentially, in the asymptotic spirit of this paper, both the hypothesis and error degrees of freedom tend to infinity at a fixed rate. It is intuitively appealing to consider asymptotics of this type because, for example, in random or mixed effects models, the levels of the main random factors are assumed to be a random sample from a large population of levels.For the asymptotic results of this paper to hold, we do not require any distributional assumption on the errors. That means the results can be used in real-life applications where normality assumption is not tenable.As it happens, the asymptotic distributions of the three statistics are normal. The statistics have been found to be asymptotically null robust against the departure from normality in the balanced designs. The expressions for the asymptotic means and variances are fairly simple. That makes the results an attractive alternative to the standard asymptotic results. These statements are favorably supported by the numerical results

The effects of immediate vision on implicit hand maps

Perceiving the external spatial location of the limbs using position sense requires that immediate proprioceptive afferent signals be combined with a stored body model specifying the size and shape of the body. Longo and Haggard (Proc Natl Acad Sci USA 107:11727–11732, 2010) developed a method to isolate and measure this body model in the case of the hand in which participants judge the perceived location in external space of several landmarks on their occluded hand. The spatial layout of judgments of different landmarks is used to construct implicit hand maps, which can then be compared with actual hand shape. Studies using this paradigm have revealed that the body model of the hand is massively distorted, in a highly stereotyped way across individuals, with large underestimation of finger length and overestimation of hand width. Previous studies using this paradigm have allowed participants to see the locations of their judgments on the occluding board. Several previous studies have demonstrated that immediate vision, even when wholly non-informative, can alter processing of somatosensory signals and alter the reference frame in which they are localised. The present study therefore investigated whether immediate vision contributes to the distortions of implicit hand maps described previously. Participants judged the external spatial location of the tips and knuckles of their occluded left hand either while being able to see where they were pointing (as in previous studies) or while blindfolded. The characteristic distortions of implicit hand maps reported previously were clearly apparent in both conditions, demonstrating that the distortions are not an artefact of immediate vision. However, there were significant differences in the magnitude of distortions in the two conditions, suggesting that vision may modulate representations of body size and shape, even when entirely non-informative

A Bayesian Model of Sensory Adaptation

Recent studies reported two opposite types of adaptation in temporal perception. Here, we propose a Bayesian model of sensory adaptation that exhibits both types of adaptation. We regard adaptation as the adaptive updating of estimations of time-evolving variables, which determine the mean value of the likelihood function and that of the prior distribution in a Bayesian model of temporal perception. On the basis of certain assumptions, we can analytically determine the mean behavior in our model and identify the parameters that determine the type of adaptation that actually occurs. The results of our model suggest that we can control the type of adaptation by controlling the statistical properties of the stimuli presented

Adaptation to motor-visual and motor-auditory temporal lags transfer across modalities

Previous research has shown that the timing of a sensor-motor event is recalibrated after a brief exposure to a delayed feedback of a voluntary action (Stetson et al. 2006). Here, we examined whether it is the sensory or motor event that is shifted in time. We compared lag adaption for action-feedback in visuo-motor pairs and audio-motor pairs using an adaptation-test paradigm. Participants were exposed to a constant lag (50 or 150 ms) between their voluntary action (finger tap) and its sensory feedback (flash or tone pip) during an adaptation period (~3 min). Immediately after that, they performed a temporal order judgment (TOJ) task about the tap-feedback test stimulus pairings. The modality of the feedback stimulus was either the same as the adapted one (within-modal) or different (cross-modal). The results showed that the point of subjective simultaneity (PSS) was uniformly shifted in the direction of the exposed lag within and across modalities (motor-visual, motor-auditory). This suggests that the TRE of sensor-motor events is mainly caused by a shift in the motor component

Audiovisual time perception is spatially specific

Our sensory systems face a daily barrage of auditory and visual signals whose arrival times form a wide range of audiovisual asynchronies. These temporal relationships constitute an important metric for the nervous system when surmising which signals originate from common external events. Internal consistency is known to be aided by sensory adaptation: repeated exposure to consistent asynchrony brings perceived arrival times closer to simultaneity. However, given the diverse nature of our audiovisual environment, functionally useful adaptation would need to be constrained to signals that were generated together. In the current study, we investigate the role of two potential constraining factors: spatial and contextual correspondence. By employing an experimental design that allows independent control of both factors, we show that observers are able to simultaneously adapt to two opposing temporal relationships, provided they are segregated in space. No such recalibration was observed when spatial segregation was replaced by contextual stimulus features (in this case, pitch and spatial frequency). These effects provide support for dedicated asynchrony mechanisms that interact with spatially selective mechanisms early in visual and auditory sensory pathways

Gene set analysis for longitudinal gene expression data

<p>Abstract</p> <p>Background</p> <p>Gene set analysis (GSA) has become a successful tool to interpret gene expression profiles in terms of biological functions, molecular pathways, or genomic locations. GSA performs statistical tests for independent microarray samples at the level of gene sets rather than individual genes. Nowadays, an increasing number of microarray studies are conducted to explore the dynamic changes of gene expression in a variety of species and biological scenarios. In these longitudinal studies, gene expression is repeatedly measured over time such that a GSA needs to take into account the within-gene correlations in addition to possible between-gene correlations.</p> <p>Results</p> <p>We provide a robust nonparametric approach to compare the expressions of longitudinally measured sets of genes under multiple treatments or experimental conditions. The limiting distributions of our statistics are derived when the number of genes goes to infinity while the number of replications can be small. When the number of genes in a gene set is small, we recommend permutation tests based on our nonparametric test statistics to achieve reliable type I error and better power while incorporating unknown correlations between and within-genes. Simulation results demonstrate that the proposed method has a greater power than other methods for various data distributions and heteroscedastic correlation structures. This method was used for an IL-2 stimulation study and significantly altered gene sets were identified.</p> <p>Conclusions</p> <p>The simulation study and the real data application showed that the proposed gene set analysis provides a promising tool for longitudinal microarray analysis. R scripts for simulating longitudinal data and calculating the nonparametric statistics are posted on the North Dakota INBRE website <url>http://ndinbre.org/programs/bioinformatics.php</url>. Raw microarray data is available in Gene Expression Omnibus (National Center for Biotechnology Information) with accession number GSE6085.</p

Irrelevant tactile stimulation biases visual exploration in external coordinates

Ossandón JP, König P, Heed T. Irrelevant tactile stimulation biases visual exploration in external coordinates. Scientific Reports. 2015;5(1): 10664