We are concerned with the estimation of linear and quadratic functionals of the form \[ (1)\quad \Phi (g)=\int_{\Theta}\phi (\theta)g(\theta)\mu (d\theta),\quad and\quad (2)\quad \Omega (g)=\int_{\Theta}\omega (\theta)g^ 2(\theta)\mu (d\theta) \] in an unknown a priori density. One of the methods for obtaining the desired estimates is to estimate first g(\(\theta)\) and then substitute the result in formulas (1) and (2). However, this method is not always effective since the estimation of g(\(\theta)\) is rather tedious and the estimates are biased. We consider here a different approach which permits at once to estimate the functionals (1) and (2) and, in the case of \(\Phi\) (g), allows us to obtain an unbiased estimate with dispersion of order \(N^{-1}\).