Normal Error Distribution Research Articles

Predicting teak tree (Tectona grandis Linn F.) height using generic models and artificial neural networks

The continuous monitoring of dendrometric variables provides estimates that assist in conducting fast-growing stands. In this study, we aimed to investigate the performance of generic models and artificial neural networks to estimate total height of Tectona grandis in a forest stand in the Eastern Amazon. Continuous forest inventory was performed in this population, where total height and diameter at breast height were measured. The variables such as age and the square root of the average diameter (dg) of the plots were used to compose the methods adopted to estimate the height of the trees. The accuracy of these methods was assessed using the residual standard error of the estimate, the coefficient of correlation, and the graphical analysis of residues. The aggregated difference and ANOVA were calculated to compare the methods. The independent variables mentioned were able to describe the height behavior of individuals. We concluded that the methods have good residual dispersion, normal distribution of errors and little tendency to overestimate height. It was found that the generic models and the ANNs do not differ significantly from each other and are efficient to estimate the height of individuals. We also concluded that the ANNs, especially those that included dg, presented superior statistical indicators

Improvement of empirical formulas to estimate the reduction effects by berms on irregular wave runup over a dune-berm coast

This study formulates the reduction effects of a sandy berm on irregular wave runup over a dune-berm coast. The numerical experiments by Park and Cox (2016) are closely re-examined to develop an empirical formula describing the variability of reduction effects of a sandy berm over a broad range of conditions. Based on a sequence of regression analyses, the reduction effects are expressed as a reduction factor in terms of normalized berm width, normalized surge level, and wave steepness in deep water. The comparison with the numerical experiments demonstrates that the regression formula can satisfactorily reproduce the variability of the reduction effects over the range of numerical experiments. The analysis of prediction uncertainty demonstrated that the derived formula reproduced the reduction effects observed in the numerical experiments with negligible bias and a 90% confidence interval of approximately ±20% relative error. In addition, conversion formulas between representative runup values based on different statistical definitions are derived to enable consistent comparisons between them. The proposed reduction formula is implemented into three empirical runup models that are applicable to the quick estimations of irregular wave runup on a dune-berm coast: the models by Park and Cox (2016), Stockdon et al. (2006), and Mase et al. (2013). Consistent comparisons were conducted among the empirical predictions and numerical experiments based on the statistical conversion formulas. Combined with the proposed reduction formula, all three models well reproduced the normalized 2% runup in the numerical experiments over a wide range of conditions. On the other hand, the uncertainty in the runup prediction appeared in different forms depending on the selected model. When the proposed reduction formula was implemented in the modified Park and Cox (2016) and modified Stockdon et al. (2006) models, the uncertainty was described by a log-normal distribution of the error ratio between the empirical predictions and numerical experiments. Quantitatively, these two models predicted 90% of the normalized runup on a dune within a range of relative error of less than approximately 20–30%. When the proposed reduction formula was combined with the model by Mase et al. (2013), the uncertainty followed a normal distribution of the residual error between the empirical predictions and numerical experiments. On the normalized runup, the model prediction indicated a small conservative bias (+0.05) and a root-mean-square error of 0.13.

ANALYSIS OF THE RELATIONSHIP BETWEEN GROSS DOMESTIC PRODUCT, FOREIGN DIRECT INVESTMENTS AND INCOME INEQUALITY IN ROMANIA OVER THE PERIOD 1990-2020

The present study aims to confirm the existence of a non-linear association between economic growth, foreign direct investment (FDI) and income inequality in Romania, over the period of 1990 to 2020. Romania’s macroeconomic output expressed through the Gross Domestic Product per capita has registered a continuous growth trend in the analysed period of time. Income distribution expressed through the GINI index registered also an ascending trend dynamic, while foreign direct investment showed an oscillating evolution. Using the Ordinary Least Square (OLS) method to estimate the impact of FDI and economic growth on income inequality we revealed that the relationship between FDI and income inequality is non-linear, namely quadratic. In the estimated regression equation the sign of FDI squared coefficient is negative, confirming the existence of a U-inverted curve. This suggests that the income gap grows in a first stage, until a threshold in economy is achieved. After this maximum, the income gap could follow a decreasing trend with increasing values of FDI. We found also that economic growth expressed by the dynamics of GDP per capita contributed to the extension of income inequality in Romania for 1990 to 2020. The non-linear model is statistically validated; tests for heteroskedasticity, autocorrelation and normal distribution of errors are performed. Policy implications in the specific case of the Romanian economy are also included, as follows: fiscal measures for supporting FDI inflows, effective channels enabling FDI to have effects on reducing income inequality, increase of FDI absorptive capacity and directing FDI to specific economic sectors.

Robust evaluation of regression parameters. The fuzzy theory and other models

Linear regression parameters based on fuzzy theory are compared with other statistical approaches. A new algorithm of a simple weighted least squares method, independent of a priori information, is proposed. The algorithm was verified on model data, and its adequacy was confirmed with the use of standard criteria. The algorithm has been implemented as Python language computer program. New method of calculation of the scatter of fuzzy dependent variable around its mediane value, as well as the upper and lower bonds of fuzzy regression equations have been developed and verified. Proposed methods are shown to be useful alternatives to the most popular methods for constructing linear regression, which assume a normal distribution of errors.

GRG Non-Linear and ARWM Methods for Estimating the GARCH-M, GJR, and log-GARCH Models

Numerous variants of the basic Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have been proposed to provide good volatility estimating and forecasting. Most of the study does not work Excel’s Solver to estimate GARCH-type models. The first purpose of this study is to provide the capability analyze of the GRG non-linear method built in Excel’s Solver to estimate the GARCH models in comparison to the adaptive random walk Metropolis method in Matlab by own codes. The second contribution of this study is to evaluate some characteristics and performance of the GARCH-M(1,1), GJR(1,1), and log-GARCH(1,1) models with Normal and Student-t error distributions that fitted to financial data. Empirical analyze is based on the application of models and methods to the DJIA, S&P500, and S&P CNX Nifty stock indices. The first empirical result showed that Excel’s Solver’s Generalized Reduced Gradient (GRG) non-linear method has capability to estimate the econometric models. Second, the GJR(1,1) models provide the best fitting, followed by the GARCH-M(1,1), GARCH(1,1), and log-GARCH(1,1) models. This study concludes that Excel’s Solver’s GRG non-linear can be recommended to the practitioners that do not have enough knowledge in the programming language in order to estimate the econometrics models. It also suggests to incorporate a risk premium in the return equation and an asymmetric effect in the variance equation.

VaR prediction for GARCH (1,1) model with normal and student-t error distribution

This study aims at determining the estimated parameters of the GARCH (1.1) model establishing the prediction of the VaR value, and defining the accuracy of the VaR prediction. In this study, the error in the GARCH (1,1) model uses a normal distribution and student-t distribution. The research method focuses on parameter calculation and the prediction of VaR value within two aspects regarding analytic and numeric aspects. Analytically, the prediction of the VaR value and the accuracy of the prediction of VaR value through the VaR coverage opportunity. It isn't easy to estimate the parameters for the GARCH (1.1) model analytically. Thus, the parameters are estimated numerically using the Quansi Newton optimization method. Prediction of VaR value and VaR coverage probability will be simulated numerically by using stock return data of IBM, INDF.JK and GSPC. The results show that the GARCH (1.1) model can model stock returns for IBM, INDF.JK and GSPC. There is no significant difference between the GARCH (1,1) model with a normally distributed error and GARCH (1,1) with a student-t distribution error in determining the prediction of VaR values. The numerical simulation results show that the VaR value prediction using the GARCH (1,1) model with a normally distributed error is more accurate than the student-t-distributed error.

Forecasting Index Return Volatility of The Chittagong Stock Exchange of Bangladesh using GARCH Models

Purpose: The aim of this research is to identify the best-fitted model(s) for estimating and forecasting the return volatility of the Chittagong Stock Exchange (CSE) in Bangladesh. Methodology: The study analyzes the returns of the Chittagong Stock Exchange's (CSE) daily Selective Categories Index (CSCX) from February 4, 2013 to December 31, 2021 (as a full sample) and from July 1, 2021 to December 30, 2021 (for forecasting). The researcher used GARCH family approaches considering different error distributions, to find the well-suited model(s) for the CSCX index. The researchers used ARMA to develop the mean equation based on two popular model selection criteria: Schwarz's (1978) Bayesian information criterion (SBIC) and Akaike's (1974) information criterion (AIC). The data has been analyzed using the application software E-Views 10. Findings: The ARMA (0,1) has been adopted as the mean equation for GARCH specifications. Under all three types of error distributions, the ARCH and GARCH terms, along with the leverage terms of asymmetric models, were found to be statistically significant in all the accepted combinations of the model. The models GARCH (1,2), TGARCH (1,2), and PARCH (1,2) under generalized error distributions and EGARCH (2,1) under Student’s t error distributions have been selected as the best-fitted models for estimation. Whereas, based on root mean square error (RMSE), mean absolute error (MAE), mean absolute percent error (MAPE), and theil inequality (TI), EGARCH (1, 2), TGARCH (1, 2), and PARCH (1, 2) under generalized error distributions, and GARCH (1, 2) under student’s t error distributions and normal error distributions are found to have superior out-of-sample forecasting abilities. Practical implications and originality: This is an original research work that will help the investors and other stakeholders of the Bangladeshi stock market to estimate and forecast market volatility more efficiently. Limitations: Due to its extensive features, this study was unable to incorporate a few additional ARCH and GARCH models.

Experimental Study on the Drilling Parameter Analysis of Banana Fiber Reinforced Vajram Mixed Phenolic Resin Composite Laminates

ABSTRACT Drilling operation of fiber reinforced polymeric (FRP) composites is significantly dissimilar from conventional drilling operation of metals; hence, identification of optimum drilling process parameters for FRP composites has become mandatory. In this work, drilling parameter optimization for banana fiber reinforced Vajram mixed phenolic resin composite has been carried out using Taguchi method. Three drilling input parameters such as point angle, spindle speed, and feed rate were optimized for two output responses, namely, thrust force and torque. Two composite samples were fabricated with 5% NaOH-treated banana fiber at 30% fiber volume ratio; sample 1 with 100% phenolic resin and sample 2 with 80% Vajram + 20% phenolic resin. Signal-to-noise ratios for all the output responses were calculated, and other statistical analysis were carried out. Highly contributing factor for sample 1 thrust force was point angle with 64.34% contribution and for torque was feed rate with 28.43% contribution. Highly contributing factor for sample 2 thrust force and torque was point angle with 60.47% and 41.37%, respectively. The residuals are fall on near straight line which ensures the normal distribution of errors; hence, no abnormality was noted on any analysis.

Moving target trajectory prediction based on Dropout-LSTM and Bayesian inference for long-time multi-satellite observation

ABSTRACT Multi-satellite cooperation facilitates long-time and wide-area observation of moving targets and has received considerable attention. An accurate and real-time trajectory prediction of an observed target is the primary premise of multi-satellite cooperative observation that attempts to address the field-of-view switching problem for different satellites. However, the existing methods do not consider the non-linear and time-variant satellite observation process, and the interpretability requires improvement. Therefore, a trajectory prediction model is constructed with decoupled linear Gaussian and non-linear Gaussian parts, based on the analysis of the satellite observation process and the verification of the normal distribution of the observation error. Thereafter, a trajectory prediction method, comprising long short-term memory networks and Bayesian inference, is proposed. The proposed method not only enables the long short-term memory with dropout variational inference to automatically extract features and learn more complex spatiotemporal patterns, but also employs Bayesian inference to introduce the satellite orbit and attitude information as known variables and improve the spatiotemporal smoothness. Finally, a simulation system of moving target trajectory prediction is established, and the results indicate that our approach is superior in terms of the prediction accuracy and generalization properties, compared with the existing methods, particularly when the observed target is manoeuvring rapidly. Consequently, the proposed approach provides a technical basis for achieving long-time multi-satellite observation of the moving target.

Memristive Equivalent Circuit Model for Battery

The design of mathematical models is based on conservation laws and also on the fundamental principles of modeling: structure, parameters, and physical meaning. Those kinds of modeling should have specific capabilities to deal with different working conditions and environments coping with challenges that include but are not limited to battery capacity, life-cycle, or the attempts to manipulate the current profiles during operation. Introducing memristive elements in batteries will be ideal to satisfy these fundamentals and goals of modeling, whereas addressing the recycling and sustainability concerns on the environmental impact by the placement of TiO2 memristor into this model can promote a recovery hierarchy via recycling and dispatching a slight amount to disposal as the previous focus was mainly concentrated on availability. As for battery materials, modeling, performing, and manufacturing all have proliferated to grasp the possible sustainability challenges inherited in these systems. This paper investigated electrochemical impedance spectroscopy to study this model and the dynamic behavior inside the battery. We found a solution to address the existing battery limitations that elucidate the battery degradation without affecting the performance, correspondingly by employing the dampest least-squares combination with nonlinear autoregressive exogenous for identifying such model and its associated parameters because of its embedded memory and fast convergence to diminish the influence of the vanishing gradient. Lastly, we found that this model is proven to be efficient and accurate compared to actual experimented data to validate our theory and show the value of the proposed model in real life while assuming Normal Gaussian distribution of data error with outstanding results; the auto-correlations were within the 95% confidence limit, the best validation was 2.7877, and an overall regression of 0.99993 was achieved.

Development of a new modified hogg type adaptive scheme for multilevel models with diverse error distributions

The rank-based method is a well-known robust estimation technique in analyzing the linear models for non normal error distributions. The efficiency of rank-based analysis can be upgraded by selecting a suitable score function according to the probability distribution of the error term. In this study, a modified version of Hogg’s type adaptive scheme is developed by introducing a new set of cutoff values. The novel idea is to use the rank-based estimation by using the score functions selected through Hogg’s and modified Hogg’s schemes for multilevel models that generate cluster-correlated errors. The efficiency of both schemes is compared for symmetric, asymmetric, and light-tailed to heavy-tailed error distributions under various sample sizes through simulation study based on bias, variance, mean square error, the selected score function, and precision. The modified Hogg’s scheme produces a more efficient rank-based fit than Hogg’s scheme in case of skewed error distribution and produces equal efficiency for symmetric heavy, moderate, and light-tailed distributions. The empirical comparison of score selection through both schemes is also illustrated via a real example. The modified Hogg’s scheme considered the skewness and selected an appropriate score function, giving a more efficient fit than Hogg’s scheme that ignores the skewness.

From consumer to enterprise grade: How the choice of four UAS impacts point cloud quality

AbstractUncrewed aerial systems (UAS), combined with structure‐from‐motion photogrammetry, has already proven to be very powerful for a wide range of geoscience applications and different types of UAS are used for scientific and commercial purposes. However, the impact of the UAS used on the accuracy of the point clouds derived is not fully understood, especially for the quantitative analysis of geomorphic changes in complex terrain. Therefore, in this study, we aim to quantify the magnitude of systematic and random error in digital elevation models derived from four commonly used UAS (XR6/Sony α6000, Inspire 2/X4s, Phantom 4 Pro+, Mavic Pro) following different flight patterns. The vertical error of each elevation model is evaluated through comparison with 156 GNSS reference points and the normal distribution and spatial correlation of errors are analysed. Differences in mean errors (−0.4 to −1.8 cm) for the XR6, Inspire 2 and Phantom 4 Pro are significant but not relevant for most geomorphological applications. The Mavic Pro shows lower accuracies with mean errors up to 4.3 cm, thus showing a higher influence of random errors. QQ plots revealed a deviation of errors from a normal distribution in almost all data. All UAS data except Mavic Pro exhibit a pure nugget semivariogram, suggesting spatially uncorrelated errors. Compared to the other UAS, the Mavic Pro data show trends (i.e. differences increase with distance across the survey—doming) and the range of semivariances is 10 times greater. The lower accuracy of Mavic Pro can be attributed to the lower GSD at the same flight altitude and most likely, the rolling shutter sensor has an effect on the accuracy of the camera calibration. Overall, our study shows that accuracies depend highly on the chosen data sampling strategy and that the survey design used here is not suitable for calibrating all types of UAS camera equally.

Sources of conjugated linoleic acid and lauric acid inoculated into the eggs of quails and its effects on immunity

The objective of this study is to evaluate the effects of in-egg inoculation with sources of conjugated linoleic acid (CLA) and lauric acid (AL), going by the weight of lymphoid organs and the biochemical profile of the blood of cut quails, from one to 35 days of age. We used 360 quails distributed in a completely randomized design, in six treatments and six replicates of 10 birds per plot. Corn oil (OM) was used to dilute the CLA and AL. The experimental treatments were: healthy eggs (control); eggs inoculated with OM thinner; eggs inoculated with CLA 120 mg / 50 mL OM; eggs inoculated with CLA 240 mg / 50 mL OM; eggs inoculated with AL 60 mg / 50 mL OM and eggs inoculated with AL 90 mg / 50 mL OM. The results were analyzed through Program R at the level of 5% significance. To verify the normal distribution of errors, the Shapiro-Wilk normality test was applied. At 21 days, an effect of p < 0.05 was observed for the total blood cholesterol content, inoculations with CLA reduced, even as AL increased, regardless of the level. At 35 days, it was found (p < 0.05) that the levels of total cholesterol and AST in the blood decreased with inoculations of CLA and AL at the lower levels, compared to those that did not receive the inoculations. The CLA and AL levels supplemented via egg inoculations did not interfere with the weight of the lymphoid organs (thymus, Fabricius bursa) of the birds, at both ages. Supplementation in eggs of cut quails with CLA 240 mg reduced the total blood cholesterol content compared to CLA 120 mg, at 21 days of age. At 35 days of age, higher concentrations of CLA and AL increased the total cholesterol and AST in the blood of birds and AL had a greater effect on the increase than CLA.

Co-Estimation of State of Charge and Capacity for Lithium-Ion Batteries with Multi-Stage Model Fusion Method

Lithium-ion batteries (LIBs) have emerged as the preferred energy storage systems for various types of electric transports, including electric vehicles, electric boats, electric trains, and electric airplanes. The energy management of LIBs in electric transports for all-climate and long-life operation requires the accurate estimation of state of charge (SOC) and capacity in real-time. This study proposes a multi-stage model fusion algorithm to co-estimate SOC and capacity. Firstly, based on the assumption of a normal distribution, the mean and variance of the residual error from the model at different ageing levels are used to calculate the weight for the establishment of a fusion model with stable parameters. Secondly, a differential error gain with forward-looking ability is introduced into a proportional–integral observer (PIO) to accelerate convergence speed. Thirdly, a fusion algorithm is developed by combining a multi-stage model and proportional–integral–differential observer (PIDO) to co-estimate SOC and capacity under a complex application environment. Fourthly, the convergence and anti-noise performance of the fusion algorithm are discussed. Finally, the hardware-in-the-loop platform is set up to verify the performance of the fusion algorithm. The validation results of different aged LIBs over a wide range of temperature show that the presented fusion algorithm can realize a high-accuracy estimation of SOC and capacity with the relative errors within 2% and 3.3%, respectively.

Modelling the Monetary Impact of Oil Price Volatility in Nigeria: Evidence from GARCH Models

This paper investigated the impact of oil price volatility on some monetary variables in Nigeria under the framework of the GARCH models. The paper utilized three alternative error distributions in order to assist in providing better model fits and thus avoid biased results. Using monthly series over a period of 2006-2019, our findings revealed that, apart from the usual normal error distribution other error distributions perform better in the modelling of the impact of oil price volatility on monetary variables in Nigeria. The findings of the study also revealed that the asymmetric parameters of the models show evidence of leverage effect and oil price volatility plays a significant role in the determination of volatility of monetary variables. We, therefore, recommend that in modelling volatility of oil price and monetary variables in Nigeria, different error distributions should be considered.

Experimental kinematic analysis of an intermittent motion planetary mechanism with elliptical gears

Intermittent motion mechanisms are widely used in semiautomatic and automatic machinery. Currently, the most common are mechanisms with a one-way coupling or mechanisms of variable structure. The intermittent movement in these mechanisms is provided by breaking the kinematic chain, so their use is undesirable in high-speed machines. The paper presents and analyzes kinematics of planetary transmission with elliptical gears, which performs intermittent motion of output link without interruption of kinematic chain. A kinematic model of the mechanism is constructed, and there are obtained equations for determining the velocity analogue of the output link of the planetary gear. An experimental verification of the adequacy of the developed mathematical model was carried out on the example of studying the position function of the mechanism. The measurement errors were estimated using statistical methods. Using the chi-squared test, the hypothesis of a normal distribution of measurement errors was verified, and confidence interval was determined.

Predicting the reliability of friction type bearings with zirconium ceramic bushing

The paper considers the issues of assessing the reliability of friction type bearing when installing a zirconium ceramic bushing. The allegations regarding the possibility of calculating the reliability of a bearing based on the results of friction pair wear tests at a laboratory setup were made. On a universal friction machine, the tribological characteristics of a friction pair are investigated using a disk-finger scheme. The methodology of constructing the elemental wear law is substantiated, according to which the wear intensity of the ceramic bearing bushing is adjusted according to the conditions of its operation. Particular attention is paid to the reliability of the obtained laboratory tests for friction and wear. Only parametric bearing failure based on the accumulation of wear damage is considered. A procedure has been developed for calculating the reliability and service life of a friction type bearing, taking into account the real angle of contact zone contact, variation of the sizes and tolerances of the shaft and bearing bushing, the normal distribution of errors, as well as the load and sliding velocity in the bearing.

TRIPLE PROBABILITY DENSITY DISTRIBUTION MODEL IN THE TASK OF AVIATION RISK ASSESSMENT

The probability of an airplane deviation from pre-planned trajectory is a core of aviation safety analysis. We propose to use a mixture of three probability density distribution functions it the task of aviation risk assessment. Proposed model takes into account the effect of navigation system error, flight technical error, and occurrence of rare events. Univariate Generalized Error Distribution is used as a basic component of distribution functions, that configures the error distribution model from the normal error distribution to double exponential distribution function. Statistical fitting of training sample by proposed Triple Univariate Generalized Error Distribution (TUGED) is supported by Maximum Likelihood Method. Optimal set of parameters is estimated by sequential approximation method with defined level of accuracy. The developed density model has been used in risk assessment of airplane lateral deviation from runway centreline during take-off and landing phases of flight. The efficiency of the developed model is approved by Chi-square, Akaike’s, and Bayes information criteria. The results of TUGED fitting indicate better performance in comparison with double probability density distribution model. The risk of airplane veering off the runway is considered as the probability of a rare event occurrence and is estimated as an area under the TUGED.

Efficient estimation of reduced-rank partial envelope model in multivariate linear regression

In order to further improve the efficiency of parameter estimation and reduce the number of estimated parameters, we adopt dimension reduction ideas of partial envelope model proposed by [Su and Cook, Partial envelopes for efficient estimation in multivariate linear regression, Biometrika 98 (2011) 133–146.] to center on some predictors of special interest. Based on the research results of [Cook et al., Envelopes and reduced-rank regression, Biometrika 102 (2015) 439–456.], we combine partial envelopes with reduced-rank regression to form reduced-rank partial envelope model which can reduce dimension efficiently. This method has the potential to perform better than both. Further, we demonstrate maximum likelihood estimators for the reduced-rank partial envelope model parameters, and exhibit asymptotic distribution and theoretical properties under normality. Meanwhile, we show selections of rank and partial envelope dimension. At last, under the normal and non-normal error distributions, simulation studies are carried out to compare our proposed reduced-rank partial envelope model with the other four methods, including ordinary least squares, reduced-rank regression, partial envelope model and reduced-rank envelope model. A real data analysis is also given to support the theoretic claims. The reduced-rank partial envelope estimators have shown promising performance in extensive simulation studies and real data analysis.

Robustification of Linear Regression and Its Application in Genome-Wide Association Studies.

Regression analysis is one of the most popular statistical techniques that attempt to explore the relationships between a response (dependent) variable and one or more explanatory (independent) variables. To test the overall significance of regression, F-statistic is used if the parameters are estimated by the least-squares estimators (LSEs), while if the parameters are estimated by the maximum likelihood estimators (MLEs), the likelihood ratio test (LRT) statistic is used. However, both procedures produce misleading results and often fail to provide good fits to the reasonable space of the dataset in the presence of outlying observations. Moreover, outliers occur very frequently in any real datasets as well as in the molecular OMICS datasets. Hence, an effort is made in this study to robustify MLE based regression analysis by maximizing the β-likelihood function. The tuning parameter β is selected by cross-validation. For β = 0, the proposed method reduces to the classical MLE based regression analysis. We inspect the performance of the proposed method using both synthetic and real data analysis. The results of simulations indicate that the proposed method performs better than traditional methods in both outliers and high leverage points to estimate the parameters and mean square errors. The results of relative efficiency analysis show that the proposed estimator is relatively less affected than the popular estimators, including S, MM, and fast-S for normal error distribution in case high dimension and outliers. Also, real data analysis results demonstrated that the proposed method shows robust properties with respect to data contaminations, overcome the drawback of the traditional methods. Genome-wide association studies (GWAS) by the proposed method identify the vital gene influencing hypertension and iron level in the liver and spleen of mice. Furthermore, we have identified 15 and 21 significant SNPs for chalkiness degree and chalkiness percentage, respectively, by GWAS based on the proposed method. The variant of the SNPs might be provided the new resources for grain quality traits and could be used for further molecular and physiological analysis to enhance the better quality of rice grain. These results offer an important basis for further understanding of the robust regression analysis, which might be applied in various fields, including business, genetics, and bioinformatics.