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Third-order lensing statistics contain a wealth of cosmological informationthat is not captured by second-order statistics. However, the computationaleffort for estimating such statistics on forthcoming stage IV surveys isprohibitively expensive. We derive and validate an efficient estimationprocedure for the three-point correlation function (3PCF) of polar fields suchas weak lensing shear. We then use our approach to measure the shear 3PCF andthe third-order aperture mass statistics on the KiDS-1000 survey. We constructan efficient estimator for third-order shear statistics which builds on themultipole decomposition of the 3PCF. We then validate our estimator on mockellipticity catalogs obtained from $N$-body simulations. Finally, we apply ourestimator to the KiDS-1000 data and present a measurement of the third-orderaperture statistics in a tomographic setup. Our estimator provides a speedup ofa factor of $\sim$ 100-1000 compared to the state-of-the-art estimationprocedures. It is also able to provide accurate measurements for squeezed andfolded triangle configurations without additional computational effort. Wereport a significant detection of the tomographic third-order aperture massstatistics in the KiDS-1000 data $(\mathrm{S/N}=6.69)$. Our estimator will makeit computationally feasible to measure third-order shear statistics inforthcoming stage IV surveys. Furthermore, it can be used to constructempirical covariance matrices for such statistics.

A roadmap to cosmological parameter analysis with third-order shear  statistics III: Efficient estimation of third-order shear correlation  functions and an application to the KiDS-1000 data