by Golomb et al. (2021) for data from the Gemini Planet Imager. If the spatial correlation length is large, a spacing of 1 PSF FWHM might not be sufficient to ensure that the noise observations in *X* are independent. At 6 FWHM the FWHM of the local correlations is slightly smaller than the PSF FWHM. If we use PCA, the local correlations at 2 FWHM change while they stay the same at 6 FWHM. Future work should further investigate this behavior to understand better the spatial correlations of speckle noise in real data. A possible path for this could be bootstrapping for dependent observations (Zoubir & Iskander 2004).

## ORCID iDs

Markus J. Bonse https://orcid.org/0000-0003-2202-1745

Emily O. Garvin https://orcid.org/0000-0003-2530-9330

Timothy D. Gebhard https://orcid.org/0000-0001-9310-8579

Felix A. Dannert https://orcid.org/0000-0002-5476-2663

Faustine Cantalloube https://orcid.org/0000-0002-3968-3780

Gabriele Cugno https://orcid.org/0000-0001-7255-3251

Olivier Absil https://orcid.org/0000-0002-4006-6237

Jean Hayoz https://orcid.org/0000-0003-3768-5712

Julien Milli https://orcid.org/0000-0001-9325-2511

Markus Kasper https://orcid.org/0000-0002-8425-6606

Sascha P. Quanz https://orcid.org/0000-0003-3829-7412

## References

Absil, O., Milli, J., Mawet, D., et al. 2013, A&A, 559, L12

Aime, C., & Soummer, R. 2004, ApJL, 612, L85

Amara, A., & Quanz, S. P. 2012, MNRAS, 427, 948

Bowens, R., Meyer, M. R., Delacroix, C., et al. 2021, A&A, 653, A8

Brandl, B., Bettonvil, F., van Boekel, R., et al. 2021, Msngr, 182, 22

Cantalloube, F., Mouillet, D., Mugnier, L. M., et al. 2015, A&A, 582, A89

Cantalloube, F., Farley, O., Milli, J., et al. 2020, A&A, 638, A98

Cantalloube, F., Gomez-Gonzalez, C., Absil, O., et al. 2020, Proc. SPIE, 11448, 114485A

Casella, G., & Berger, R. L. 2002, Statistical Inference (2nd edn; Pacific Grove, CA: Thomson Learning)

Dahlqvist, C.-H., Cantalloube, F., & Absil, O. 2020, A&A, 633, A95

Delacroix, C., Absil, O., Forsberg, P., et al. 2013, A&A, 553, A98

Desidera, S., Chauvin, G., Bonavita, M., et al. 2021, A&A, 651, A70

Easterling, R. G., & Anderson, H. E. 1978, JSCS, 8, 1

Efron, B., & Tibshirani, R. 1994, An Introduction to the Bootstrap (New York: CRC Press)

Fitzgerald, M. P., & Graham, J. R. 2006, ApJ, 637, 541

Flasseur, O., Denis, L., Thiébaut, É., & Langlois, M. 2018, A&A, 618, A138

Gaudi, B. S., Seager, S., Mennesson, B., et al. 2018, arXiv:1809.09674

Gebhard, T. D., Bonse, M. J., Quanz, S. P., & Schölkopf, B. 2022, A&A, 666, A9

Golomb, J., Rocha, G., Meshkat, T., et al. 2021, AJ, 162, 304

Gomez Gonzalez, C. A., Absil, O., Absil, P.-A., et al. 2016, A&A, 589, A54

Gomez Gonzalez, C. A., Absil, O., & Van Droogenbroeck, M. 2018, A&A, 613, A71

Gomez Gonzalez, C. A., Wertz, O., Absil, O., et al. 2017, AJ, 154, 7

Hinkley, S., Carter, A. L., Ray, S., et al. 2022, PASP, 134, 095003

Hunziker, S., Quanz, S. P., Amara, A., & Meyer, M. R. 2018, A&A, 611, A23

Jensen-Clem, R., Mawet, D., Gomez Gonzalez, C. A., et al. 2017, AJ, 155, 19

Kasper, M., Urra, N. C., Pathak, P., et al. 2021, Msngr, 182, 38

Kenworthy, M. A., Snik, F., Keller, C. U., et al. 2018, Proc. SPIE, 10702, 1070246

Kuhn, J. R., Potter, D., & Parise, B. 2001, ApJL, 553, L189

Lafrenière, D., Marois, C., Doyon, R., & Barman, T. 2009, ApJL, 694, L148

Langlois, M., Gratton, R., Lagrange, A.-M., et al. 2021, A&A, 651, A71

Larsen, R. J., & Marx, M. L. 2012, An Introduction to Mathematical Statistics and Its Applications (5th edn.; Boston, MA: Prentice Hall)

Marois, C., Correia, C., Galicher, R., et al. 2014, Proc. SPIE, 9148, 91480U

Marois, C., Lafreniere, D., Doyon, R., Macintosh, B., & Nadeau, D. 2006, ApJ, 641, 556

Marois, C., Lafreniere, D., Macintosh, B., & Doyon, R. 2008, ApJ, 673, 647

Marois, C., Macintosh, B., & Véran, J.-P. 2010, Proc. SPIE, 7736, 77361J

Mawet, D., Milli, J., Wahhaj, Z., et al. 2014, ApJ, 792, 97

Mesa, D., Gratton, R., Zurlo, A., et al. 2015, A&A, 576, A121

Meshkat, T., Bailey, V., Rameau, J., et al. 2013, ApJL, 775, L40

Morzinski, K. M., Males, J. R., Skemer, A. J., et al. 2015, ApJ, 815, 108

Nielsen, E. L., De Rosa, R. J., Macintosh, B., et al. 2019, AJ, 158, 13

Norton, R. M. 1984, Am. Stat., 38, 135

Otten, G. P. P. L., Snik, F., Kenworthy, M. A., et al. 2017, ApJ, 834, 175

Pairet, B., Cantalloube, F., Gomez Gonzalez, C. A., Absil, O., & Jacques, L. 2019, MNRAS, 487, 2262

Perrin, M. D., Sivaramakrishnan, A., Makidon, R. B., Oppenheimer, B. R., & Graham, J. R. 2003, ApJ, 596, 702

Quanz, S. P., Crossfield, I., Meyer, M. R., Schmalzl, E., & Held, J. 2015, IJASB, 14, 279

Quanz, S. P., Schmid, H. M., Geissler, K., et al. 2011, ApJ, 738, 23

Quanz, S. P., Ottiger, M., Fontanet, E., et al. 2022, A&A, 664, A21

Racine, R., Walker, G. A. H., Nadeau, D., Doyon, R., & Marois, C. 1999, PASP, 111, 587

Rameau, J., Chauvin, G., Lagrange, A.-M., et al. 2013, ApJL, 772, L15

Razali, N. M., & Wah, Y. B. 2011, JSMA, 2, 21

Rochon, J., Gondan, M., & Kieser, M. 2012, BMC Med. Res. Methodol., 12, 81

Rousset, G., Lacombe, F., Puget, P., et al. 2003, Proc. SPIE, 4839, 140

Ruane, G., Ngo, H., Mawet, D., et al. 2019, AJ, 157, 118

Ruffio, J.-B., Macintosh, B., Wang, J. J., et al. 2017, ApJ, 842, 14

Ruffio, J.-B., Mawet, D., Czekala, I., et al. 2018, AJ, 156, 196

Samland, M., Bouwman, J., Hogg, D. W., et al. 2021, A&A, 646, A24

Scholz, F. W., & Stephens, M. A. 1987, JASA, 82, 918

Shaphiro, S., & Wilk, M. 1965, Biometrika, 52, 591

Soummer, R., Ferrari, A., Aime, C., & Jolissaint, L. 2007, ApJ, 669, 642

Soummer, R., Pueyo, L., & Larkin, J. 2012, ApJL, 755, L28

Sparks, W. B., & Ford, H. C. 2002, ApJ, 578, 543

Stolker, T., Bonse, M. J., Quanz, S. P., et al. 2019, A&A, 621, A59

The LUVOIR Team 2019, arXiv:1912.06219

Thompson, W., & Marois, C. 2021, AJ, 161, 236

Uyama, T., Hashimoto, J., Kuzuhara, M., et al. 2017, AJ, 153, 106

Vigan, A., Fontanive, C., Meyer, M., et al. 2021, A&A, 651, A72

Wahhaj, Z., Liu, M. C., Biller, B. A., et al. 2013, ApJ, 779, 80

Wahhaj, Z., Cieza, L. A., Mawet, D., et al. 2015, A&A, 581, A24

Xuan, W. J., Mawet, D., Ngo, H., et al. 2018, AJ, 156, 156

Zoubir, A. M., & Iskander, D. R. 2004, Bootstrap Techniques for Signal Processing (Cambridge: Cambridge Univ. Press)