@article {28080, title = {Karhunen-Lo{\`e}ve Estimation of the Power Spectrum Parameters from the Angular Distribution of Galaxies in Early Sloan Digital Sky Survey Data}, journal = {The Astrophysical Journal}, volume = {591}, year = {2003}, note = {n/a}, month = {July 1, 2003}, pages = {1-11}, abstract = {We present measurements of parameters of the three-dimensional powerspectrum of galaxy clustering from 222 square degrees of early imagingdata in the Sloan Digital Sky Survey (SDSS). The projected galaxydistribution on the sky is expanded over a set of Karhunen-Lo{\`e}ve(KL) eigenfunctions, which optimize the signal-to-noise ratio in ouranalysis. A maximum likelihood analysis is used to estimate parametersthat set the shape and amplitude of the three-dimensional power spectrumof galaxies in the SDSS magnitude-limited sample withr*\<21. Our best estimates are Γ=0.188+/-0.04 andσ8L=0.915+/-0.06 (statistical errors only), for a flatuniverse with a cosmological constant. We demonstrate that ourmeasurements contain signal from scales at or beyond the peak of thethree-dimensional power spectrum. We discuss how the results scale withsystematic uncertainties, like the radial selection function. We findthat the central values satisfy the analytically estimated scalingrelation. We have also explored the effects of evolutionary corrections,various truncations of the KL basis, seeing, sample size, and limitingmagnitude. We find that the impact of most of these uncertainties staywithin the 2 σ uncertainties of our fiducial result. }, url = {http://adsabs.harvard.edu/abs/2003ApJ...591....1S}, author = {Szalay, Alexander S. and Jain, Bhuvnesh and Matsubara, Takahiko and Scranton, Ryan and Vogeley, Michael S. and Connolly, Andrew and Dodelson, Scott and Eisenstein, Daniel and Frieman, Joshua A. and Gunn, James E. and Hui, Lam and Johnston, David and Kent, Stephen and Kerscher, Martin and Loveday, Jon and Meiksin, Avery and Narayanan, Vijay and Nichol, Robert C. and O{\textquoteright}Connell, Liam and Pope, Adrian and Scoccimarro, Roman and Sheth, Ravi K. and Stebbins, Albert and Strauss, Michael A. and Szapudi, Istv{\'a}n and Tegmark, Max and Zehavi, Idit and Annis, James and Bahcall, Neta and Brinkmann, Jon and Csabai, Istv{\'a}n and Fukugita, Masataka and Hennessy, Greg and Ivezic, Zeljko and Knapp, Gillian R. and Kunszt, Peter Z. and Lamb, Don Q. and Lee, Brian C. and Lupton, Robert H. and Munn, Jeffrey R. and Peoples, John and Pier, Jeffrey R. and Rockosi, Constance and Schlegel, David and Stoughton, Christopher and Tucker, Douglas L. and Yanny, Brian and York, Donald G. and {SDSS Collaboration}} }