Parallel algorithms for computing all possible subset regression models using the QR decomposition

In a general normal regression model, this paper first derives the least upper bound (LUB) for the covariance matrix of a generalized least squares estimator (GLSE) relative to the covariance matrix of the Gauss-Markov estimator. Second the result is applied to the (unrestricted) Zellner estimator in an N-equation seemingly unrelated regression (SUR) model and to the GLSE in a heteroscedastic model.

Estimating seemingly unrelated regression models with vector autoregressive disturbances

The omission of important variables is often encountered in econometrics, which often results in the misspecification of the model. This study considered a misspecified joint seemingly unrelated regression (SUR) model within the Bayesian context. The explanatory variables were generated from a uniform distribution for sample sizes 5, 10, 30, 50, 100 and 1000. The coefficients of were generated from the multivariate normal distribution. Different levels of correlation (0.2, 0.4, 0.5, 0.7 and 0.9) among the independent variables were considered. The choice of hyperprior distribution was explored. Due to the incorrectly defined model, the intended attribute of unbiasedness in the estimated coefficients, which depends on the fitted model's correspondence with the actual underlying data-generating process, was not attained. Irregular patterns were seen in the posterior means and standard deviations except for a few large sample sizes. Keywords: Misspecification, Multicollinearity, Posterior mean, Posterior standard deviation, Seemingly unrelated regression.

In transportation studies, variables of interest are often influenced by similar factors and have correlated latent terms (errors). In such cases, a seemingly unrelated regression (SUR) model is normally used. However, most studies ignore the potential temporal and spatial autocorrelations across observations, which may lead to inaccurate conclusions. In contrast, the SUR model proposed in this study also considers these correlations, making the model more behaviorally convincing and applicable to circumstances where a three-dimensional correlation exists, across time, space, and equations. An example of crash rates in Chinese cities is used. The results show that incorporation of spatial and temporal effects significantly improves the model. Moreover, investment in transportation infrastructure is estimated to have statistically significant effects on reducing severe crash rates, but with an elasticity of only −0.078. It is also observed that, while vehicle ownership is associated with higher per capita crash rates, elasticities for severe and non-severe crashes are just 0.13 and 0.18, respectively; much lower than one. The techniques illustrated in this study should contribute to future studies requiring multiple equations in the presence of temporal and spatial effects.

Predicting the distribution of households and employment: a seemingly unrelated regression model with two spatial processes

In this article, a seemingly unrelated Poisson regression model is presented as an alternative to using Zellner's seemingly unrelated regression model for estimating a system of recreation demand functions. The seemingly unrelated Poisson regression model provides estimates that are asymptotically more efficient than equation-by-equation Poisson estimates and circumvents the bias and inconsistency problems that result when using A. Zellner's seemingly unrelated regression model. Additionally, the seemingly unrelated Poisson regression model is applied to an empirical problem dealing with the value of recreational boating and the findings indicate that the seemingly unrelated regression model consumer surplus estimates are substantially different from those of the seemingly unrelated Poisson regression model. Copyright 1994 by MIT Press.

A seemingly unrelated regression model has been commonly used for describing a set of different regression models with correlations. This paper discusses the estimation of the covariance matrix in a seemingly unrelated regression model under Stein’s loss function. In particular, when the correlation matrix is assumed to be known, a best equivariant estimator of the covariance matrix is derived. Its properties are investigated and a connection to a best equivariant estimator of regression coefficients given in a previous study is shown. Results of numerical simulations and an illustrative example are also presented to compare the best equivariant estimator of the covariance matrix with several conventional covariance matrix estimators.

Parallel algorithms for reduction of a general matrix to upper Hessenberg form on a shared memory multiprocessor

Seemingly unrelated regression models (SURMs) are extensions of linear regression models which allow correlated errors between regression equations. The purpose of this article is to reconsider some fundamental problems on the performance and connection of ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of parametric functions under an SURM. Motivated by a variety of known results and facts on the equivalence of OLSEs and BLUEs under general linear models, this article collects a list of necessary and sufficient conditions for OLSEs to be BLUEs under an SURM and presents a variety of statistical interpretations on the equivalence of OLSEs and BLUEs under the SURM.

This paper develops an iterative estimation procedure for estimating both the parameters and covariances of the seemingly unrelated regression model with contemporaneous covariances. The method is based on the use of an efficient recursive estimation algorithm for the SUR model with known contemporaneous covariances. The components of each observation vector are used one at a time to simultaneously estimate the parameters using a Bayesian “state vector” approach. This is computationally efficient, since the only matrix inversion required is one by one. The covariances are estimated using the residuals from the fitted model. The procedure iterates between estimating the parameters and estimating the covariances until convergence. The algorithm yields the parameter estimator and an estimator for its distribution, thus providing a sound basis for inferential procedures on the parameters.

This article is a report of using seemingly unrelated regression (SUR) models to examine the determinants of different dimensions of quality of life (QoL) among childbearing age women. There are a limited number of studies on QoL and its associated factors among women in developing countries such as Iran. Therefore, more attention should be focused on identifying these issues. We administered the Persian's abbreviated version of the World Health Organization Quality of Life (WHOQOL-BREF) questionnaire to 1,067 married women aged between 15 and 49 years. The women were chosen via a multistage research design from the rural region of Shiraz, the center of Fars Province in Iran in 2008. Clinical and socio-demographic characteristics as well as their reproductive health-related characteristics were investigated. To identify associated factors of QoL dimensions, ordinary least squares (OLS) regression and SUR were used and their findings were compared. The WHOQOL-BREF showed acceptable consistency (Cronbach's alpha range: 0.62-0.75 across domains). Lower age, absence of long-term illness, economic status satisfaction, higher level of education, lower number of pregnancies, and higher body mass index were important associated factors of different dimensions of the QoL among these women. The estimated parameters for these factors were in close agreement in both OLS and SUR estimation methods. However, the SUR estimator provided the higher precision of the estimates than the OLS estimator, as the parameters obtained by SUR are characterized by lower standard errors. Women's age, income satisfaction, and level of education were common for all domains. This study presents a novel approach to simultaneously predict QoL domains using the SUR estimators and the results are relevant for implementing objective QoL. SUR estimators performed consistently better than the OLS estimators, since SUR takes the correlation between error terms into account. Thus, the SUR method could be a useful methodology for predicting QoL domains.

This study highlights drought forecasting for understanding the semi-arid area in India, where drought phenomena play vital role in the irrigation, drinking water supplies, and sustaining the ecological with economic balance for every nation. Therefore, drought forecasting is important for the future drought planning based on the machine learning (ML) models. Hence, The Standardized Precipitation Index (SPI) at 3- and 6-month periods have been selected and used for future drought forecasting scenarios in area. The combinations of ten inputs SPI-1- and SPI-10 were used for predicting modeling for SPI-3 and SPI-6 timescales, that modeling developed based on the historical SPI datasets from 1989 to 2019 years. The SPI-3 and SPI-6 maximum and minimum values are shown SPI-3 (2.03 and -5.522) and SPI-6 (1.94 and -6.93). The SPI is a popular method for estimating the drought analysis and has been used everywhere at global level. The developed models have been compared with each other, with the best combination of input variables selected using subset regression models and sensitivity studies. After that, the active input parameters were used for forecasting of SPI-3 and SPI-6 values to understanding of drought in semi-arid area. The finest input variables combination have been used in the Ml models and established the novel five models such as robust linear regression, bagged trees, boosted trees, support vector regression (SVM-Linear), and Matern Gaussian Process Regression (Matern GPR) models. Such kind of models first time has been applied for the forecasting of future drought conditions. Whole models were fine and improved modeling by using hyperparameters tuning, bagging, and boosting models. Entire ML models’ accuracy was compared using different statistical metrics. Compared with five ML models accuracy, we have found that the Matern GPR model better accuracy than other ML models. The best model accuracy is R2 = 0.95 and 0.93, RMSE, MSE, MAE, MARE, and NSE values, respectively, for predicting SPI-3 and SPI-6 values in the area. Therefore, the Matern GPR model was identified as the finest ML algorithm for predicting SPI-3 and SPI-6 associated with other algorithms. This research demonstrates the Matern GPR model's efficacy in predicting multiscale SPI-3 and SPI-6 under climate variations. It can be helpful in soil and water resource conservation planning and management and understanding droughts in the entire basin areas of the country India.

A new method to retrieve aerosol optical thickness from satellite images on a parallel system

This paper proposes to forecast foreign exchange rates by means of an error components-seemingly unrelated nonlinear regression (EC-SUNR) model and, simultaneously, explore the interrelationships among currencies from newly industrializing economies with those of highly industrialized countries. Based on the empirical results, we find that the EC-SUNR model improves on the performance of forecasting foreign exchange rates in comparison with an intrinsically nonlinear dynamic speed of adjustment model that has been shown to outperform several other important models in the forecasting literature. We also find evidence showing that the foreign exchange markets of the newly industrializing countries are influenced by those of the highly industrialized countries and vice versa, and that such interrelationships affect the accuracy of currency forecasting. Copyright © 2005 John Wiley & Sons, Ltd.

Parallel graph generation algorithms for shared and distributed memory machines