Global non-smooth optimization in robust multivariate regression

Robust regression in statistics leads to challenging optimization problems. Here, we study one such problem, in which the objective is non-smooth, non-convex and expensive to calculate. We study the numerical performance of several derivative-free optimization algorithms with the aim of computing robust multivariate estimators. Our experiences demonstrate that the existing algorithms often fail to deliver optimal solutions. We introduce three new methods that use Powell's derivative-free algorithm. The proposed methods are reliable and can be used when processing very large data sets containing outliers.

An extended multivariate autoregressive framework for EEG-based information flow analysis of a brain network

Recently effective connectivity studies have gained significant attention among the neuroscience community as Electroencephalography (EEG) data with a high time resolution can give us a wider understanding of the information flow within the brain. Among other tools used in effective connectivity analysis Granger Causality (GC) has found a prominent place. The GC analysis, based on strictly causal multivariate autoregressive (MVAR) models does not account for the instantaneous interactions among the sources. If instantaneous interactions are present, GC based on strictly causal MVAR will lead to erroneous conclusions on the underlying information flow. Thus, the work presented in this paper applies an extended MVAR (eMVAR) model that accounts for the zero lag interactions. We propose a constrained adaptive Kalman filter (CAKF) approach for the eMVAR model identification and demonstrate that this approach performs better than the short time windowing-based adaptive estimation when applied to information flow analysis.

Univariate and multivariate process yield indices based on location-scale family of distributions

Several measures of process yield, defined on univariate and multivariate normal process characteristics, have been introduced and studied by several authors. These measures supplement several well-known Process Capacity Indices (PCI) used widely in assessing the quality of products before being released into the marketplace. In this paper, we generalise these yield indices to the location-scale family of distributions which includes the normal distribution as one of its member. One of the key contributions of this paper is to demonstrate that under appropriate conditions, these indices converge in distribution to a normal distribution. Several numerical examples will be used to illustrate our procedures and show how they can be applied to perform statistical inferences on process capability.

Rapid discrimination and determination of polyunsaturated fatty acid composition in marine oils by FTIR Spectroscopy and Multivariate Data Analysis

A rapid analytical approach for discrimination and quantitative determination of polyunsaturated fatty acid (PUFA) contents, particularly eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA), in a range of oils extracted from marine resources has been developed by using attenuated total reflection Fourier transform infrared spectroscopy and multivariate data analysis. The spectral data were collected without any sample preparation; thus, no chemical preparation was involved, but data were rather processed directly using the developed spectral analysis platform, making it fast, very cost effective, and suitable for routine use in various biotechnological and food research and related industries. Unsupervised pattern recognition techniques, including principal component analysis and unsupervised hierarchical cluster analysis, discriminated the marine oils into groups by correlating similarities and differences in their fatty acid (FA) compositions that corresponded well to the FA profiles obtained from traditional lipid analysis based on gas chromatography (GC). Furthermore, quantitative determination of unsaturated fatty acids, PUFAs, EPA and DHA, by partial least square regression analysis through which calibration models were optimized specifically for each targeted FA, was performed in both known marine oils and totally independent unknown n - 3 oil samples obtained from an actual commercial product in order to provide prospective testing of the developed models towards actual applications. The resultant predicted FAs were achieved at a good accuracy compared to their reference GC values as evidenced through (1) low root mean square error of prediction, (2) good coefficient of determination close to 1 (i.e., R 2≥ 0.96), and (3) the residual predictive deviation values that indicated the predictive power at good and higher levels for all the target FAs. © 2014 Springer Science+Business Media New York.

Estimating capability index in multivariate processes using bootstrap sequential sampling procedures

Capability indices in both univariate and multivariate processes are extensively employed in quality control to assess the quality status of production batches before their release for operational use. It is traditionally a measure of the ratio of the allowable process spread and the actual spread. In this paper, we will adopt a bootstrap and sequential sampling procedures to determine the optimal sample size for estimating a multivariate capability index introduced by Pearns et. al. [12]. Bootstrap techniques have the distinct advantage of placing very minimum requirement on the distributions of the underlying quality characteristics, thereby rendering them more relevant under a wide variety of situations. Finally, we provide several numerical examples where the sequential sampling procedures are evaluated and compared.

Energy consumption and income in six Asian developing countries: a multivariate cointegration analysis

 This article examines the short- and long-run causal relationship between energy consumption and GDP of six emerging economies of Asia. Based on cointegration and vector error correction modeling the empirical results show that there exists unidirectional short- and long-run causality running from energy consumption to GDP for China, uni-directional short-run causality from output to energy consumption for India, whilst bi-directional short-run causality for Thailand. Neutrality between energy consumption and income is found for Indonesia, Malaysia and Philippines. Both the generalized variance decompositions and impulse response functions confirm the direction of causality. These findings have important policy implications for the countries concerned. The results suggest that while India may directly initiate energy conservation measures, China and Thailand may opt for a balanced combination of alternative polices.

Application of extended multivariate modeling for information flow analysis of event related responses

Event related potential (ERP) analysis is one of the most widely used methods in cognitive neuroscience research to study the physiological correlates of sensory, perceptual and cognitive activity associated with processing information. To this end information flow or dynamic effective connectivity analysis is a vital technique to understand the higher cognitive processing under different events. In this paper we present a Granger causality (GC)-based connectivity estimation applied to ERP data analysis. In contrast to the generally used strictly causal multivariate autoregressive model, we use an extended multivariate autoregressive model (eMVAR) which also accounts for any instantaneous interaction among variables under consideration. The experimental data used in the paper is based on a single subject data set for erroneous button press response from a two-back with feedback continuous performance task (CPT). In order to demonstrate the feasibility of application of eMVAR models in source space connectivity studies, we use cortical source time series data estimated using blind source separation or independent component analysis (ICA) for this data set.

Multivariate adaptive autoregressive modeling and kalman filtering for motor imagery BCI

Adaptive autoregressive (AAR) modeling of the EEG time series and the AAR parameters has been widely used in Brain computer interface (BCI) systems as input features for the classification stage. Multivariate adaptive autoregressive modeling (MVAAR) also has been used in literature. This paper revisits the use of MVAAR models and propose the use of adaptive Kalman filter (AKF) for estimating the MVAAR parameters as features in a motor imagery BCI application. The AKF approach is compared to the alternative short time moving window (STMW) MVAAR parameter estimation approach. Though the two MVAAR methods show a nearly equal classification accuracy, the AKF possess the advantage of higher estimation update rates making it easily adoptable for on-line BCI systems.

Multivariate autoregressive-based neuronal network flow analysis for in-vitro recorded bursts

Neuroscientific studies of in vitro neuron cell cultures has attracted paramount attention to investigate the behaviour of neuronal networks in response to different environmental conditions and external stimuli such as drugs, optical and electrical stimulations. Microelec trodearray (MEA) technology has been widely adopted as a tool for this investigation. In this work, we present a new approach to estimate interconnectivity of neural spikes using multivariate autoregressive (MVAR) analysis and Partial Directed Coherence (PDC). The proposed approach has the potential to discover hidden intra-burst causal connectivity patterns and to help understand the spatiotemporal communication patterns within bursts, pre and post stimulations.

Learning entry profiles of children with autism from multivariate treatment information using restricted boltzmann machines

Entry profiles can be generated before children with Autism Spectrum Disorders (ASD) begin to traverse an intervention program. They can help evaluate the progress of each child on the dedicated syllabus in addition to enabling narrowing down the best intervention course over time. However, the traits of ASD are expressed in different ways in every individual affected. The resulting spectrum nature of the disorder makes it challenging to discover profiles of children with ASD. Using data from 491 children, traversing the syllabus of a comprehensive intervention program on iPad called TOBY Playpad, we learn the entry profiles of the children based on their age, sex and performance on their first skills of the syllabus. Mixed-variate restricted Boltzmann machines allow us to integrate the heterogeneous data into one model making it a suitable technique. The data based discovery of entry profiles may assist in developing systems that can automatically suggest best suitable paths through the syllabus by clustering the children based on the characteristics they present at the beginning of the program. This may open the pathway for personalised intervention.

Comparing two multivariate unit root tests

In this essay, a method for comparing the asymptotic power of the multivariate unit root tests proposed in Phillips & Durlauf (1986) and Flˆores, Preumont & Szafarz (1996) is proposed. In order to determine the asymptotic power of the tests the asymptotic distributions under the null hypothesis and under the set of alternative hypotheses described in Phillips (1988) are determined. In addition, a test which combines characteristics of both tests is proposed and its distributions under the null hypothesis and the same set of alternative hypotheses are determined. This allows us to determine what causes any difference in the asymptotic power of the two tests against the set of alternative hypotheses considered

Output convergence in Mercosur: multivariate time series evidence

The aim of this paper is to provide evidence on output convergence among the Mercosur countries and associates, using multivariate time-series tests. The methodology is based on a combination of tests and estimation procedures, both univariate and multivariate, applied to the differences in per capita real income. We use the definitions of time-series convergence proposed by Bernard & Durlauf and apply unit root and tests proposed by Abuaf & Jorion and Taylor & Sarno. In this same multivariate context, the Flôres, Preumont & Szafarz and Breuer, MbNown & Wallace tests, which allow for the existence of correlations across the series without imposing a common speed of mean reversion, identify the countries that convergence. Concerning the empirical results, there is evidence of long-run convergence or, at least, catching up, for the smaller countries, Bolivia, Paraguay, Peru and Uruguay, towards Brazil and, to some extent, Argentina. In contrast, the evidence on convergence for the larger countries is weaker, as they have followed different (or rather opposing) macroeconomic policy strategies. Thus the future of the whole area will critically depend on the ability of Brazil, Argentina and Chile to find some scope for more cooperative policy actions.