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This communication gives some extensions of the original Bühlmann model. The paper is devoted to semi-linear credibility, where one examines functions of the random variables representing claim amounts, rather than the claim amounts themselves. The main purpose of semi-linear credibility theory is the estimation of ${\mu }_0\left(\theta \right)=E\left[f_0\left(X_{t+1}\right)\right|\theta ]$ (the net premium for a contract with risk parameter $\theta$) by a linear combination of given functions of the observable variables: ${\underline{X}}^{\text{'}}=(X_1,X_2,...,X_t)$. So the estimators mainly considered here are linear...

This paper presents and analyzes the estimators of the structural parameters, in the Bühlmann-Straub model, involving complicated mathematical properties of conditional expectations and of conditional covariances. So to enable to use the better linear credibility results obtained in this model, we will provide useful estimators for the structure parameters. From the practical point of view it is stated the attractive property of unbiasedness for these estimators.