The distribution of the sample minimum-variance frontier

In this paper, we present a finite sample analysis of the sample minimum-variance frontier under the assumption that the returns are independent and multivariate normally distributed. We show that the sample minimum-variance frontier is a highly biased estimator of the population frontier, and we propose an improved estimator of the population frontier. In addition, we provide the exact distribution of the out-of-sample mean and variance of sample minimum-variance portfolios. This allows us to understand the impact of estimation error on the performance of in-sample optimal portfolios. Key Words: minimum-variance frontier; efficiency set constants; finite sample distribution

Mean and variance of estimates of the bispectrum of a harmonic random process-an analysis including leakage effects

Analytical expressions are derived for the mean and variance, of estimates of the bispectrum of a real-time series assuming a cosinusoidal model. The effects of spectral leakage, inherent in discrete Fourier transform operation when the modes present in the signal have a nonintegral number of wavelengths in the record, are included in the analysis. A single phase-coupled triad of modes can cause the bispectrum to have a nonzero mean value over the entire region of computation owing to leakage. The variance of bispectral estimates in the presence of leakage has contributions from individual modes and from triads of phase-coupled modes. Time-domain windowing reduces the leakage. The theoretical expressions for the mean and variance of bispectral estimates are derived in terms of a function dependent on an arbitrary symmetric time-domain window applied to the record. the number of data, and the statistics of the phase coupling among triads of modes. The theoretical results are verified by numerical simulations for simple test cases and applied to laboratory data to examine phase coupling in a hypothesis testing framework

Reduced variance in monozygous twins for multiple MR parameters : implications for disease studies and the genetic basis of brain structure

Twin studies offer the opportunity to determine the relative contribution of genes versus environment in traits of interest. Here, we investigate the extent to which variance in brain structure is reduced in monozygous twins with identical genetic make-up. We investigate whether using twins as compared to a control population reduces variability in a number of common magnetic resonance (MR) structural measures, and we investigate the location of areas under major genetic influences. This is fundamental to understanding the benefit of using twins in studies where structure is the phenotype of interest. Twenty-three pairs of healthy MZ twins were compared to matched control pairs. Volume, T2 and diffusion MR imaging were performed as well as spectroscopy (MRS). Images were compared using (i) global measures of standard deviation and effect size, (ii) voxel-based analysis of similarity and (iii) intra-pair correlation. Global measures indicated a consistent increase in structural similarity in twins. The voxel-based and correlation analyses indicated a widespread pattern of increased similarity in twin pairs, particularly in frontal and temporal regions. The areas of increased similarity were most widespread for the diffusion trace and least widespread for T2. MRS showed consistent reduction in metabolite variation that was significant in the temporal lobe N-acetylaspartate (NAA). This study has shown the distribution and magnitude of reduced variability in brain volume, diffusion, T2 and metabolites in twins. The data suggest that evaluation of twins discordant for disease is indeed a valid way to attribute genetic or environmental influences to observed abnormalities in patients since evidence is provided for the underlying assumption of decreased variability in twins.

A novel method for analysing lighting variance

Robust descriptor matching across varying lighting conditions is important for vision-based robotics. We present a novel strategy for quantifying the lighting variance of descriptors. The strategy works by utilising recovered low dimensional mappings from Isomap and our measure of the lighting variance of each of these mappings. The resultant metric allows different descriptors to be compared given a dataset and a set of keypoints. We demonstrate that the SIFT descriptor typically has lower lighting variance than other descriptors, although the result depends on semantic class and lighting conditions.

Improving short utterance i-vector speaker verification using utterance variance modelling and compensation techniques

This paper proposes techniques to improve the performance of i-vector based speaker verification systems when only short utterances are available. Short-length utterance i-vectors vary with speaker, session variations, and the phonetic content of the utterance. Well established methods such as linear discriminant analysis (LDA), source-normalized LDA (SN-LDA) and within-class covariance normalisation (WCCN) exist for compensating the session variation but we have identified the variability introduced by phonetic content due to utterance variation as an additional source of degradation when short-duration utterances are used. To compensate for utterance variations in short i-vector speaker verification systems using cosine similarity scoring (CSS), we have introduced a short utterance variance normalization (SUVN) technique and a short utterance variance (SUV) modelling approach at the i-vector feature level. A combination of SUVN with LDA and SN-LDA is proposed to compensate the session and utterance variations and is shown to provide improvement in performance over the traditional approach of using LDA and/or SN-LDA followed by WCCN. An alternative approach is also introduced using probabilistic linear discriminant analysis (PLDA) approach to directly model the SUV. The combination of SUVN, LDA and SN-LDA followed by SUV PLDA modelling provides an improvement over the baseline PLDA approach. We also show that for this combination of techniques, the utterance variation information needs to be artificially added to full-length i-vectors for PLDA modelling.

Back to the roots : mean-variance analysis of relevance estimations

Recently, mean-variance analysis has been proposed as a novel paradigm to model document ranking in Information Retrieval. The main merit of this approach is that it diversifies the ranking of retrieved documents. In its original formulation, the strategy considers both the mean of relevance estimates of retrieved documents and their variance. How- ever, when this strategy has been empirically instantiated, the concepts of mean and variance are discarded in favour of a point-wise estimation of relevance (to replace the mean) and of a parameter to be tuned or, alternatively, a quantity dependent upon the document length (to replace the variance). In this paper we revisit this ranking strategy by going back to its roots: mean and variance. For each retrieved document, we infer a relevance distribution from a series of point-wise relevance estimations provided by a number of different systems. This is used to compute the mean and the variance of document relevance estimates. On the TREC Clueweb collection, we show that this approach improves the retrieval performances. This development could lead to new strategies to address the fusion of relevance estimates provided by different systems.

The effect of preferential sampling on sampling variance

We examine some variations of standard probability designs that preferentially sample sites based on how easy they are to access. Preferential sampling designs deliver unbiased estimates of mean and sampling variance and will ease the burden of data collection but at what cost to our design efficiency? Preferential sampling has the potential to either increase or decrease sampling variance depending on the application. We carry out a simulation study to gauge what effect it will have when sampling Soil Organic Carbon (SOC) values in a large agricultural region in south-eastern Australia. Preferential sampling in this region can reduce the distance to travel by up to 16%. Our study is based on a dataset of predicted SOC values produced from a datamining exercise. We consider three designs and two ways to determine ease of access. The overall conclusion is that sampling performance deteriorates as the strength of preferential sampling increases, due to the fact the regions of high SOC are harder to access. So our designs are inadvertently targeting regions of low SOC value. The good news, however, is that Generalised Random Tessellation Stratification (GRTS) sampling designs are not as badly affected as others and GRTS remains an efficient design compared to competitors.

Short utterance PLDA speaker verification using SN-WLDA and variance modelling techniques

This paper proposes a combination of source-normalized weighted linear discriminant analysis (SN-WLDA) and short utterance variance (SUV) PLDA modelling to improve the short utterance PLDA speaker verification. As short-length utterance i-vectors vary with the speaker, session variations and phonetic content of the utterance (utterance variation), a combined approach of SN-WLDA projection and SUV PLDA modelling is used to compensate the session and utterance variations. Experimental studies have found that a combination of SN-WLDA and SUV PLDA modelling approach shows an improvement over baseline system (WCCN[LDA]-projected Gaussian PLDA (GPLDA)) as this approach effectively compensates the session and utterance variations.

Real or imagined? A study exploring the existence of common method variance effects in road safety research

Common method variance (CMV) has received little attention within the field of road safety research despite a heavy reliance on self-report data. Two surveys were completed by 214 motorists over a two-month period, allowing associations between social desirability and key road safety variables and relationships between scales across the two survey waves to be examined. Social desirability was found to have a strong negative correlation with the Driver Behaviour Questionnaire (DBQ) sub-scales as well as age, but not with crashes and offences. Drivers who scored higher on the social desirability scale were also less likely to report aberrant driving behaviours as measured by the DBQ. Controlling for social desirability did not substantially alter the predictive relationship between the DBQ and the crash and offences variables. The strength of the correlations within and between the two waves were also compared with the results strongly suggesting that effects associated with CMV were present. Identification of CMV would be enhanced by the replication of this study with a larger sample size and comparing self-report data with official sources.

Online estimation of Allan variance parameters

A new online method is presented for estimation of the angular randomwalk and rate randomwalk coefficients of inertial measurement unit gyros and accelerometers. In the online method, a state-space model is proposed, and recursive parameter estimators are proposed for quantities previously measured from offline data techniques such as the Allan variance method. The Allan variance method has large offline computational effort and data storage requirements. The technique proposed here requires no data storage and computational effort of approximately 100 calculations per data sample.

On-line estimation of Allan variance parameters

A new online method is presented for estimation of the angular random walk and rate random walk coefficients of IMU (inertial measurement unit) gyros and accelerometers. The online method proposes a state space model and proposes parameter estimators for quantities previously measured from off-line data techniques such as the Allan variance graph. Allan variance graphs have large off-line computational effort and data storage requirements. The technique proposed here requires no data storage and computational effort of O(100) calculations per data sample.