9Terrestrial LiDAR becomes more and more popular to estimate leaf and plant area density. 10Voxel-based approaches account for this vegetation heterogeneity and significant work has 11 been done in this recent research field, but no general theoretical analysis is available.
2• Our unbiased estimators are consistent in a wider range of validity than the usual ones, 26 especially for the unbiased MLE, which is consistent when the beam number is as low as 5. 27The unbiased MLE is efficient, meaning it reaches the lowest residual errors that can be 28 expected (for an unbiased estimator). Also the unbiased MLE does not require any bias 29 correction when path lengths are unequal. 30• When elements are small (or voxel is large), 10 3 beams entering the voxel leads to some 31 confidence intervals ≈ ±10%, but when elements are larger (or voxel smaller), it can remain 32 wider than ±50%, even for a large beam number. This is explained by the variability of 33 element positions between vegetation samples. Such a result shows that a significant part of 34 residual error can be explained by random effects. 35• Confidence intervals are much smaller (±5 to 10%) when LAD estimates are averaged over 36 several small voxels, typically within a horizontal layer or in the crown of individual plants. 37In this context, our unbiased estimators show a reduction of 50% of the radius of confidence 38 intervals, in comparison to usual estimators. 39Our study provides some new ready-to-use estimators and confidence intervals for attenuation 40 coefficients, which are consistent and efficient within a fairly large range of parameter values. 41The consistency is achieved for a low beam number, which is promising for application to 42 airborne LiDAR data. They entail to raise the level of understanding and confidence on LAD Highlights: 52• Voxel-based estimations of LAD/PAD may lack of consistency and efficiency 53• We propose new estimators based on theoretical derivation and numerical simulations 54• Estimators for confidence intervals are also provided 55• New estimators should help determine the most appropriate voxel resolution 56 57