Generalized Least-squares Method Research Articles

Generalized least‐squares in dimension expansion method for nonstationary processes

AbstractIn this article, we consider the problem of modeling nonstationary spatial random processes. Bornn et al.(2012) proposed a dimension expansion method, a novel technique for modeling nonstationary processes, aiming to find a dimensionally sparse projection in which the originally nonstationary field exhibits stationarity. However, their dimension expansion approach is a lasso‐penalized least‐squares method that does not account for the covariance structure of the empirical semivariogram. We thus propose a general latent dimension estimation method by replacing the least‐squares method with generalized least‐squares (GLS). Furthermore, we improve the GLS method by weighted least‐squares, which is more computationally efficient and accurate. The performance of the proposed methods is demonstrated through simulations and real data examples.

The association between coffee intake and breast cancer risk: a meta-analysis and dose-response analysis using recent evidence.

To assess the association between coffee intake and breast cancer risk using data from studies published during the past 15 years. Articles published between January 2005 and May 2020 were collected from PubMed, Embase, and Web of Science databases, and the Cochrane library. Coffee consumption was set as the exposure factor of breast cancer risk, and relative risk (RR) was set as the assessment indicator. Random-effects or fixed-effects models were used for the meta-analysis, depending on the level of heterogeneity. The linear and non-linear dose-response relationship was assessed using the generalized least-squares method and restricted cubic spline model. Articles were evaluated by sensitivity analysis, and Begg's and Egger's tests and funnel plots were used to evaluate publication bias. The process of meta-analysis referred to Meta-analyses of Observational Studies in Epidemiology (MOOSE). We retrieved 26 relevant studies in the dose-response analysis and meta-analysis. A negative correlation was found between coffee consumption and breast cancer risk (RR: 0.95; 95% CI: 0.92-0.99). A linear and marginal dose-response relationship was found for six case-control studies (RR: 0.98; 95% CI: 0.95-1.00) and 10 cohort studies (RR: 0.98; 95% CI: 0.97-1.00). Subgroup analysis showed that the relationship between coffee consumption and breast cancer risk was moderated by menstrual status and geographic region. Overall, the meta-analysis found a negative correlation between coffee intake and breast cancer risk, especially in postmenopausal and European women.

Bias Estimation of Linear Regression Model with Autoregressive Scheme using Simulation Study

In regression modeling, first-order auto correlated errors are often a problem, when the data also suffers from independent variables. Generalized Least Squares (GLS) estimation is no longer the best alternative to Ordinary Least Squares (OLS). The Monte Carlo simulation illustrates that regression estimation using data transformed according to the GLS method provides estimates of the regression coefficients which are superior to OLS estimates. In GLS, we observe that in sample size $200$ and $\sigma$=3 with correlation level $0.90$ the bias of GLS $\beta_0$ is $-0.1737$, which is less than all bias estimates, and in sample size $200$ and $\sigma=1$ with correlation level $0.90$ the bias of GLS $\beta_0$ is $8.6802$, which is maximum in all levels. Similarly minimum and maximum bias values of OLS and GLS of $\beta_1$ are $-0.0816$, $-7.6101$ and $0.1371$, $0.1383$ respectively. The average values of parameters of the OLS and GLS estimation with different size of sample and correlation levels are estimated. It is found that for large samples both methods give similar results but for small sample size GLS is best fitted as compared to OLS.

Cross sections Data Adjustment For KRITZ-2:13

Over the past years, the cross-sections reaction data has been re-evaluated several times, in order to approximate the nuclear model measurements with the predictions with great reliability. In our work, uncertainty analysis caused by the data on the neutron factor (Keff) and the reactivity temperature coefficient (RTC), in addition to nuclear data adjustment related to the nuclear reactor physics have been done for KRITZ-2:13 reactor, with ENDF/B - VII.1, ENDF/B - VIII.0 and JENDL - 4.0 evaluations by the nuclear code MCNP6.1. Our analysis detects that the greatest uncertainty on Keff and RTC in the studied libraries comes from the capture and fission reaction contributions respectively, for U-238 and U-235. The previous reactions and their covariances were adjusted using the generalized least squares method (GLLSM), in order to contribute to improve the data needed for neutron simulation of experiments and to ensure the installations safety, where Keff and RTC represent neutron parameters reflecting the modification effects in the data.

Generalized Space Time Autoregressive Integrated Moving Average with Exogenous (GSTARIMA-X) Models

Space time data is data that relates to events at previous times and locations. One of the models that used to analyze space time data is the Generalized Space Time Autoregressive Moving Average (GSTARMA) model. GSTARMA model uses parameters p and λk to represent the time order and spatial order respectively. Hence, this model can be called GSTARMA(p, λk ). Because in fact there are more models with different parameters for different locations, GSTARMA(p, λk ) model is more realistic. If space time data is not stationary, a different order is added so that the model becomes GSTARIMA(p, d, λk ). In modelling sometimes the accuracy of the model can increase by other influence variables. These variables are named exogenous variables. The GSTARIMA model with exogenous variables is named the GSTARIMA-X(p, d, λk ) model. This research aims to examine the model and its estimation of parameters. Model parameters are estimated using the Generalized Least Square (GLS) method. The method in this writing is literature study obtained from several articles, journals, and books that support in achieving research. The results of the study show that with the GLS method, parameter estimates can be obtained with the assumption of time order 1 and spatial order 1.

Impacts of Climate Factors Influencing Rice Production in Bangladesh

This study aims to study the climate change pattern, assess the situation of climate change, finding the influences of climate change on the production of rice, estimating a model between climate change and rice production in Bangladesh. Ordinary Least Squares (OLS), Generalized Least Squares (GLS), Feasible Generalized Least Squares (FGLS) were used in this study to compare the results. This study included all 64 districts of Bangladesh with a time span from 2011 to 2018. It included panel data of the production of Aus rice, Aman rice, Boro rice as well as HYV of each rice (Aus, Aman, Boro) of 64 districts of Bangladesh for agricultural data, temperature, rainfall and humidity of 64 districts for climate data. This study estimates the stochastic production function formulated by Just and Pope (1978, 1979), which allows the effect of inputs on the mean yield to differ from that on yield variance. The results showed that increased climate variability, climate extremes; in particular, exacerbate risk on Rice production in Bangladesh. Rice yields are sensitive to rainfall extremes, with both deficient and surplus rainfall increasing variability. For 1% increase in annual total rainfall, Mean Yield will decrease by 0.139%, 0.141%, 0.132% in OLS, GLS and FGLS method respectively, if other variables remaining the same. For 1% increase in annual average percentage of humidity, Mean Yield increases by 1.352%, 1.340%, 1.362% in OLS, GLS and FGLS method respectively, if other variables remaining the same. for 1% increase in HYV area, Mean Yield increases by 0.831% in OLS, GLS and FGLS method, if other variables remaining the same. Additionally, climate inputs, non-climate input, high yielding variety seeds are found to increase average yield.

Constructing a summary index using the standardized inverse-covariance weighted average of indicators

Researchers often want to examine the relationship between a variable of interest and multiple related outcomes. To avoid problems of inference that arise from testing multiple hypotheses, one can create a summary index of the outcomes. Summary indices facilitate generalizing findings and can be more powerful than individual tests. In this article, we introduce a command, swindex, that implements the generalized least-squares method of index construction proposed by Anderson (2008, Journal of the American Statistical Association 103: 1481–1495). We describe the command and its options and provide an example based on Blattman, Fiala, and Martinez’s (2014, Quarterly Journal of Economics 129: 697–752) evaluation of a cash transfer program in Uganda.

Mapping coastal circulations using moving vehicle acoustic tomography.

With the increased availability of highly maneuverable unmanned surface/underwater vehicles, abundant ocean data can now be collected. This study uses tomographic techniques to extend the survey area covered by moving vehicles. An acoustic reciprocal transmission experiment was conducted using three tomographic sensors installed on an autonomous underwater vehicle, a fishing ship, and a buoy. The distributed sensing method is applied for currents estimation. The estimated currents near the ship show consistent results with the direct measurements. In particular, an anticyclonic circulation was revealed. Further, a general least-squares method is employed to improve the estimate of this vortical structure.

Impact of Credit Risk Management on Profitability of Commercial Banks in Bangladesh: An estimation of Dynamic Panel Data Model

This paper attempts to reveal how several credit risk factors are affecting the profitability of commercial banks considering the econometric models estimated with Random effect, Fixed effect, Pooled OLS and Cross-sectional Generalized least square (GLS) method followed by dynamic panel data model estimated with one-step GMM (generalized methods of moments) approach to incorporate the issue of endogeneity, unobserved heterogeneity and profit persistence of data set collected from annual report of banks covering from year 2010 to 2019 in Bangladesh. We have also adopted several diagnostic checks such as Model specification test, test of heteroskedasticty, cross sectional dependence test followed by test of autocorrelation and unit root test to examine the validity of the models selected for this study. The first part of our empirical investigation of the estimated models considering all methods reveals that out of all the independent credit risk factors such as Total loans to total assets ratio, Total loans to equity ratio, NPL to total loans, NPL to Total equity ratio, Provision for loan losses to total equity, total equity to total assets ratio, Total loans to total deposits ratio and provision for loan losses to NPL ratio, only provision for loan losses to NPL ratio is significantly affecting the dependent variable measured with NIM (Net interest margin) ratio of banks under fixed effect method. The next part of our empirical results of estimated models considering same methods divulges that NPL to total loans ratio, NPL to Total equity ratio and Provision for loan losses to total equity are also significantly affecting the dependent variable measured with ROE (Return on equity) of banks. The third segment of our empirical findings of estimated models considering same approaches shows that only NPL to total loans ratio is statistically significant under all methods but the NPL to total equity ratio is significant under fixed effect and GLS method and Provision for loan losses to total equity is significant under GLS method only in explaining the changes in ROA (Return on equity) measuring profitability of banks. Further investigation reveals that the dynamic impact of the said credit risk factors on profitability measured with ROE of banks has been successfully adopted by one-step system GMM approach considering all conditions required for estimation.

Circadian Rhythm of Salivary Immunoglobulin A and Associations with Cortisol as A Stress Biomarker in Captive Asian Elephants (Elephas maximus)

Simple SummarySalivary immunoglobulin A (sIgA) and cortisol concentrations were measured in Asian elephants to determine circadian rhythm effects and the relationship between both biomarkers. Saliva samples were collected every 4 h from 06:00 to 22:00 h for 3 consecutive days (n = 15 samples/elephant). We used enzyme immunoassays for quantification of sIgA and cortisol concentrations. Both sIgA and cortisol followed a circadian rhythm, although the patterns differed. For both, the highest concentrations were in the early morning hours when elephants began the work day; however, sIgA concentrations were more variable during the day. There was no correlation between the two indices because the pattern of sIgA was quartic, while that of cortisol was linear. We provide basic knowledge for further studies using sIgA as a welfare biomarker.Salivary immunoglobulin A (sIgA) has been proposed as a potential indicator of welfare for various species, including Asian elephants, and may be related to adrenal cortisol responses. This study aimed to distinguish circadian rhythm effects on sIgA in male and female Asian elephants and compare patterns to those of salivary cortisol, information that could potentially have welfare implications. Subjects were captive elephants at an elephant camp in Chiang Mai province, Thailand (n = 5 males, 5 females). Salivette® kits were used to collect saliva from each elephant every 4 h from 06:00 to 22:00 h for 3 consecutive days (n = 15 samples/elephant). Enzyme immunoassays were used to quantify concentrations of IgA and cortisol in unextracted saliva. Circadian rhythm patterns were determined using a generalized least-squares method. Both sIgA and cortisol followed a circadian rhythm, although the patterns differed. sIgA displayed a daily quartic trend, whereas cortisol concentrations demonstrated a decreasing linear trend in concentrations throughout the day. There was no clear relationship between patterns of sIgA and salivary cortisol, implying that mechanisms of control and secretion differ. Results demonstrate for the first time that circadian rhythms affect sIgA, and concentrations follow a daily quartic pattern in Asian elephants, so standardizing time of collection is necessary.

Does Banking in Indonesia tend to be Concentrated?

The banking in Indonesia has undergone several changes in the market structure that ultimately impacts the prevailing policies and regulations. This study aims to examine the impact of changes in the banking market structure identified through the level of market concentration in the banking environment and examine the factors that influence the level of concentration of the banking market from 2005 to 2016. The study also examined the impact of changes in banking structure during the global crisis. The measurement of banking concentration used in this study is the Herfindahl-Hirschman Index (HHI). Furthermore, the influential factors consist of: (1) Bank specification, including bank size (Size), credit risk (NPL), profitability (ROE), banksoundness(CAR),(2)Market specification,namely the number of standingbank (NUM), and (3) Global crisis. The study used GLS (Generalized Least Square) method to detect autocorrelation on each variable.The results show that banks in Indonesia tended to have a low level of market concentration. The results are also in accordance with the SCP paradigm which states that banks tend to generate high profits when the level of banking market concentration is high.Keywords : Market Concentration, Competition, Dual-Banking, Bank Specification, Market Specification, Global Crisis.

Analisis Masalah Heteroskedastisitas Menggunakan Generalized Least Square dalam Analisis Regresi

Regression analysis is one statistical method that allows users to analyze the influence of one or more independent variables (X) on a dependent variable (Y).The most commonly used method for estimating linear regression parameters is Ordinary Least Square (OLS). But in reality, there is often a problem with heteroscedasticity, namely the variance of the error is not constant or variable for all values of the independent variable X. This results in the OLS method being less effective. To overcome this, a parameter estimation method can be used by adding weight to each parameter, namely the Generalized Least Square (GLS) method. This study aims to examine the use of the GLS method in overcoming heteroscedasticity in regression analysis and examine the comparison of estimation results using the OLS method with the GLS method in the case of heteroscedasticity.The results show that the GLS method was able to maintain the nature of the estimator that is not biased and consistent and able to overcome the problem of heteroscedasticity, so that the GLS method is more effective than the OLS method.

Green Loan as a Tool for Green Financing

The article describes one of the main tools of green financing — the green loan. This is a loan designed for environmental projects related to agriculture, renewable energy sources, environmentally friendly industry, etc. The tasks are to analyze the current research on this topic, to study the regulatory aspects of green lending, its main types, impact on the bank economic indicators, advantages and disadvantages. The analysis of the current research has shown insufficient development of the idea of the green loan. It is only the theoretical aspect of its influence on the bank activities that has been defined, not its practical effect. The authors studied the green loan impact on the results of the bank activities on the example of overdue loans. For the analysis, they used the panel data of 10 out of 24 largest banks in China in 2012–2017. The evaluation is based on a random effects model. The calculations have been done by means of the generalized least-squares method in MSEXCEL. It has been revealed that green loans in the loan portfolio of the bank contribute to the overdue loans decrease. It has been determined that the main factors influencing the decision making by the borrower and the lender are reputation, public, equity and regulatory pressure, alternative capital pools, credit profiles, availability, capital requirements. However, there is no standard credit documentation for the green loan today. To make this financial tool efficient and sound, it is necessary to further develop regulations, to change approaches to disclosing information on sustainability issues in the non-financial part of annual reporting. The authors have made a conclusion about the rapid development and expansion of the green loan due to the flexible conditions for its provision and availability.

Array auto-calibration using a generalized least-squares method

This paper introduces a new class of auto-calibration algorithms, based on a generalized least-squares (GLS) cost function. This class supports both gain-phase calibration and mutual coupling calibration and it is independent of array shape. The GLS cost function is minimized cyclically with respect to the direction of arrivals (DOA) and calibration parameters. These two minimization steps are repeated until convergence. In the DOA estimation step, minimization leads to the SPICE (SParse Iterative Covariance-based Estimation) DOA estimation algorithm. In fact, the innovation of this paper mainly lies in the calibration step. In the DOA estimation step, a generalized form of the SPICE algorithm should be used in the coherent sources case. Consequently, the proposed auto-calibration algorithm is able to support coherent source cases. Moreover, the proposed algorithm does not need multi-dimensional search. The necessary condition for the existence of a solution is studied as well. Using simulations, the performance of the proposed algorithm is compared with several other auto-calibration algorithms. Simulation results show that the proposed algorithm is more robust than the other algorithms and usually has better performance.

Individual and flock immunity responses of naïve ducks on smallholder farms after vaccination with H5N1 Avian Influenza vaccine: a study in a province of the Mekong Delta, Vietnam.

In Vietnam, vaccination has played a crucial role in the national strategy for the prevention and control of H5 highly pathogenic avian influenza (HPAI). This study aimed to evaluate antibody responses of immunologically naïve domestic ducks to H5N1 avian influenza vaccine currently used in the national mass vaccination program of Vietnam. Blood samples of 166 ducks reared on smallholder farms were individually collected at three sampling time points, namely, right before vaccination, 21 days after primary vaccination, and 21 days after booster vaccination. Vaccine-induced antibody titers of duck sera were measured by the hemagglutination inhibition assay. Temporal differences in mean antibody titers were analyzed using the generalized least-squares method. No sampled ducks showed anti-H5 seropositivity pre-vaccination. The geometric mean titer (GMT) of the vaccinated ducks was 5.30 after primary vaccination, with 80% of the vaccinated ducks showing seropositivity. This result indicates that the immunity of duck flocks met the targets of the national poultry H5N1 HPAI mass vaccination program. GMT and seropositive rates of the ducks were 6.48 and 96.3%, respectively, after booster vaccination, which were significantly higher than those after primary vaccination. Flock-level seroprotection rate significantly increased from 68% to 84.7%, whereas variability in GMT titers decreased from 34.87% to 26.3%. This study provided important information on humoral immune responses of ducks to the currently used H5N1 vaccine under field conditions. Our findings may help guide veterinary authorities in planning effective vaccine protocols for the prevention and control of H5N1 in the target poultry population.

Generalized Least Squares Based Channel Estimation for FBMC-OQAM

The presence of intrinsic inter-carrier interference (ICI) and inter-symbol interference (ISI) at the output of the matched filter receiver in filter bank multi-carrier with offset quadrature amplitude modulation (FBMC-OQAM) systems complicates the task of channel estimation (CE). The conventional approach is to use a pilot symbol preamble structure, such as in the interference approximation/cancellation methods (IAM/ICM), together with a simple virtual symbol (VS) based CE scheme. However, this virtual symbol approach ignores the residual interference from the data portion of the FMBC burst as well as the correlation of the noise across the sub-carriers; both of these factors ultimately limit the performance. In this paper, we propose a generalized least squares (GLS) based CE scheme which, when applied to the IAM/ICM pilot structures, takes into account both the correlated noise and data interference effects. Closed-form expressions are derived for the channel estimation mean-squared error (CE-MSE) of the proposed GLS method and for the conventional VS method, and it is shown that the proposed method leads to a significant reduction of the CE-MSE by up to 6 dB when compared with the VS based method. This is demonstrated to result in improved bit error rate (BER) performance, especially when higher-order modulation is employed, making it an attractive channel estimation method for many modern deployment scenarios. The proposed GLS-based channel estimation scheme is parameterized allowing a flexible trade-off between channel frequency selectivity, estimation complexity and CE-MSE gain. Finally, symmetry properties of the intrinsic interference coefficients for a general FBMC-OQAM system are also proved, which facilitate the computation of the noise and interference autocorrelation matrices required by the proposed algorithm.

Numerical Simulation of Propagation Characteristics of Hazardous Noxious Substances Spilled from Transport Ships

This study numerically investigates the propagation characteristics of hazardous noxious substances (HNSs) spilled from transport ships and suggests the metal model for predicting the HNS propagation velocity varied with the current velocity and HNS density. The commercial computational fluid dynamics (CFD) code ANSYS FLUENT (V. 17.2) was used for two-dimensional simulation based on the Reynolds-averaged Navier–Stokes (RANS) equation together with the standard k–ε model. The scalar transport equation was also solved to estimate the spatial and transient behaviors of HNS. The main parameters to analyze the near-field propagation characteristics of HNSs spilled from the ship were layer thickness, HNS concentration, and propagation velocity. It was found that advection becomes more dominant in propagating an HNS layer that becomes thinner as the current velocity increases. When the current velocity increased beyond a certain level (~0.75 m/s), the mixing effect made the HNS layer less dense but thicker. Consequently, lower-density HNS causes increased HNS concentrations at sea level. As the current velocity increased, the concentration distribution became homogeneous regardless of HNS density. In particular, the second-order response surface model provided for three variables on the basis of the numerical results for 15 cases with the use of the general least-squares regression method, showing a good fit. This model would be useful in estimating the propagation velocity of HNS spilled from a ship.

Efficient and accurate computation of base generation allele frequencies

Allele frequencies are used for several aspects of genomic prediction, with the assumption that these are equal to the allele frequency in the base generation of the pedigree. The current standard method, however, calculates allele frequencies from the current genotyped population. We compared the current standard method with BLUP and general least squares (GLS) methods explicitly targeting the base population to determine whether there is a more accurate and still efficient method of calculating allele frequencies that better represents the base generation. A data set based on a typical dairy population was simulated for 325,266 animals; the last 100,078 animals in generations 9 to 12 of the population were genotyped, with 1,670 SNP markers. For the BLUP method, several SNP genotypes were analyzed with a multitrait model by assuming a heritability of 0.99 and no genetic correlation among them. This method was limited by the time required for each BLUP to converge (approximately 6 min per BLUP run of 15 SNP). The GLS method had 2 implementations. The first implementation, using imputation on the fly and multiplication of sparse matrices, was very efficient and required just 49 s and 1.3 GB of random access memory. The second implementation, using a dense full A22-1 matrix, was very inefficient and required more than 1 d of wall clock time and more than 118.2 GB of random access memory. When no selection was considered in the simulations, all methods predicted equally well. When selection was introduced, higher correlations between the estimated allele frequency and known base generation allele frequency were observed for BLUP (0.96 ± 0.01) and GLS (0.97 ± 0.01) compared with the current standard method (0.87 ± 0.01). The GLS method decreased in accuracy when introducing incomplete pedigree, with 25% of sires in the first 5 generations randomly replaced as unknown to erroneously identify founder animals (0.93 ± 0.01) and a further decrease for 8 generations (0.91 ± 0.01). There was no change in accuracy when introducing 5% genotyping errors (0.97 ± 0.01), 5% missing genotypes (0.97 ± 0.01), or both 5% genotyping errors and missing genotypes (0.97 ± 0.01). The GLS method provided the most accurate estimates of base generation allele frequency and was only slightly slower compared with the current method. The efficient implementation of the GLS method, therefore, is very well suited for practical application and is recommended for implementation.

Meta-Analytical SEM: Equivalence Between Maximum Likelihood and Generalized Least Squares

Meta-analysis plays a key role in combining studies to obtain more reliable results. In social, behavioral, and health sciences, measurement units are typically not well defined. More meaningful results can be obtained by standardizing the variables and via the analysis of the correlation matrix. Structural equation modeling (SEM) with the combined correlations, called meta-analytical SEM (MASEM), is a powerful tool for examining the relationship among latent constructs as well as those between the latent constructs and the manifest variables. Three classes of methods have been proposed for MASEM: (1) generalized least squares (GLS) in combining correlations and in estimating the structural model, (2) normal-distribution-based maximum likelihood (ML) in combining the correlations and then GLS in estimating the structural model (ML-GLS), and (3) ML in combining correlations and in estimating the structural model (ML). The current article shows that these three methods are equivalent. In particular, (a) the GLS method for combining correlation matrices in meta-analysis is asymptotically equivalent to ML, (b) the three methods (GLS, ML-GLS, ML) for MASEM with correlation matrices are asymptotically equivalent, (c) they also perform equally well empirically, and (d) the GLS method for SEM with the sample correlation matrix in a single study is asymptotically equivalent to ML, which has being discussed extensively in the SEM literature regarding whether the analysis of a correlation matrix yields consistent standard errors and asymptotically valid test statistics. The results and analysis suggest that a sample-size weighted GLS method is preferred for combining correlations and for MASEM.

A least-squares method for the inverse reflector problem in arbitrary orthogonal coordinates

In this article we solve the inverse reflector problem for a light source emitting a parallel light bundle and a target in the far-field of the reflector by use of a least-squares method. We derive the Monge–Ampère equation, expressing conservation of energy, while assuming an arbitrary coordinate system. We generalize a Cartesian coordinate least-squares method presented earlier by Prins et al. [13] to arbitrary orthogonal coordinate systems. This generalized least-squares method provides us the freedom to choose a coordinate system suitable for the shape of the light source. This results in significantly increased numerical accuracy. Decrease of errors by factors up to 104 is reported. We present the generalized least-squares method and compare its numerical results with the Cartesian version for a disk-shaped light source.