Academic literature on the topic 'Median regression, quantile regression'

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Journal articles on the topic "Median regression, quantile regression"

1

Koenker, Roger, and Kevin F. Hallock. "Quantile Regression." Journal of Economic Perspectives 15, no. 4 (2001): 143–56. http://dx.doi.org/10.1257/jep.15.4.143.

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Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions. The central special case is the median regression estimator which minimizes a sum of absolute errors. Other conditional quantile functions are estimated by minimizing an asymmetrically weighted sum of absolute errors. Quantile regression methods are illustrated with applications to models for CEO pay, food expenditure, and infant birthweight.
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2

Aviral, Kumar Tiwari, and Krishnankutty Raveesh. "Determinants of Capital Structure: A Quantile Regression Analysis." Studies in Business and Economics 10, no. 1 (2015): 16–34. http://dx.doi.org/10.1515/sbe-2015-0002.

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Abstract In this study, we attempted to analyze the determinants of capital structure for Indian firms using a panel framework and to investigate whether the capital structure models derived from Western settings provide convincing explanations for capital structure decisions of the Indian firms. The investigation is performed using balanced panel data procedures for a sample 298 firms (from the BSE 500 firms based on the availability of data) during 2001-2010. We found that for lowest quantile LnSales and TANGIT are significant with positive sign and NDTS and PROFIT are significant with negative sign. However, in case of 0.25th quantile LnSales and LnTA are significant with positive sign and PROFIT is significant with negative sign. For median quantile PROFIT is found to be significant with negative sign and TANGIT is significant with positive sign. For 0.75th quantile, in model one, LnSales and PROFIT are significant with negative sign and TANGIT and GROWTHTA are significant with positive sign whereas, in model two, results of 0.75th quantile are similar to the median quantile of model two. For the highest quantile, in case of model one, results are similar to the case of 0.75th quantile with exception that now GROWTHTA in model one (and GROWTHSA in model two).
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3

CAI, YUZHI. "A COMPARATIVE STUDY OF MONOTONE QUANTILE REGRESSION METHODS FOR FINANCIAL RETURNS." International Journal of Theoretical and Applied Finance 19, no. 03 (2016): 1650016. http://dx.doi.org/10.1142/s0219024916500163.

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Quantile regression methods have been used widely in finance to alleviate estimation problems related to the impact of outliers and the fat-tailed error distribution of financial returns. However, a potential problem with the conventional quantile regression method is that the estimated conditional quantiles may cross over, leading to a failure of the analysis. It is noticed that the crossing over issues usually occur at high or low quantile levels, which are the quantile levels of great interest when analyzing financial returns. Several methods have appeared in the literature to tackle this problem. This study compares three methods, i.e. Cai & Jiang, Bondell et al. and Schnabel & Eilers, for estimating noncrossing conditional quantiles by using four financial return series. We found that all these methods provide similar quantiles at nonextreme quantile levels. However, at extreme quantile levels, the methods of Bondell et al. and Schnabel & Eilers may underestimate (overestimate) upper (lower) extreme quantiles, while that of Cai & Jiang may overestimate (underestimate) upper (lower) extreme quantiles. All methods provide similar median forecasts.
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4

Chiu, Yohann Moanahere, Fateh Chebana, Belkacem Abdous, Diane Bélanger, and Pierre Gosselin. "Cardiovascular Health Peaks and Meteorological Conditions: A Quantile Regression Approach." International Journal of Environmental Research and Public Health 18, no. 24 (2021): 13277. http://dx.doi.org/10.3390/ijerph182413277.

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Cardiovascular morbidity and mortality are influenced by meteorological conditions, such as temperature or snowfall. Relationships between cardiovascular health and meteorological conditions are usually studied based on specific meteorological events or means. However, those studies bring little to no insight into health peaks and unusual events far from the mean, such as a day with an unusually high number of hospitalizations. Health peaks represent a heavy burden for the public health system; they are, however, usually studied specifically when they occur (e.g., the European 2003 heatwave). Specific analyses are needed, using appropriate statistical tools. Quantile regression can provide such analysis by focusing not only on the conditional median, but on different conditional quantiles of the dependent variable. In particular, high quantiles of a health issue can be treated as health peaks. In this study, quantile regression is used to model the relationships between conditional quantiles of cardiovascular variables and meteorological variables in Montreal (Canada), focusing on health peaks. Results show that meteorological impacts are not constant throughout the conditional quantiles. They are stronger in health peaks compared to quantiles around the median. Results also show that temperature is the main significant variable. This study highlights the fact that classical statistical methods are not appropriate when health peaks are of interest. Quantile regression allows for more precise estimations for health peaks, which could lead to refined public health warnings.
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5

UTHAMI, IDA AYU PRASETYA, I. KOMANG GDE SUKARSA, and I. PUTU EKA NILA KENCANA. "REGRESI KUANTIL MEDIAN UNTUK MENGATASI HETEROSKEDASTISITAS PADA ANALISIS REGRESI." E-Jurnal Matematika 2, no. 1 (2013): 6. http://dx.doi.org/10.24843/mtk.2013.v02.i01.p021.

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In regression analysis, the method used to estimate the parameters is Ordinary Least Squares (OLS). The principle of OLS is to minimize the sum of squares error. If any of the assumptions were not met, the results of the OLS estimates are no longer best, linear, and unbiased estimator (BLUE). One of the assumptions that must be met is the assumption about homoscedasticity, a condition in which the variance of the error is constant (same). Violation of the assumptions about homoscedasticity is referred to heteroscedasticity. When there exists heteroscedas­ticity, other regression techniques are needed, such as median quantile regression which is done by defining the median as a solution to minimize sum of absolute error. This study intended to estimate the regression parameters of the data were known to have heteroscedasticity. The secondary data were taken from the book Basic Econometrics (Gujarati, 2004) and analyzing method were performed by EViews 6. Parameter estimation of the median quantile regression were done by estimating the regression parameters at each quantile ?th, then an estimator was chosen on the median quantile as regression coefficients estimator. The result showed heteroscedasticity problem has been solved with median quantile regression although error still does not follow normal distribution properties with a value of R2 about 71 percent. Therefore it can be concluded that median quantile regression can overcome heteroscedasticity but the data still abnormalities.
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6

I. O., Ajao,, Obafemi, O. S., and Osunronbi, F.A. "MEASURING THE IMPACT OF TAU VECTOR ON PARAMETER ESTIMATES IN THE PRESENCE OF HETEROSCEDASTIC DATA IN QUANTILE REGRESSION ANALYSIS." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (2023): 3220–29. http://dx.doi.org/10.47191/ijmcr/v11i1.15.

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The ordinary least squares (OLS) regression models only the conditional mean of the response and is computationally less expensive. Quantile regression on the other hand is more expensive and rigorous but capable of handling vectors of quantiles and outliers. Quantile regression does not assume a particular parametric distribution for the response, nor does it assume a constant variance for the response, unlike least squares regression. This paper examines the impact of various quantiles (tau vector) on the parameter estimates in the models generated by the quantile regression analysis. Two data sets, one with normal random error with non-constant variances and the other with a constant variance were simulated. It is observed that with heteroscedastic data the intercept estimate does not change much but the slopes steadily increase in the models as the quantile increase. Considering homoscedastic data, results reveal that most of the slope estimates fall within the OLS confidence interval bounds, only few quartiles are outside the upper bound of the OLS estimates. The hypothesis of quantile estimates equivalence is rejected, which shows that the OLS is not appropriate for heteroscedastic data, but the assumption is not rejected in the case of homoscedastic data at 5% level of significance, which clearly proved that the quantile regression is not necessary in a constant variance data. Using the following accuracy measures, mean absolute percentage error (MAPE), the median absolute deviation (MAD) and the mean squared deviation (MSD), the best model for the heteroscedastic data is obtained at the first quantile level (tau = 0.10).
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7

Conaway, Mark. "Reference data and quantile regression." Muscle & Nerve 40, no. 5 (2009): 751–52. http://dx.doi.org/10.1002/mus.21562.

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8

Pan, Wen-Tsao, and Yungho Leu. "An Analysis of Bank Service Satisfaction Based on Quantile Regression and Grey Relational Analysis." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/1475148.

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Bank service satisfaction is vital to the success of a bank. In this paper, we propose to use the grey relational analysis to gauge the levels of service satisfaction of the banks. With the grey relational analysis, we compared the effects of different variables on service satisfaction. We gave ranks to the banks according to their levels of service satisfaction. We further used the quantile regression model to find the variables that affected the satisfaction of a customer at a specific quantile of satisfaction level. The result of the quantile regression analysis provided a bank manager with information to formulate policies to further promote satisfaction of the customers at different quantiles of satisfaction level. We also compared the prediction accuracies of the regression models at different quantiles. The experiment result showed that, among the seven quantile regression models, the median regression model has the best performance in terms of RMSE, RTIC, and CE performance measures.
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9

Sánchez, Luis, Víctor Leiva, Helton Saulo, Carolina Marchant, and José M. Sarabia. "A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications." Mathematics 9, no. 21 (2021): 2768. http://dx.doi.org/10.3390/math9212768.

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Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.
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10

Olsen, Cody S., Amy E. Clark, Andrea M. Thomas, and Lawrence J. Cook. "Comparing Least-squares and Quantile Regression Approaches to Analyzing Median Hospital Charges." Academic Emergency Medicine 19, no. 7 (2012): 866–75. http://dx.doi.org/10.1111/j.1553-2712.2012.01388.x.

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