scholarly journals The Simulation Study to Test the Performance of Quantile Regression Method With Heteroscedastic Error Variance

CAUCHY ◽  
2017 ◽  
Vol 5 (1) ◽  
pp. 36
Author(s):  
Ferra Yanuar

<div><p class="Keywords">The purpose of this article was to describe the ability of the quantile regression method in overcoming the violation of classical assumptions. The classical assumptions that are violated in this study are variations of non-homogeneous error or heteroscedasticity. To achieve this goal, the simulated data generated with the design of certain data distribution. This study did a comparison between the models resulting from the use of the ordinary least squares and the quantile regression method to the same simulated data. Consistency of both methods was compared with conducting simulation studies as well. This study proved that the quantile regression method had standard error, confidence interval width and mean square error (MSE) value smaller than the ordinary least squares method. Thus it can be concluded that the quantile regression method is able to solve the problem of heteroscedasticity and produce better model than the ordinary least squares. In addition the ordinary least squares is not able to solve the problem of heteroscedasticity.</p></div>

2014 ◽  
Vol 3 (2) ◽  
pp. 174
Author(s):  
Yaser Abdelhadi

Linear transformations are performed for selected exponential engineering functions. The Optimum values of parameters of the linear model equation that fits the set of experimental or simulated data points are determined by the linear least squares method. The classical and matrix forms of ordinary least squares are illustrated. Keywords: Exponential Functions; Linear Modeling; Ordinary Least Squares; Parametric Estimation; Regression Steps.


2020 ◽  
Vol 50 (1) ◽  
Author(s):  
Guilherme Alves Puiatti ◽  
Paulo Roberto Cecon ◽  
Moysés Nascimento ◽  
Ana Carolina Campana Nascimento ◽  
Antônio Policarpo Souza Carneiro ◽  
...  

ABSTRACT: The objective of this study was to adjust nonlinear quantile regression models for the study of dry matter accumulation in garlic plants over time, and to compare them to models fitted by the ordinary least squares method. The total dry matter of nine garlic accessions belonging to the Vegetable Germplasm Bank of Universidade Federal de Viçosa (BGH/UFV) was measured in four stages (60, 90, 120 and 150 days after planting), and those values were used for the nonlinear regression models fitting. For each accession, there was an adjustment of one model of quantile regression (τ=0.5) and one based on the least squares method. The nonlinear regression model fitted was the Logistic. The Akaike Information Criterion was used to evaluate the goodness of fit of the models. Accessions were grouped using the UPGMA algorithm, with the estimates of the parameters with biological interpretation as variables. The nonlinear quantile regression is efficient for the adjustment of models for dry matter accumulation in garlic plants over time. The estimated parameters are more uniform and robust in the presence of asymmetry in the distribution of the data, heterogeneous variances, and outliers.


FLORESTA ◽  
2021 ◽  
Vol 51 (3) ◽  
pp. 596
Author(s):  
Jadson Coelho De Abreu ◽  
Carlos Pedro Boechat Soares ◽  
Helio Garcia Leite ◽  
Daniel Henrique Breda Binoti ◽  
Gilson Fernandes Da Silva

The objective of this study was to evaluate three estimation methods to fit volume equations in the presence of influential or leverage data. To do so, data from the forest inventory carried out by the Centro Tecnológico de Minas Gerais Foundation were used to fit the Schumacher and Hall (1933) model in its nonlinear form for Cerradão forest, considering the quantile regression (QR), the RANSAC algorithm and the nonlinear Ordinary Least Squares (OLS) method. The correlation coefficient ( ) between the observed and estimated volumes, root-mean-square error (RMSE), as well as graphical analysis of the dispersion and distribution of the residuals were used as criteria to evaluate the performance of the methods. After the analysis, the nonlinear least squares method presented a slightly better result in terms of the goodness-of-fit statistics, however it altered the expected trend of the fitted curve due to the presence of influential data, which did not happen with the QR and the RANSAC algorithm, as these were more robust in the presence of discrepant data.


2016 ◽  
Vol 7 (3) ◽  
pp. 369-383 ◽  
Author(s):  
Xuan Vinh Vo ◽  
Dang Bao Anh Phan

Abstract This study examines the herd behavior in Vietnam stock market using a sample of firms listed on the Ho Chi Minh City Stock Exchange covering the time period 2005–2015. We find evidence of herding in both rising and falling market employing the common least squares estimation. Further analysis by applying quantile regression method also confirms the evidence of herding during the whole period. The results are robust when we split the data into two sub-periods.


2015 ◽  
Vol 14 (1) ◽  
pp. 2-19 ◽  
Author(s):  
Wuchun Chi ◽  
Huichi Huang ◽  
Hong Xie

Purpose – This paper aims to investigate whether there is heterogeneity in the relationship between the bank loan interest rate and its determinants using the quantile regression method and to reconcile some conflicting findings in prior literature. Design/methodology/approach – First, the effects of 18 determinants were examined on the bank loan interest rate using the ordinary least squares method (OLS). Second, it was investigated whether the relationship between the loan rate and its determinants is heterogeneous across quantiles of loan rates using the quantile regression method. Findings – Considerable heterogeneity was found in the relationship between the loan rate and its determinants. Specifically, a determinant that is beneficial for the bank loan rate, on average, as revealed by the OLS method may become unimportant or even detrimental for firms located at extremely high or low loan rate quantiles. By revealing extreme heterogeneity in the relationship between the loan rate and some of its determinants, the authors potentially explain two conflicting findings in prior literature. Originality/value – The conventional OLS method masks the heterogeneity in the relationship between the bank loan interest rate and its determinants. Quantile regression can be used to supplement the OLS estimates to gain a more detailed and complete picture of the relationship between the dependent variable and explanatory variables.


2020 ◽  
Author(s):  
Hui Tian ◽  
Andrew Yim ◽  
David P. Newton

We show that quantile regression is better than ordinary-least-squares (OLS) regression in forecasting profitability for a range of profitability measures following the conventional setup of the accounting literature, including the mean absolute forecast error (MAFE) evaluation criterion. Moreover, we perform both a simulated-data and an archival-data analysis to examine how the forecasting performance of quantile regression against OLS changes with the shape of the profitability distribution. Considering the MAFE and mean squared forecast error (MSFE) criteria together, we see that the quantile regression is more accurate relative to OLS when the profitability to be forecast has a heavier-tailed distribution. In addition, the asymmetry of the profitability distribution has either a U-shape or an inverted-U-shape effect on the forecasting accuracy of quantile regression. An application of the distributional shape analysis framework to cash flow forecasting demonstrates the usefulness of the framework beyond profitability forecasting, providing additional empirical evidence on the positive effect of tail-heaviness and supporting the notion of an inverted-U-shape effect of asymmetry. This paper was accepted by Shiva Rajgopal, accounting.


Vestnik MGSU ◽  
2015 ◽  
pp. 140-151 ◽  
Author(s):  
Aleksey Alekseevich Loktev ◽  
Daniil Alekseevich Loktev

In modern integrated monitoring systems and systems of automated control of technological processes there are several essential algorithms and procedures for obtaining primary information about an object and its behavior. The primary information is characteristics of static and moving objects: distance, speed, position in space etc. In order to obtain such information in the present work we proposed to use photos and video detectors that could provide the system with high-quality images of the object with high resolution. In the modern systems of video monitoring and automated control there are several ways of obtaining primary data on the behaviour and state of the studied objects: a multisensor approach (stereovision), building an image perspective, the use of fixed cameras and additional lighting of the object, and a special calibration of photo or video detector.In the present paper the authors develop a method of determining the distances to objects by analyzing a series of images using depth evaluation using defocusing. This method is based on the physical effect of the dependence of the determined distance to the object on the image from the focal length or aperture of the lens. When focusing the photodetector on the object at a certain distance, the other objects both closer and farther than a focal point, form a spot of blur depending on the distance to them in terms of images. Image blur of an object can be of different nature, it may be caused by the motion of the object or the detector, by the nature of the image boundaries of the object, by the object’s aggregate state, as well as by different settings of the photo-detector (focal length, shutter speed and aperture).When calculating the diameter of the blur spot it is assumed that blur at the point occurs equally in all directions. For more precise estimates of the geometrical parameters determination of the behavior and state of the object under study a statistical approach is used to determine the individual parameters and estimate their accuracy. A statistical approach is used to evaluate the deviation of the dependence of distance from the blur from different types of standard functions (logarithmic, exponential, linear). In the statistical approach the evaluation method of least squares and the method of least modules are included, as well as the Bayesian estimation, for which it is necessary to minimize the risks under different loss functions (quadratic, rectangular, linear) with known probability density (we consider normal, lognormal, Laplace, uniform distribution). As a result of the research it was established that the error variance of a function, the parameters of which are estimated using the least squares method, will be less than the error variance of the method of least modules, that is, the evaluation method of least squares is more stable. Also the errors’ estimation when using the method of least squares is unbiased, whereas the mathematical expectation when using the method of least modules is not zero, which indicates the displacement of error estimations. Therefore it is advisable to use the least squares method in the determination of the parameters of the function.In order to smooth out the possible outliers we use the Kalman filter to process the results of the initial observations and evaluation analysis, the method of least squares and the method of least three standard modules for the functions after applying the filter with different coefficients.


2019 ◽  
Vol 8 (1) ◽  
pp. 24-34
Author(s):  
Eka Destiyani ◽  
Rita Rahmawati ◽  
Suparti Suparti

The Ordinary Least Squares (OLS) is one of the most commonly used method to estimate linear regression parameters. If multicollinearity is exist within predictor variables especially coupled with the outliers, then regression analysis with OLS is no longer used. One method that can be used to solve a multicollinearity and outliers problems is Ridge Robust-MM Regression. Ridge Robust-MM  Regression is a modification of the Ridge Regression method based on the MM-estimator of Robust Regression. The case study in this research is AKB in Central Java 2017 influenced by population dencity, the precentage of households behaving in a clean and healthy life, the number of low-weighted baby born, the number of babies who are given exclusive breastfeeding, the number of babies that receiving a neonatal visit once, and the number of babies who get health services. The result of estimation using OLS show that there is violation of multicollinearity and also the presence of outliers. Applied ridge robust-MM regression to case study proves ridge robust regression can improve parameter estimation. Based on t test at 5% significance level most of predictor variables have significant effect to variable AKB. The influence value of predictor variables to AKB is 47.68% and MSE value is 0.01538.Keywords:  Ordinary  Least  Squares  (OLS),  Multicollinearity,  Outliers,  RidgeRegression, Robust Regression, AKB.


2020 ◽  
pp. 636-645
Author(s):  
Hussain Karim Nashoor ◽  
Ebtisam Karim Abdulah

Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calculate these estimates can be obtained. Practically, values for these estimates can be obtained only by referring to numerical methods. This research paper is dedicated to estimate parameters of the Epsilon Skew Normal General Linear Model (ESNGLM) using an adaptive least squares method, as along with the employment of the ordinary least squares method for estimating parameters of the General Linear Model (GLM). In addition, the coefficient of determination was used as a criterion to compare the models’ preference. These methods were applied to real data represented by dollar exchange rates. The Matlab software was applied in this work and the results showed that the ESNGLM represents a satisfactory model. 


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