  The continuous nanohertz gravitational waves (GWs) from individual
supermassive binary black holes (SMBBHs) can be encoded in the timing residuals
of pulsar timing arrays (PTAs). For each pulsar, the residuals actually contain
an Earth term and a pulsar term, but usually only the Earth term is considered
as signal and the pulsar term is dropped, which leads to parameter-estimation
biases (PEBs) for the SMBBHs, and currently there are no convenient evaluations
of the PEBs. In this article, we formulate the PEBs for a SMBBH with an
eccentric orbit. In our analyses, the unknown phases of pulsar terms are
treated as random variables obeying the uniform distribution $U[0,2\pi)$, due
to the fact that pulsar distances are generally poorly measured. Our analytical
results are in accordance with the numerical work by Zhu et. al. (2016) at
$1.5\sigma$ level, implying that our formulae are effective in estimating
magnitudes of the PEBs. Additionally, we find that for two parameters -- Earth
term phase $\varphi^E$ and orbital eccentricity $e$, their biases $\Delta
\varphi^E$ and $\Delta e/e$ monotonically decrease as $e$ increases, which
partly confirms a hypothesis in our previous work Chen & Zhang (2018).
Furthermore, we also calculate the PEBs caused by the recently observed
common-spectrum process (CSP), finding that if the strain amplitude of the
continuous GW is significantly stronger ($3$ times larger, in our cases) than
the stochastic GW background, the PEBs from pulsar terms are larger than those
from the CSP. Our formulae of the PEBs can be conveniently applied in the
future PTA data analyses.
