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.

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