Statistics of the estimates of tricoherence are obtained analytically for nonlinear harmonic random processes with known true tricoherence. Expressions are presented for the bias, variance, and probability distributions of estimates of tricoherence as functions of the true tricoherence and the number of realizations averaged in the estimates. The expressions are applicable to arbitrary higher order coherence and arbitrary degree of interaction between modes. Theoretical results are compared with those obtained from numerical simulations of nonlinear harmonic random processes. Estimation of true values of tricoherence given observed values is also discussed.