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

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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).