Using angular pair upweighting to improve 3D clustering measurements

Three dimensional galaxy clustering measurements provide a wealth of cosmological information. However, obtaining spectra of galaxies is expensive, and surveys often only measure redshifts for a subsample of a target galaxy population. Provided that the spectroscopic data is representative, we argue that angular pair upweighting should be used in these situations to improve the 3D clustering measurements. We present a toy model showing mathematically how such a weighting can improve measurements, and provide a practical example of its application using mocks created for the Baryon Oscillation Spectroscopic Survey (BOSS). Our analysis of mocks suggests that, if an angular clustering measurement is available over twice the area covered spectroscopically, weighting gives a $\sim$10-20% reduction of the variance of the monopole correlation function on the BAO scale.