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.

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.

Aging and fluctuation-dissipation ratio in a nonequilibrium q-state lattice model

A generalized version of the nonequilibrium linear Glauber model with q states in d dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the q states. Exact expressions for the two-time autocorrelation and response functions on a d-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.

Contribution margin model applied to the marketing planning of a container liner carrier

The implementation of confidential contracts between a container liner carrier and its customers, because of the Ocean Shipping Reform Act (OSRA) 1998, demands a revision in the methodology applied in the carrier's planning of marketing and sales. The marketing and sales planning process should be more scientific and with a better use of operational research tools considering the selection of the customers under contracts, the duration of the contracts, the freight, and the container imbalances of these contracts are basic factors for the carrier's yield. This work aims to develop a decision support system based on a linear programming model to generate the business plan for a container liner carrier, maximizing the contribution margin of its freight.

Real time optimization (RTO) with model predictive control (MPC)

This paper studies a simplified methodology to integrate the real time optimization (RTO) of a continuous system into the model predictive controller in the one layer strategy. The gradient of the economic objective function is included in the cost function of the controller. Optimal conditions of the process at steady state are searched through the use of a rigorous non-linear process model, while the trajectory to be followed is predicted with the use of a linear dynamic model, obtained through a plant step test. The main advantage of the proposed strategy is that the resulting control/optimization problem can still be solved with a quadratic programming routine at each sampling step. Simulation results show that the approach proposed may be comparable to the strategy that solves the full economic optimization problem inside the MPC controller where the resulting control problem becomes a non-linear programming problem with a much higher computer load. (C) 2010 Elsevier Ltd. All rights reserved.

Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

Classification model based on Raman spectra of selected morphological and biochemical tissue constituents for identification of atherosclerosis in human coronary arteries

This study presents the results of Raman spectroscopy applied to the classification of arterial tissue based on a simplified model using basal morphological and biochemical information extracted from the Raman spectra of arteries. The Raman spectrograph uses an 830-nm diode laser, imaging spectrograph, and a CCD camera. A total of 111 Raman spectra from arterial fragments were used to develop the model, and those spectra were compared to the spectra of collagen, fat cells, smooth muscle cells, calcification, and cholesterol in a linear fit model. Non-atherosclerotic (NA), fatty and fibrous-fatty atherosclerotic plaques (A) and calcified (C) arteries exhibited different spectral signatures related to different morphological structures presented in each tissue type. Discriminant analysis based on Mahalanobis distance was employed to classify the tissue type with respect to the relative intensity of each compound. This model was subsequently tested prospectively in a set of 55 spectra. The simplified diagnostic model showed that cholesterol, collagen, and adipocytes were the tissue constituents that gave the best classification capability and that those changes were correlated to histopathology. The simplified model, using spectra obtained from a few tissue morphological and biochemical constituents, showed feasibility by using a small amount of variables, easily extracted from gross samples.

Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma

A mixture model incorporating long-term survivors has been adopted in the field of biostatistics where some individuals may never experience the failure event under study. The surviving fractions may be considered as cured. In most applications, the survival times are assumed to be independent. However, when the survival data are obtained from a multi-centre clinical trial, it is conceived that the environ mental conditions and facilities shared within clinic affects the proportion cured as well as the failure risk for the uncured individuals. It necessitates a long-term survivor mixture model with random effects. In this paper, the long-term survivor mixture model is extended for the analysis of multivariate failure time data using the generalized linear mixed model (GLMM) approach. The proposed model is applied to analyse a numerical data set from a multi-centre clinical trial of carcinoma as an illustration. Some simulation experiments are performed to assess the applicability of the model based on the average biases of the estimates formed. Copyright (C) 2001 John Wiley & Sons, Ltd.

A zero-augmented gamma mixed model for longitudinal data with many zeros

In many occupational safety interventions, the objective is to reduce the injury incidence as well as the mean claims cost once injury has occurred. The claims cost data within a period typically contain a large proportion of zero observations (no claim). The distribution thus comprises a point mass at 0 mixed with a non-degenerate parametric component. Essentially, the likelihood function can be factorized into two orthogonal components. These two components relate respectively to the effect of covariates on the incidence of claims and the magnitude of claims, given that claims are made. Furthermore, the longitudinal nature of the intervention inherently imposes some correlation among the observations. This paper introduces a zero-augmented gamma random effects model for analysing longitudinal data with many zeros. Adopting the generalized linear mixed model (GLMM) approach reduces the original problem to the fitting of two independent GLMMs. The method is applied to evaluate the effectiveness of a workplace risk assessment teams program, trialled within the cleaning services of a Western Australian public hospital.

Nonlinear mixture model for hyperspectral unmixing

Proceedings of International Conference - SPIE 7477, Image and Signal Processing for Remote Sensing XV - 28 September 2009

Encapsulation and controlled release of bioactive compounds in lactoferrin-glycomacropeptide nanohydrogels : curcumin and caffeine as model compounds

Curcumin and caffeine (used as lipophilic and hydrophilic model compounds, respectively) were successfully encapsulated in lactoferrin-glycomacropeptide (Lf-GMP) nanohydrogels by thermal gelation showing high encapsulation efficiencies (>90 %). FTIR spectroscopy confirmed the encapsulation of bioactive compounds in Lf-GMP nanohydrogels and revealed that according to the encapsulated compound different interactions occur with the nanohydrogel matrix. The successful encapsulation of bioactive compounds in Lf-GMP nanohydrogels was also confirmed by fluorescence measurements and confocal laser scanning microscopy. TEM images showed that loaded nanohydrogels maintain their spherical shape with sizes of 112 and 126 nm for curcumin and caffeine encapsulated in Lf-GMP nanohydrogels, respectively; in both cases a polydispersity of 0.2 was obtained. The release mechanisms of bioactive compounds through Lf-GMP nanohydrogels were evaluated at pH 2 and pH 7, by fitting the Linear Superimposition Model to the experimental data. The bioactive compounds release was found to be pH-dependent: at pH 2, relaxation is the governing phenomenon for curcumin and caffeine compounds and at pH 7 Ficks diffusion is the main mechanism of caffeine release while curcumin was not released through Lf-GMP nanohydrogels.

Determination of displacement, stress- and strain-distribution in the human heart: a FE-model on the basis of MR imaging.

The determination of characteristic cardiac parameters, such as displacement, stress and strain distribution are essential for an understanding of the mechanics of the heart. The calculation of these parameters has been limited until recently by the use of idealised mathematical representations of biventricular geometries and by applying simple material laws. On the basis of 20 short axis heart slices and in consideration of linear and nonlinear material behaviour we have developed a FE model with about 100,000 degrees of freedom. Marching Cubes and Phong's incremental shading technique were used to visualise the three dimensional geometry. In a quasistatic FE analysis continuous distribution of regional stress and strain corresponding to the endsystolic state were calculated. Substantial regional variation of the Von Mises stress and the total strain energy were observed at all levels of the heart model. The results of both the linear elastic model and the model with a nonlinear material description (Mooney-Rivlin) were compared. While the stress distribution and peak stress values were found to be comparable, the displacement vectors obtained with the nonlinear model were generally higher in comparison with the linear elastic case indicating the need to include nonlinear effects.