On Estimation of Bi‑liner Regression Parameters

Abstract

<jats:p>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.</jats:p>