  In this paper, we study the power iteration algorithm for the spiked tensor
model, as introduced in [44]. We give necessary and sufficient conditions for
the convergence of the power iteration algorithm. When the power iteration
algorithm converges, for the rank one spiked tensor model, we show the
estimators for the spike strength and linear functionals of the signal are
asymptotically Gaussian; for the multi-rank spiked tensor model, we show the
estimators are asymptotically mixtures of Gaussian. This new phenomenon is
different from the spiked matrix model. Using these asymptotic results of our
estimators, we construct valid and efficient confidence intervals for spike
strengths and linear functionals of the signals.
