  In this paper, we are interested in least squares estimator for a class of
path-dependent McKean-Vlasov stochastic differential equations (SDEs). More
precisely, we investigate the consistency and asymptotic distribution of the
least squares estimator for the unknown pa- rameters involved by establishing
an appropriate contrast function. Comparing to the existing results in the
literature, the innovations of our paper lie in three aspects: (i) We adopt a
tamed Euler-Maruyama algorithm to establish the contrast function under the
monotone condition, under which the Euler-Maruyama scheme no longer works; (ii)
We take the advantage of linear interpolation with respect to the discrete-time
observations to approximate the functional solu- tion; (iii) Our model is more
applicable and practice as we are dealing with SDEs with irregular coefficients
(e.g., H"older continuous) and path-distribution dependent.
