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We present an estimate of the black hole mass function (BHMF) of broad linequasars (BLQSOs) that self-consistently corrects for incompleteness and thestatistical uncertainty in the mass estimates, based on a sample of 9886quasars at 1 < z < 4.5 drawn from the Sloan Digital Sky Survey. We findevidence for `cosmic downsizing' of black holes in BLQSOs, where the peak intheir number density shifts to higher redshift with increasing black hole mass.The cosmic mass density for black holes seen as BLQSOs peaks at z ~ 2. Weestimate the completeness of the SDSS as a function of black hole mass andEddington ratio, and find that at z > 1 it is highly incomplete at M_BH < 10^9M_Sun and L / L_Edd < 0.5. We also estimate a lower limit on the lifetime of asingle BLQSO phase and we place constraints on the maximum mass of a black holein a BLQSO. Our estimated distribution of BLQSO Eddington ratios peaks at L /L_Edd ~ 0.05 and has a dispersion of ~ 0.4 dex, implying that most BLQSOs arenot radiating at or near the Eddington limit; however the location of the peakis subject to considerable uncertainty. The steep increase in number density ofBLQSOs toward lower Eddington ratios is expected if the BLQSO accretion ratemonotonically decays with time. Furthermore, our estimated lifetime andEddington ratio distributions imply that the majority of the most massive blackholes spend a significant amount of time growing in an earlier obscured phase,a conclusion which is independent of the unknown obscured fraction. Theseresults are consistent with models for self-regulated black hole growth, atleast for massive systems at z > 1, where the BLQSO phase occurs at the end ofa fueling event when black hole feedback unbinds the accreting gas, halting theaccretion flow.

Constraints on Black Hole Growth, Quasar Lifetimes, and Eddington Ratio Distributions from the SDSS Broad Line Quasar Black Hole Mass Function