On Estimation of Bi‑liner Regression Parameters

Grzegorz Antoni Sitek; Janusz Leszek Wywiał

doi:10.18778/0208-6018.332.06

Authors

Grzegorz Antoni Sitek University of Economics in Katowice, Faculty of Management, Department of Statistics, Econometrics and Mathematics
Janusz Leszek Wywiał

DOI:

https://doi.org/10.18778/0208-6018.332.06

Keywords:

bi lines function, linear regression, least squares method for an implicit interdependence, mixture of probability distribution

Abstract

Two non‑parallel lines will be named as bi‑lines. The relationship between the definition of the bi‑lines function and linear regression functions of the distribution mixture is considered. The bi‑lines function parameters are estimated using the least squares method for an implicit interdependence. In general, values of parameter estimators are evaluated by means of an approximation numerical method. In a particular case, the exact expressions for the parameter estimators were derived. In this particular case, the properties of the estimators are examined in details. The bi‑lines are also used to estimate the regression functions of the distribution mixture. The accuracy of the parameter estimation is analyzed.

Downloads

Download data is not yet available.

References

Antoniewicz R. (1988), Metoda najmniejszych kwadratów dla zależności niejawnych i jej zastosowanie w ekonomii, Wydawnictwo Akademii Ekonomicznej we Wrocławiu, Wrocław.
Google Scholar

Antoniewicz R. (2001), Biproste regresji, “Zeszyty Naukowe Uniwersytetu Szczecińskiego”, nr 318, “Prace Katedry Ekonometrii i Statystyki”, nr 10, pp. 9–15.
Google Scholar

Cramér H. (1946), Mathematical Methods of Statistics, Princeton University Press, Princeton.
Google Scholar

Gabriel K.R. (1998), Generalised Bilinear Regression, “Biometrika”, vol. 85, pp. 689–700.
Google Scholar

Lindsay B., Basak P. (1993), Multivariate normal mixtures: A fast consistent method of moments, “Journal of the American Statistical Association”, vol. 88(422), pp. 468–476.
Google Scholar

McLachlan G.J., Peel D. (2000), Finite Mixture Models, John Wiley & Sons, New York.
Google Scholar

Quandt R.E. (1972), A new approach to estimating switching regressions, “Journal of the American Statistical Association”, vol. 67, no. 338, pp. 306–310.
Google Scholar

Sitek G. (2016), Estimation of regression parameters of two dimensional probability distribution mixtures, Submitted to “Studia Ekonomiczne. Zeszyty Naukowe Uniwersytetu Ekonomicznego w Katowicach”.
Google Scholar