Calcul d'un indice des loyers par post-stratification

The paper establishes the theoretical properties of a synthesized index number computed from an a posteriori stratified sample. The index number considered can be expressed as a weighted mean of the mean ratios computed for the subsamples. In the first part, we show that the index has a biais in 1 / n and that its variance can be expressed as the sum of two terms reflecting the uncertainty on the size of the subsamples and the uncertainty on the ratio in each stratum. In the second part, we apply the theoretical results to the data from the recent survey of housing rent prices in Lausanne.