E. Keihänen, V. Lindholm, P. Monaco, L. Blot, C. Carbone, K. Kiiveri, A. G. Sánchez, A. Viitanen, J. Valiviita, A. Amara, N. Auricchio, M. Baldi, D. Bonino, E. Branchini, M. Brescia, **J. Brinchmann**, S. Camera, V. Capobianco, J. Carretero, M. Castellano, S. Cavuoti, A. Cimatti, R. Cledassou, G. Congedo, L. Conversi, Y. Copin, L. Corcione, M. Cropper, **A. C. da Silva**, H. Degaudenzi, M. Douspis, F. Dubath, C. A. J. Duncan, X. Dupac, S. Dusini, A. Ealet, S. Farrens, S. Ferriol, M. Frailis, E. Franceschi, M. Fumana, B. R. Gillis, C. Giocoli, A. Grazian, F. Grupp, L. Guzzo, S. V. H. Haugan, H. Hoekstra, W. A. Holmes, F. Hormuth, K. Jahnke, M. Kümmel, S. Kermiche, A. Kiessling, T. D. Kitching, M. Kunz, H. Kurki-Suonio, S. Ligori, P. B. Lilje, I. Lloro, E. Maiorano, O. Mansutti, O. Marggraf, F. Marulli, R. Massey, M. Melchior, M. Meneghetti, G. Meylan, M. Moresco, B. Morin, L. Moscardini, E. Munari, S. M. Niemi, C. Padilla, S. Paltani, F. Pasian, K. Pedersen, V. Pettorino, S. Pires, G. Polenta, M. Poncet, L. Popa, F. Raison, A. Renzi, J. D. Rhodes, E. Romelli, R. Saglia, B. Sartoris, P. Schneider, T. Schrabback, A. Secroun, G. Seidel, C. Sirignano, G. Sirri, L. Stanco, C. Surace, P. Tallada-Crespí, D. Tavagnacco, A. N. Taylor, **I. Tereno**, R. Toledo-Moreo, F. Torradeflot, E. A. Valentijn, L. Valenziano, T. Vassallo, Y. Wang, J. Weller, G. Zamorani, J. Zoubian, S. Andreon, D. Maino, S. de la Torre

**Abstract**

We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy-Szalay estimator. The standard way of evaluating the covariance matrix consists in running the estimator on a large number of mock catalogs, and evaluating their sample covariance. With large random catalog sizes (random-to-data objects' ratio M ≫ 1) the computational cost of the standard method is dominated by that of counting the data-random and random-random pairs, while the uncertainty of the estimate is dominated by that of data-data pairs. We present a method called Linear Construction (LC), where the covariance is estimated for small random catalogs with a size of M = 1 and M = 2, and the covariance for arbitrary M is constructed as a linear combination of the two. We show that the LC covariance estimate is unbiased. We validated the method with PINOCCHIO simulations in the range r = 20 − 200 h^{−1} Mpc. With M = 50 and with 2 h^{−1} Mpc bins, the theoretical speedup of the method is a factor of 14. We discuss the impact on the precision matrix and parameter estimation, and present a formula for the covariance of covariance.

**Keywords**

cosmology: observations / large-scale structure of Universe / methods: data analysis / methods: statistical

**Notes**

This paper is published on behalf of the Euclid Consortium.

**Astronomy & Astrophysics**

Volume 666, Article Number A129, Number of pages 17

2022 October