5. Density estimation by projection

We now give some indications of a global method for estimating f. The principle is to develop f as a series of orthogonal functions and to estimate the coefficients of this development using empirical averages. We begin with an important special case.

• Trigonometric series

  On the interval [0,1], the orthonormal system of trigonometric functions is defined by e ₀ (x) = 1 and $e_{2j-1}\left(x\right)=\sqrt{2}\mathrm{ }\sin \left(2\mathrm{\pi }\mathit{jx}\right)$...