Testing the difference between two sets of data using comparison two linear regression functions


This study aims to compare two sets of data with each having a linear relationship between the independent and dependent variables. The problem is solved by testing the equality of two regression functions. The test statistics based on empirical distribution : the Kolmogorov-Smirnov and Kuiper type statistics are considered, under the alternative hypotheses comprised of a constant shift and an affine shift. Additionally, the rejection proportion is calculated using the bootstrap method. The  test statistics are also applied to the analysis of two sets of data, the characteristics of which are found to be consistent with the p-value after 1,000 trials of bootstrapping.

DOI Code: 10.1285/i20705948v7n2p279

Keywords: regression function, linear relationship, empirical distribution, bootstrap procedure, expectation function, error distribution


. Brame, R., Paternoster, R., Mazerolle, P., Piquero, A. (1998). Testing for the Equality of

Maximum-Likelihood Regression Coefficients Between Two Independent Equations. Journal of Quantitative Criminology, 14, 245 – 261.

. Clogg, C.C., Petkova, E., Haritou, A. (1995). Statistical methods for comparing

regression coefficients between models. Sociol, 100, 1261 – 1293.

. Pardo – Fernandez , J.C. (2007). Comparison of Error Distributions in Nonparametric

Regression. Statistics &Probability, 77, 350 – 356.

. Pardo – Fernandez, J.C., Keilegom, I.V., Gonzalez – Manteiga, W. (2007). Testing for

the equality of k regression curves. Statistica Sinica, 17, 1115 – 1137.

. Neumeyer, N., Dette, H. (2003). Nonparametric Comparison of Regression Curves: An

Empirical Process Approach. The Annals of Statistics, 31, 880 – 920.

. Akritas, M.G., Keilegom, I.V. (2001). Non - Parametric Estimation of the Residual

Distribution. Scand. J. Statist, 28,549 – 567.

. Donsker, M.D. (1952). Justification and extension of Doob’s heuristic approach to

the kolmogorov-Smirnov theorems. Annals of Mathematical Statistics, 23, 277 – 281.

. Freedman, D.A. (1981). Bootstrapping regression models. Ann. Statist, 9,1218 – 1288.

. Silverman, B.W., Wellner, J.A. (1996). The bootstrap: To smooth or not to smooth?.

Biometrika, 74, 469 – 479.

. National Statistical Officer Thailand (2009). This is a sample. http://www.

nso.go.th/nso/nsopublish/download/files /ictDev53.pdf.

Full Text: pdf

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.