Choice of Appropriate Power Transformation of Skewed Distribution for Quantile Regression Model

Onyegbuchulem B.O.^1, , Nwakuya M.T², Nwabueze J.C³ and Otu Archibong Otu⁴

¹Department of Maths/Statistics, Imo State Polytechnic Umuagwo, Nigeria

²Department of Maths/Statistics, University of Port Harcourt, River State, Nigeria

³Department of Statistics, Federal University of Agriculture Umudike, Nigeria

⁴Department of Research and Statistics, Central Bank of Nigeria, Owerri

Cite this paper

Onyegbuchulem B.O., Nwakuya M.T, Nwabueze J.C and Otu Archibong Otu. Choice of Appropriate Power Transformation of Skewed Distribution for Quantile Regression Model. American Journal of Applied Mathematics and Statistics. 2019; 7(3):105-111. doi: 10.12691/AJAMS-7-3-4

Abstract

Quantile Regression (QR) performed better than Ordinary Least Square (OLS) when the Data is skewed. Its best result can be achieved when the Data is transformed. Quantreg package of R software was used to illustrate the various power transformation fitness for quantile regression model. The analysis shows that the best result was obtained from the square root of y transformation with an average error term of 0.9539, -0.0494, 0.0238, -0.5309 and -0.7544 for 10th, 25th, 50th, 75th and 90^th quantile respectively. From the results obtained, it shows that model transformation can greatly improve the result of quantile regression model.

Keywords

Quantile Regression, skewed distribution, power transformation and model selection

Copyright

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]	Arshad, I. A., Younas, U., Shaikh,A.W & Chandio,M.S (2016). Quantile Regression Analysis of Monthly Earnings in Pakistan; Sindh Univ. Res. Jour. (Sci. Ser.) Vol. 48 (4) 919-924 (2016).
[2]	Bartlett, M.S (1974). The use of Transformation, Biometrica 3, 39-52.
[3]	Chaudhuri, P. &Loh, W.-Y. (2002). Nonparametric estimation of conditional quantiles using quantile regression trees, Bernoulli, 8, 561-576.
[4]	Frost, J (2012) How to Identify the Distribution of Your Data using Minitab, http://www.scribd.com/doc/84506538/Body-Fat-Data-for-Identifying-Distribution-in-Minitab.
[5]	[Hao L. &Naiman, D.Q., (2007). Quantile Regression; 01-Hao.qxd. 3/13/2007.3.28.
[6]	Iwueze, S.I., Nwogu, E.C., Ohakwe, J. & Ajaraogu, J.C. (2011) Uses of the Buys-Ballot Table in Time Series Analysis, Applied Mathematics Journal. (2) 633-645.
[7]	Koenker, R. (2005). Quantile Regression, Econometric Society Monograph Series, Cambridge University Press. (6)6.
[8]	Koenker,R & Bassett, G. (1978); Regression Quantiles, Econometrica, Vol. 46, No. 1, pp. 33-50.
[9]	Koenker, R. &D’Orey, V. (1987). Algorithm AS229: Computing regression quantiles, Applied Statistics, 36, 383-393.
[10]	Koenker, R. & Machado J.A (1999) Goodness of fit and related inference processes for quantile regression. Journal of Econometrics, 93, 327-344
[11]	Lee, B.-J. & Lee, M. J. (2006). Quantile regression analysis of wage determinants in the Korean labor market, The Journal of the Korean Economy, 7, 1-31.
[12]	Loh, W.-Y. (2002). Regression trees with unbiased variable selection and interaction detection, Statistica Sinica, 12, 361-386.
[13]	McMillen, D.P. (2013). Quantile Regression for Spatial Data, Springer Briefs in Regional Science.
[14]	Meinshausen, N. (2006); Quantile Regression Forests, Journal of Machine Learning Research, (7) 983-99.
[15]	Wen-ShuennDeng,Yi-Chen Lin &JinguoGong (2012) A smooth coefficient quantile regression approach to the social capital–economic growth nexus; Economic Modelling journal homepage: www.elsevier.com/locate/ecmod.
[16]	Young, T.M., Shaffer, L.B., Guess, F. M., Bensmail, H. &Leon, R.V (2008), A comparison of multiple linear regression and quantile regression for modeling the internal bond of medium density fiberboard; Forest Products Journal, 58(4).