Dynamic spectrum access under channel uncertainties is considered. With the goal of maximizing the secondary user (SU) throughput subject to constraints on the primary user (PU) outage probability we formulate a joint problem of spectrum sensing and channel state estimation. The problem is cast into a sequential framework since sensing time minimization is crucial for throughput maximization. In the optimum solution, the sensing decision rule is coupled with the channel estimator, making the separate treatment of the sensing and channel estimation strictly suboptimal. Using such a joint structure for spectrum sensing and channel estimation we propose a distributed (cooperative) dynamic spectrum access scheme under statistical channel state information (CSI). In the proposed scheme, the SUs report their sufficient statistics to a fusion center (FC) via level-triggered sampling, a nonuniform sampling technique that is known to be bandwidth-and-energy efficient. Then, the FC makes a sequential spectrum sensing decision using local statistics and channel estimates, and selects the SU with the best transmission opportunity. The selected SU, using the sensing decision and its channel estimates, computes the transmit power and starts data transmission. Simulation results demonstrate that the proposed scheme significantly outperforms its conventional counterparts, under the same PU outage constraints, in terms of the achievable SU throughput.