stacked sample compared to a random position. This effect has been discussed in detail by several authors [e.g., @Bavouzet2008; @Bethermin2010b; @Kurczynski2010; @Bethermin2012b; @Bourne2012; @Viero2013b]. In @Magdis2012b, the authors estimated that this bias is lower than the 1$\sigma$ statistical uncertainties and was not corrected. The number of sources to stack in COSMOS compared to the GOODS fields used by @Magdis2012b is much larger and hence the signal-to-noise ratio is much better. The bias caused by clustering is thus non-negligible in COSMOS. Because of the complex edge effects caused by the absence of data around bright stars, the methods using the position of the sources to deblend the contamination caused by the clustering cannot be applied [@Kurczynski2010; @Viero2013b]. Consequently, we developed a method based on realistic simulations of the *Spitzer*, *Herschel*, LABOCA, and AzTEC maps to correct this effect, which induces biases up to 50% at 500$\mu$m around z$\sim$2. The technical details and discussion of these corrections are presented in Appendix\[Annexestacking\].\
The uncertainties on the fluxes are measured using a bootstrap technique [@Jauzac2011]. This method takes into account both the errors coming from the instrumental noise, the confusion, and the sample variance of the galaxy population [@Bethermin2012b]. These uncertainties are combined quadratically 