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This paper makes use of local polynomial Wigner-Ville distribution (LPWVD), originally designed for nonparametric instantaneous frequency (IF) estimation of transient signals, to propose a parametric IF estimation for polynomial phase signals (PPSs). Statistical performance such as asymptotic bias and variance of the LPWVD-based parametric IF estimator is derived in closed-form. Based on the analytical results, we extend the statistical efficiency of the Wigner-Ville distribution (WVD) for a second-order PPS only to that of the LP-WVD for an arbitrary order, when the IF is estimated at the middle of sample observations. Simulation results verify the analytical performance and comparisons with the polynomial Wigner-Ville distribution (PWVD) show that the LPWVD-based parametric IF estimator can provide better performance.