Comparison of Some Improved Estimators for Linear Regression Model under Different Conditions

Multiple linear regression model plays a key role in statistical inference and it has extensive applications in business, environmental, physical and social sciences. Multicollinearity has been a considerable problem in multiple regression analysis. When the regressor variables are multicollinear, it becomes difficult to make precise statistical inferences about the regression coefficients. There are some statistical methods that can be used, which are discussed in this thesis are ridge regression, Liu, two parameter biased and LASSO estimators. Firstly, an analytical comparison on the basis of risk was made among ridge, Liu and LASSO estimators under orthonormal regression model. I found that LASSO dominates least squares, ridge and Liu estimators over a significant portion of the parameter space for large dimension. Secondly, a simulation study was conducted to compare performance of ridge, Liu and two parameter biased estimator by their mean squared error criterion. I found that two parameter biased estimator performs better than its corresponding ridge regression estimator. Overall, Liu estimator performs better than both ridge and two parameter biased estimator.

Chemical structure based prediction of PAN and oxidized PAN fiber density through a non-linear mathematical model

The production of carbon fiber, particularly the oxidation/stabilization step, is a complex process. In the present study, a non-linear mathematical model has been developed for the prediction of density of polyacrylonitrile (PAN) and oxidized PAN fiber (OPF), as a key physical property for various applications, such as energy and material optimization, modeling, and design of the stabilization process. The model is based on the available functional groups in PAN and OPF. Expected functional groups, including [Formula presented], [Formula presented], –CH2, [Formula presented], and [Formula presented], were identified and quantified through the full deconvolution analysis of Fourier transform infrared attenuated total reflectance (FT-IR ATR) spectra obtained from fibers. These functional groups form the basis of three stabilization rendering parameters, representing the cyclization, dehydrogenation and oxidation reactions that occur during PAN stabilization, and are used as the independent variables of the non-linear predictive model. The k-fold cross validation approach, with k = 10, has been employed to find the coefficients of the model. This model estimates the density of PAN and OPF independent of operational parameters and can be expanded to all operational parameters. Statistical analysis revealed good agreement between the governing model and experiments. The maximum relative error was less than 1% for the present model.

Análise Espacial Multivariada Aplicada na Avaliação da Fertilidade do Solo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-linear dynamics of a tower orchard sprayer based on an inverted pendulum model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Cholesky Residuals for Assessing Normal Errors in a Linear Model with Correlated Outcomes: Technical Report

Despite the widespread popularity of linear models for correlated outcomes (e.g. linear mixed models and time series models), distribution diagnostic methodology remains relatively underdeveloped in this context. In this paper we present an easy-to-implement approach that lends itself to graphical displays of model fit. Our approach involves multiplying the estimated margional residual vector by the Cholesky decomposition of the inverse of the estimated margional variance matrix. The resulting "rotated" residuals are used to construct an empirical cumulative distribution function and pointwise standard errors. The theoretical framework, including conditions and asymptotic properties, involves technical details that are motivated by Lange and Ryan (1989), Pierce (1982), and Randles (1982). Our method appears to work well in a variety of circumstances, including models having independent units of sampling (clustered data) and models for which all observations are correlated (e.g., a single time series). Our methods can produce satisfactory results even for models that do not satisfy all of the technical conditions stated in our theory.

A linear relational DEA model to evaluate two-stage processes with shared inputs

Two-stage data envelopment analysis (DEA) efficiency models identify the efficient frontier of a two-stage production process. In some two-stage processes, the inputs to the first stage are shared by the second stage, known as shared inputs. This paper proposes a new relational linear DEA model for dealing with measuring the efficiency score of two-stage processes with shared inputs under constant returns-to-scale assumption. Two case studies of banking industry and university operations are taken as two examples to illustrate the potential applications of the proposed approach.

Adapting a generic BEAMnrc model of the BrainLAB m3 micro-multileaf collimator to simulate a local collimation device

This work is focussed on developing a commissioning procedure so that a Monte Carlo model, which uses BEAMnrc’s standard VARMLC component module, can be adapted to match a specific BrainLAB m3 micro-multileaf collimator (μMLC). A set of measurements are recommended, for use as a reference against which the model can be tested and optimised. These include radiochromic film measurements of dose from small and offset fields, as well as measurements of μMLC transmission and interleaf leakage. Simulations and measurements to obtain μMLC scatter factors are shown to be insensitive to relevant model parameters and are therefore not recommended, unless the output of the linear accelerator model is in doubt. Ultimately, this note provides detailed instructions for those intending to optimise a VARMLC model to match the dose delivered by their local BrainLAB m3 μMLC device.

Do anti-inflammatory agents promote linear ablation lesion discontinuities? : an electrophysiological examination

Background: Catheter ablation for atrial fibrillation (AF) is more efficacious than antiarrhythmic therapy. Post ablation recurrences reduce ablation effectiveness and are contributed by lesion discontinuity in the fibrotic linear ablation lesions. The anti-fibrotic role of statins in reducing AF is being assessed in current trials. By reducing the chronic pathological fibrosis that occurs in AF they may reduce AF. However if statins also have an effect on the acute therapeutic fibrosis of an ablation, this could exacerbate lesion discontinuity and AF recurrence. We tested the hypothesis that statins attenuate ablation lesion continuity in a recognised pig atrial linear ablation model. Aims: To assess whether Atorvastatin diminishes the bi-directional conduction block produced by a linear atrial ablation lesion. Methods: Sixteen pigs were randomised to statin (n=8) or placebo (n=8) with drug pre-treatment for 3 days and a further 4 weeks. At initial electrophysiological study (EPS1) 3D right atrium (RA) mapping and a vertical ablation linear lesion in the posterior RA with bidirectional conduction block were completed (Gepstein Circ 1999). Follow-up electrophysiological assessment (EPS2) at 28 days assessed bidirectional conduction block maintenance. Results: Data of 15/16 (statin=7) pigs were analysed. Mean lesion length was 3.7 ± 0.8cm with a mean of 17.9 ± 5.7 lesion applications. Bi-directional conduction block was confirmed in 15/15 pigs (100%) at EPS1 and EPS2. Conclusions: Atorvastatin did not affect ablation lesion continuity in this pig atrial linear ablation model. If patients are on long-term statins for AF reduction, periablation cessation is probably not necessary.

The impact of mobile phone distraction on the braking behaviour of young drivers : a hazard-based duration model

Braking is a crucial driving task with a direct relationship with crash risk, as both excess and inadequate braking can lead to collisions. The objective of this study was to compare the braking profile of young drivers distracted by mobile phone conversations to non-distracted braking. In particular, the braking behaviour of drivers in response to a pedestrian entering a zebra crossing was examined using the CARRS-Q Advanced Driving Simulator. Thirty-two licensed drivers drove the simulator in three phone conditions: baseline (no phone conversation), hands-free, and handheld. In addition to driving the simulator, each participant completed questionnaires related to driver demographics, driving history, usage of mobile phones while driving, and general mobile phone usage history. The drivers were 18–26 years old and split evenly by gender. A linear mixed model analysis of braking profiles along the roadway before the pedestrian crossing revealed comparatively increased decelerations among distracted drivers, particularly during the initial 20 kph of deceleration. Drivers’ initial 20 kph deceleration time was modelled using a parametric accelerated failure time (AFT) hazard-based duration model with a Weibull distribution with clustered heterogeneity to account for the repeated measures experiment design. Factors found to significantly influence the braking task included vehicle dynamics variables like initial speed and maximum deceleration, phone condition, and driver-specific variables such as licence type, crash involvement history, and self-reported experience of using a mobile phone whilst driving. Distracted drivers on average appear to reduce the speed of their vehicle faster and more abruptly than non-distracted drivers, exhibiting excess braking comparatively and revealing perhaps risk compensation. The braking appears to be more aggressive for distracted drivers with provisional licenses compared to drivers with open licenses. Abrupt or excessive braking by distracted drivers might pose significant safety concerns to following vehicles in a traffic stream.

Temperature variation between neighboring days and mortality: a distributed lag non-linear analysis

Objectives To investigate whether a sudden temperature change between neighboring days has significant impact on mortality. Methods A Poisson generalized linear regression model combined with a distributed lag non-linear models was used to estimate the association of temperature change between neighboring days with mortality in a subtropical Chinese city during 2008–2012. Temperature change was calculated as the current day’s temperature minus the previous day’s temperature. Results A significant effect of temperature change between neighboring days on mortality was observed. Temperature increase was significantly associated with elevated mortality from non-accidental and cardiovascular diseases, while temperature decrease had a protective effect on non-accidental mortality and cardiovascular mortality. Males and people aged 65 years or older appeared to be more vulnerable to the impact of temperature change. Conclusions Temperature increase between neighboring days has a significant adverse impact on mortality. Further health mitigation strategies as a response to climate change should take into account temperature variation between neighboring days.

A differential transformation technique for the analysis of a class of non-linear time varying systems

The scope of the differential transformation technique, developed earlier for the study of non-linear, time invariant systems, has been extended to the domain of time-varying systems by modifications to the differential transformation laws proposed therein. Equivalence of a class of second-order, non-linear, non-autonomous systems with a linear autonomous model of second order is established through these transformation laws. The feasibility of application of this technique in obtaining the response of such non-linear time-varying systems is discussed.

Prediction of solid block masonry prism compressive strength using FE model

Masonry strength is dependent upon characteristics of the masonry unit,the mortar and the bond between them. Empirical formulae as well as analytical and finite element (FE) models have been developed to predict structural behaviour of masonry. This paper is focused on developing a three dimensional non-linear FE model based on micro-modelling approach to predict masonry prism compressive strength and crack pattern. The proposed FE model uses multi-linear stress-strain relationships to model the non-linear behaviour of solid masonry unit and the mortar. Willam-Warnke's five parameter failure theory developed for modelling the tri-axial behaviour of concrete has been adopted to model the failure of masonry materials. The post failure regime has been modelled by applying orthotropic constitutive equations based on the smeared crack approach. Compressive strength of the masonry prism predicted by the proposed FE model has been compared with experimental values as well as the values predicted by other failure theories and Eurocode formula. The crack pattern predicted by the FE model shows vertical splitting cracks in the prism. The FE model predicts the ultimate failure compressive stress close to 85 of the mean experimental compressive strength value.

Dense granular flow down an inclined plane A comparison between the hard particle model and soft particle simulations

The granular flow down an inclined plane is simulated using the discrete element (DE) technique to examine the extent to which the dynamics of an unconfined dense granular flow can be well described by a hard particle model First, we examine the average coordination number for the particles in the flow down an inclined plane using the DE technique using the linear contact model with and without friction, and the Hertzian contact model with friction The simulations show that the average coordination number decreases below 1 for values of the spring stiffness corresponding to real materials, such as sand and glass, even when the angle of inclination is only 10 larger than the angle of repose Additional measures of correlations in the system, such as the fraction of particles with multibody contact, the force ratio (average ratio of the magnitudes of the largest and the second largest force on a particle), and the angle between the two largest forces on the particle, show no evidence of force chains or other correlated motions in the system An analysis of the bond-orientational order parameter indicates that the flow is in the random state, as in event-driven (ED) simulations V Kumaran, J Fluid Mech 632, 107 (2009), J Fluid Mech 632, 145 (2009)] The results of the two simulation techniques for the Bagnold coefficients (ratio of stress and square of the strain rate) and the granular temperature (mean square of the fluctuating velocity) are compared with the theory V Kumaran, J Fluid Mech 632, 107 (2009), J Fluid Mech 632, 145 (2009)] and are found to be in quantitative agreement In addition, we also conduct a comparison of the collision frequency and the distribution of the precollisional relative velocities of particles in contact The strong correlation effects exhibited by these two quantities in event-driven simulations V Kumaran, J Fluid Mech 632, 145 (2009)] are also found in the DE simulations (C) 2010 American Institute of Physics doi 10 1063/1 3504660]

Large-MIMO Receiver based on Linear Regression of MMSE Residual

Multiple input multiple output (MIMO) systems with large number of antennas have been gaining wide attention as they enable very high throughputs. A major impediment is the complexity at the receiver needed to detect the transmitted data. To this end we propose a new receiver, called LRR (Linear Regression of MMSE Residual), which improves the MMSE receiver by learning a linear regression model for the error of the MMSE receiver. The LRR receiver uses pilot data to estimate the channel, and then uses locally generated training data (not transmitted over the channel), to find the linear regression parameters. The proposed receiver is suitable for applications where the channel remains constant for a long period (slow-fading channels) and performs quite well: at a bit error rate (BER) of 10(-3), the SNR gain over MMSE receiver is about 7 dB for a 16 x 16 system; for a 64 x 64 system the gain is about 8.5 dB. For large coherence time, the complexity order of the LRR receiver is the same as that of the MMSE receiver, and in simulations we find that it needs about 4 times as many floating point operations. We also show that further gain of about 4 dB is obtained by local search around the estimate given by the LRR receiver.

The cold mode: a phenomenological model for the evolution of density perturbations in the intracluster medium

Cool cluster cores are in global thermal equilibrium but are locally thermally unstable. We study a non-linear phenomenological model for the evolution of density perturbations in the intracluster medium (ICM) due to local thermal instability and gravity. We have analysed and extended a model for the evolution of an overdense blob in the ICM. We find two regimes in which the overdense blobs can cool to thermally stable low temperatures. One for large t(cool)/t(ff) (t(cool) is the cooling time and t(ff) is the free-fall time), where a large initial overdensity is required for thermal runaway to occur; this is the regime which was previously analysed in detail. We discover a second regime for t(cool)/t(ff) less than or similar to 1 (in agreement with Cartesian simulations of local thermal instability in an external gravitational field), where runaway cooling happens for arbitrarily small amplitudes. Numerical simulations have shown that cold gas condenses out more easily in a spherical geometry. We extend the analysis to include geometrical compression in weakly stratified atmospheres such as the ICM. With a single parameter, analogous to the mixing length, we are able to reproduce the results from numerical simulations; namely, small density perturbations lead to the condensation of extended cold filaments only if t(cool)/t(ff) less than or similar to 10.