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Measuring the clustering of galaxies from surveys allows us to estimate thepower spectrum of matter density fluctuations, thus constraining cosmologicalmodels. This requires careful modelling of observational effects to avoidmisinterpretation of data. In particular, signals coming from differentdistances encode information from different epochs. This is known as"light-cone effect" and is going to have a higher impact as upcoming galaxysurveys probe larger redshift ranges. Generalising the method by Feldman et al.(1994), I define a minimum-variance estimator of the linear power spectrum at afixed time, properly taking into account the light-cone effect. An analyticexpression for the estimator is provided, and that is consistent with thefindings of previous works in the literature. I test the method within thecontext of the halo model, assuming Planck 2014 cosmological parameters. I showthat the estimator presented recovers the fiducial linear power spectrum atpresent time within 5% accuracy up to $k \sim 0.80\;h\,\mathrm{Mpc}^{-1}$ andwithin 10% up to $k \sim 0.94\;h\,\mathrm{Mpc}^{-1}$, well into the non-linearregime of the growth of density perturbations. As such, the method could beuseful in the analysis of the data from future large-scale surveys, likeEuclid.

An Optimally Weighted Estimator of the Linear Power Spectrum Disentangling the Growth of Density Perturbations Across Galaxy Surveys