Sequential Quantiles via Hermite Series Density Estimation

Sequential quantile estimation refers to incorporating observations into quantile estimates in an incremental fashion thus furnishing an online estimate of one or more quantiles at any given point in time. Sequential quantile estimation is also known as online quantile estimation. This area is relevant to the analysis of data streams and to the one-pass analysis of massive data sets. Applications include network traffic and latency analysis, real time fraud detection and high frequency trading. We introduce new techniques for online quantile estimation based on Hermite series estimators in the settings of static quantile estimation and dynamic quantile estimation. In the static quantile estimation setting we apply the existing Gauss-Hermite expansion in a novel manner. In particular, we exploit the fact that Gauss-Hermite coefficients can be updated in a sequential manner. To treat dynamic quantile estimation we introduce a novel expansion with an exponentially weighted estimator for the Gauss-Hermite coefficients which we term the Exponentially Weighted Gauss-Hermite (EWGH) expansion. These algorithms go beyond existing sequential quantile estimation algorithms in that they allow arbitrary quantiles (as opposed to pre-specified quantiles) to be estimated at any point in time. In doing so we provide a solution to online distribution function and online quantile function estimation on data streams. In particular we derive an analytical expression for the CDF and prove consistency results for the CDF under certain conditions. In addition we analyse the associated quantile estimator. Simulation studies and tests on real data reveal the Gauss-Hermite based algorithms to be competitive with a leading existing algorithm.Comment: 43 pages, 9 figures. Improved version incorporating referee comments, as appears in Electronic Journal of Statistic

Caregiver burden: Support needed for those who support others and the National Health Service

This literature review focuses on the complexities and inequalities of informal caregiving in the UK and was inspired by the story of the following individual: EL is a 68-year-old Caucasian lady who attended Movement Disorder Clinic and was diagnosed with Parkinson\u27s Disease Dementia following many years of symptoms. The diagnosis came as a big relief to EL and her daughter (SL) who were eager to get treatment started as soon as possible. EL lives alone with SL and solely relies on her for care and support. SL does not have children and devotes her daily routine to looking after her mother, never spending more than a few hours away from her. SL has found this situation very challenging, while EL has felt she has lost her independence. This frustration on a background of mutual love and concern was evident from both parties during the appointment. Informal carers play a crucial role in looking after individuals and provide massive relief to healthcare systems but are often left without support. This puts themselves and the people they care for at risk of poor physical and psychological outcomes. The number of informal carers continues to rise but staggering rates of burnout are still observed. By understanding the complexities and emotional impact of this role, together with the inadequacies of current social care policies, we can strive to reveal areas of improvement that can grant carers the support they deserve to carry on performing their invaluable roles. Experience Framework This article is associated with the Staff & Provider Engagement lens of The Beryl Institute Experience Framework (https://theberylinstitute.org/experience-framework/). Access other PXJ articles related to this lens. Access other resources related to this lens

Living with Multiple Sclerosis as a former marathon runner: Impact of attitude and past behaviour on self-care maintenance and perseverance

As healthcare professionals, we have a duty to promote the wellbeing of individuals living with chronic diseases and this could be accomplished through the establishment of self-care strategies that are both collaborative and self-directed. Insight into the complex behaviours and backgrounds of individuals who show initiative in dealing with chronic disease could help achieve this by revealing drivers of health-seeking and engaging behaviours. Therefore, by deducing the complex interactions between attitude, past experiences and disease outlook, broader patient welfare could be championed through the implementation of targeted interventions which promote self-care in chronic disease. This article aims to explore these ideas by focusing on the story of a former marathon runner and proactive secondary progressive Multiple Sclerosis sufferer, Mr. Evans, who has taken charge in leading an active and healthy lifestyle to manage his condition. His sense of patience and self-worth are rooted in his attitude and upbringing and are factors which have championed his ongoing wellbeing and understanding of his condition. Experience Framework This article is associated with the Patient, Family & Community Engagement lens of The Beryl Institute Experience Framework (https://www.theberylinstitute.org/ExperienceFramework). Access other PXJ articles related to this lens. Access other resources related to this lens

Exact Multi-Restricted Schur Polynomial Correlators

We derive a product rule satisfied by restricted Schur polynomials. We focus mostly on the case that the restricted Schur polynomial is built using two matrices, although our analysis easily extends to more than two matrices. This product rule allows us to compute exact multi-point correlation functions of restricted Schur polynomials, in the free field theory limit. As an example of the use of our formulas, we compute two point functions of certain single trace operators built using two matrices and three point functions of certain restricted Schur polynomials, exactly, in the free field theory limit. Our results suggest that gravitons become strongly coupled at sufficiently high energy, while the restricted Schur polynomials for totally antisymmetric representations remain weakly interacting at these energies. This is in perfect accord with the half-BPS (single matrix) results of hep-th/0512312. Finally, by studying the interaction of two restricted Schur polynomials we suggest a physical interpretation for the labels of the restricted Schur polynomial: the composite operator $\chi_{R,(r_n,r_m)}(Z,X)$ is constructed from the half BPS ``partons'' $\chi_{r_n}(Z)$ and $\chi_{r_m}(X)$.Comment: 42 page

Sequential nonparametric estimation via Hermite series estimators

Algorithms for estimating the statistical properties of streams of data in real time, as well as for the efficient analysis of massive data sets, are becoming particularly pertinent given the increasing ubiquity of such data. In this thesis we introduce novel approaches to sequential (online) estimation in both stationary and non-stationary settings based on Hermite series density estimators. In the univariate context we apply Hermite series based distribution function estimators to sequential cumulative distribution function estimation. These distribution function estimators are particularly useful because they allow the sequential estimation of the full cumulative distribution function. This is in contrast to the empirical distribution function estimator and smooth kernel distribution function estimator which only allow sequential cumulative probability estimation at predefined values on the support of the associated density function. We explore the asymptotic consistency and robustness properties of the Hermite series based cumulative distribution function estimator thereby redressing a gap in the literature. Given the sequential Hermite series based distribution function estimator, we obtain sequential quantile estimates numerically. Our algorithms go beyond existing sequential quantile estimation algorithms in that they allow arbitrary quantiles (as opposed to pre-specified quantiles) to be estimated at any point in time, in both the static and dynamic quantile estimation settings. In the bivariate context we introduce a Hermite series based sequential estimator for the Spearman's rank correlation coefficient and provide algorithms applicable in both the stationary and non-stationary settings. To treat the the non-stationary setting, we introduce a novel, exponentially weighted estimator for the Spearman's rank correlation, which allows the local nonparametric correlation of a bivariate data stream to be tracked. To the best of our knowledge this is the first algorithm to be proposed for estimating a time-varying Spearman's rank correlation that does not rely on a moving window approach. We explore the practical effectiveness of the Hermite series based estimators through real data and simulation studies, demonstrating competitive performance compared to leading existing algorithms. The potential applications of this work are manifold. Our sequential distribution function and quantile estimation algorithms can be applied to real time anomaly and outlier detection, real time provisioning for future demand as well as real time risk estimation for example. The Hermite series based Spearman's rank correlation estimator can be applied to fast and robust online calculation of correlation which may vary over time. Possible machine learning applications include fast feature selection and hierarchical clustering on massive data sets amongst others

Nonparametric Transient Classification using Adaptive Wavelets

Classifying transients based on multi band light curves is a challenging but crucial problem in the era of GAIA and LSST since the sheer volume of transients will make spectroscopic classification unfeasible. Here we present a nonparametric classifier that uses the transient's light curve measurements to predict its class given training data. It implements two novel components: the first is the use of the BAGIDIS wavelet methodology - a characterization of functional data using hierarchical wavelet coefficients. The second novelty is the introduction of a ranked probability classifier on the wavelet coefficients that handles both the heteroscedasticity of the data in addition to the potential non-representativity of the training set. The ranked classifier is simple and quick to implement while a major advantage of the BAGIDIS wavelets is that they are translation invariant, hence they do not need the light curves to be aligned to extract features. Further, BAGIDIS is nonparametric so it can be used for blind searches for new objects. We demonstrate the effectiveness of our ranked wavelet classifier against the well-tested Supernova Photometric Classification Challenge dataset in which the challenge is to correctly classify light curves as Type Ia or non-Ia supernovae. We train our ranked probability classifier on the spectroscopically-confirmed subsample (which is not representative) and show that it gives good results for all supernova with observed light curve timespans greater than 100 days (roughly 55% of the dataset). For such data, we obtain a Ia efficiency of 80.5% and a purity of 82.4% yielding a highly competitive score of 0.49 whilst implementing a truly "model-blind" approach to supernova classification. Consequently this approach may be particularly suitable for the classification of astronomical transients in the era of large synoptic sky surveys.Comment: 14 pages, 8 figures. Published in MNRA

ASG Student Social and Emotional Health Report

This report presents the results of sophisticated Rasch measurement analysis and multi-level modelling to validate and support the use of the ACER Social and Emotional Wellbeing (SEWB) student and teacher surveys for reporting on the social and emotional well-being of students from the early years of schooling through to senior secondary school levels. It describes the social and emotional well-being of over 10,000 students attending 81 schools across Australia. Among the more important findings of this research are the characteristics of students with low levels of social and emotional well-being compared with students with higher levels of social and emotional well-being

Political and economic events 1988 to 1998 : their impact on the specification of the nonlinear multifactor asset pricing model described by the arbitrage pricing theory for the financial and industrial sector of the Johannesburg Stock Exchange

The impact of political and economic events on the asset pricing model described by the arbitrage pricing theory (APTM) was examined in order to establish if they had caused any changes in its specification. It was concluded that the APTM is not stationary and that it must be continuously tested before it can be used as political and economic events can change its specification. It was also found that political events had a more direct effect on the specification of the APTM, in that their effect is more immediate, than did economic events, which influenced the APTM by first influencing the economic environment in which it operated. The conventional approach that would have evaluated important political and economic events, case by case, to determine whether they affected the linear factor model (LFM), and subsequently the APTM, could not be used since no correlation was found between the pricing of a risk factor in the LFM and its subsequent pricing in the APTM. A new approach was then followed in which a correlation with a political or economic event was sought whenever a change was detected in the specification of the APTM. This was achieved by first finding the best subset LFM, chosen for producing the highest adjusted R2 , month by month, over 87 periods from 20 October1991 to 21 June 1998, using a combination of nine prespecified risk factors (five of which were proxies for economic events and one for political events). Multivariate analysis techniques were then used to establish which risk factors were priced most often during the three equal subperiods into which the 87 periods were broken up. Using the above methodology, the researcher was able to conclude that political events changed the specification of the APTM in late 1991. After the national elections in April 1994 it was found that the acceptance of South Africa into the world economic community had again changed the specification of the APTM and the two most important factors were proxies for economic events.Business LeadershipDB

The dynamics of open string-membrane systems

In this dissertation, the interacting Cuntz chain Hamiltonian for an open string - giant graviton system with an arbitrary number of strings attached is derived, thus generalizing the single string results of hep-th/0701067. The open strings considered carry angular momentum on an S3 embedded in the S5 of the AdS5£S5 background. In the process, we construct operators in the N = 4 super Yang-Mills theory dual to states with open strings ending on boundstates of sphere giant gravitons. The techniques we develop facilitate the computation of one-loop anomalous dimensions of these operators. The problem of computing the one loop anomalous dimensions is replaced with the problem of diagonalizing an interacting Cuntz oscillator Hamiltonian. Our Cuntz oscillator dynamics illustrates how the Chan-Paton factors for open strings propagating on multiple branes can arise dynamically