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We present a comprehensive assessment of multiparameter tests of general relativity (GR) in the inspiral regime of compact binary coalescences using principal component analysis (PCA). Our analysis is based on an extensive set of simulated gravitational-wave (GW) signals, including both general relativistic and non-GR sources, injected into zero-noise data colored by the noise power spectral densities of the LIGO and Virgo GW detectors at their designed sensitivities. We evaluate the performance of PCA-based methods in the context of two established frameworks: and . For GR-consistent signals, we find that PCA enables stringent constraints on potential deviations from GR, even in the presence of multiple free parameters. Applying the method to simulated signals that explicitly violate GR, we demonstrate that PCA is effective at identifying such deviations. We further test the method using numerical relativity waveforms of eccentric binary black hole systems and show that missing physical effects—such as orbital eccentricity—can lead to apparent violations of GR if not properly included in the waveform models used for analysis. Finally, we apply our PCA-based test to selected real gravitational-wave events from GWTC-3, including GW190814 and GW190412. We present joint constraints from selected binary black hole events in GWTC-3, finding that the 90% credible bound on the most informative PCA parameter is ${0.03}_{-0.08}^{+0.08}$in the framework and $-0.01_{-0.04}^{+0.05}$in the framework, both of which are consistent with GR. These results highlight the sensitivity and robustness of the PCA-based approach and demonstrate its readiness for application to future observational data from the fourth observing runs of LIGO, Virgo, and KAGRA. 

The detectable component of gravitational waves, known as the oscillatory waveform, is predicted to have a smaller, lower frequency counterpart called the memory: a permanent warping of space-time. The memory component is low-frequency (below the usual LIGO frequency band starting at 20 Hz), and low amplitude. Low frequency noise sources on earth make it difficult for ground based detectors to reach the SNR (signal to noise ratio) needed to detect this component. We use Bayesian parameter estimation on simulated events with future detector sensitivities, to determine the detector noise spectrum, event masses, and detected SNR required to detect gravitational wave memory.