We present a comprehensive investigation of the $\mathcal{F}\text{−}\mathrm{statistic}$ method for parameter estimation of gravitational wave (GW) signals from compact binary coalescences. By analytically maximizing the likelihood over the luminosity distance and polarization angle, this approach reduces the dimensionality of the parameter space to enhance computational efficiency. We also introduce a novel formulation for calculating the Bayesian evidence for the $\mathcal{F}\text{−}\mathrm{statistic}$, enabling a quantitative assessment of its performance against standard full frequency-domain (FFD) Bayesian inference. Applying these two methods to analyze several representative GW events (GW190412, GW190814, and GW170817), we find that the $\mathcal{F}\text{−}\mathrm{statistic}$ consistently yields results in good agreement with the FFD approach, while offering a significant reduction in computational cost. We demonstrate that including calibration uncertainty generally improves the agreement between the two methods. Furthermore, under the assumption of physical priors, the $\mathcal{F}\text{−}\mathrm{statistic}$-based analyses consistently yield higher Bayesian evidence than the corresponding FFD analyses. While the $\mathcal{F}\text{−}\mathrm{statistic}$ produces slightly broader constraints on some parameters, we argue this represents a more honest uncertainty quantification, particularly in high-dimensional parameter spaces with complex posterior structures. These results highlight the significant advantages of the $\mathcal{F}\text{−}\mathrm{statistic}$ method for GW data analysis, positioning it as a powerful tool for the era of high-rate detections with future observatories.

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• Gravitational wave sources
• Gravitational waves