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.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

Prediction of surface roughness during hard turning of AISI 4340 steel (69 HRC)

In this study, 39 sets of hard turning (HT) experimental trials were performed on a Mori-Seiki SL-25Y (4-axis) computer numerical controlled (CNC) lathe to study the effect of cutting parameters in influencing the machined surface roughness. In all the trials, AISI 4340 steel workpiece (hardened up to 69 HRC) was machined with a commercially available CBN insert (Warren Tooling Limited, UK) under dry conditions. The surface topography of the machined samples was examined by using a white light interferometer and a reconfirmation of measurement was done using a Form Talysurf. The machining outcome was used as an input to develop various regression models to predict the average machined surface roughness on this material. Three regression models - Multiple regression, Random Forest, and Quantile regression were applied to the experimental outcomes. To the best of the authors’ knowledge, this paper is the first to apply Random Forest or Quantile regression techniques to the machining domain. The performance of these models was compared to each other to ascertain how feed, depth of cut, and spindle speed affect surface roughness and finally to obtain a mathematical equation correlating these variables. It was concluded that the random forest regression model is a superior choice over multiple regression models for prediction of surface roughness during machining of AISI 4340 steel (69 HRC).

Differentiated effect of advertising: Joint vs. separate consumption

In a context of intense competition, cooperative advertising between firms is critical. Accordingly, the objective of this article is to analyze the potential differentiated effect of advertising on two basic consumption patterns: individual products (i.e. hotel, restaurant) vs. bundle (i.e. hotel + restaurant). This research adds to the extant literature in that, for the first time, this potential differentiated effect is examined through a hierarchical modelling framework that reflects the way people make their decisions: first, they decide whether to visit or not a region; second, whether to purchase an advertised product in that region; and third, whether to buy products together or separately at the region. The empirical analysis, applied to a sample of 11,288 individuals, shows that the influence of advertising is positive for the decisions to visit and to purchase; however, when it comes to the joint or separate consumption, advertising has a differentiated effect: its impact is much greater on the joint alternative (“hotel + restaurant”) than the separate options (“hotel” and “restaurant”). Also, the variable distance moderates the advertising effect.

Evaluating the environmental Kuznets curve

We examine the empirical evidence for an environmental Kuznets curve using a semiparametric smooth coefficient regression model that allows us to incorporate flexibility in the parameter estimates, while maintaining the basic econometric structure that is typically used to estimate the pollution-income relationship. This allows us to assess the sensitivity to parameter heterogeneity of typical parametric models used to estimate the relationship between pollution and income, as well as identify why the results from such models are seldom found to be robust. Our results confirm that the resulting relationship between pollution and income is fragile; we show that the estimated pollution-income relationship depends substantially on the heterogeneity of the slope coefficients and the parameter values at which the relationship is evaluated. Different sets of parameters obtained from the semiparametric model give rise to many different shapes for the pollution-income relationship that are commonly found in the literature.

Random regression analyses using B-splines functions to model growth from birth to adult age in Canchim cattle

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Variance component estimates applying random regression models for test-day milk yield in Caracu heifers (Bos taurus Artiodactyla, Bovidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

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

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.

Segmentation of cone-beam CT using a hidden Markov random field with informative priors

Purpose: Flat-detector, cone-beam computed tomography (CBCT) has enormous potential to improve the accuracy of treatment delivery in image-guided radiotherapy (IGRT). To assist radiotherapists in interpreting these images, we use a Bayesian statistical model to label each voxel according to its tissue type. Methods: The rich sources of prior information in IGRT are incorporated into a hidden Markov random field (MRF) model of the 3D image lattice. Tissue densities in the reference CT scan are estimated using inverse regression and then rescaled to approximate the corresponding CBCT intensity values. The treatment planning contours are combined with published studies of physiological variability to produce a spatial prior distribution for changes in the size, shape and position of the tumour volume and organs at risk (OAR). The voxel labels are estimated using the iterated conditional modes (ICM) algorithm. Results: The accuracy of the method has been evaluated using 27 CBCT scans of an electron density phantom (CIRS, Inc. model 062). The mean voxel-wise misclassification rate was 6.2%, with Dice similarity coefficient of 0.73 for liver, muscle, breast and adipose tissue. Conclusions: By incorporating prior information, we are able to successfully segment CBCT images. This could be a viable approach for automated, online image analysis in radiotherapy.

Estimation of genetic parameters for partial egg production periods by means of random regression models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and Bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records. © 2013 American Dairy Science Association.

Comparison of random regression models to estimate genetic parameters for milk production in Guzerat (Bos indicus) cows

Random regression models have been widely used to estimate genetic parameters that influence milk production in Bos taurus breeds, and more recently in B. indicus breeds. With the aim of finding appropriate random regression model to analyze milk yield, different parametric functions were compared, applied to 20,524 test-day milk yield records of 2816 first-lactation Guzerat (B. indicus) cows in Brazilian herds. The records were analyzed by random regression models whose random effects were additive genetic, permanent environmental and residual, and whose fixed effects were contemporary group, the covariable cow age at calving (linear and quadratic effects), and the herd lactation curve. The additive genetic and permanent environmental effects were modeled by the Wilmink function, a modified Wilmink function (with the second term divided by 100), a function that combined third-order Legendre polynomials with the last term of the Wilmink function, and the Ali and Schaeffer function. The residual variances were modeled by means of 1, 4, 6, or 10 heterogeneous classes, with the exception of the last term of the Wilmink function, for which there were 1, from 0.20 to 0.33. Genetic correlations between adjacent records were high values (0.83-0.99), but they declined when the interval between the test-day records increased, and were negative between the first and last records. The model employing the Ali and Schaeffer function with six residual variance classes was the most suitable for fitting the data. © FUNPEC-RP.