A three-phase sampling extension of the generalized regression estimator with partially exhaustive information

We consider three-phase sampling schemes in which one component of the auxiliary information is known in the very large sample of the so-called null phase and the second component is available only in the large sample of the first phase, whereas the second phase provides the terrestrial inventory data. We extend to three-phase sampling the generalized regression estimator that applies when the null phase is exhaustive, for global and local estimation, and derive its asymptotic design-based variance. The new three-phase regression estimator is particularly useful for reducing substantially the computing time required to treat exhaustively very large data sets generated by modern remote sensing technology such as LiDAR.

Outlier-resistant estimators for Poisson sampling: a note

Poisson (3P) sampling is a commonly used method for generating estimates of timber volume. The usual estimator employed is the adjusted estimator, Y hata. The efficiency of this estimator can be greatly influenced by the presence of outliers. We formalize such a realistic situation for high-value timber estimation for which Y hata is inefficient. Here, yi approx beta xi for all but a few units in a population for which yi is large and xi very small. This situation can occur when estimating the net volume of high-value standing timber, such as that found in the Pacific Northwest region of the United States. A generalized regression estimator and an approximate Srivastava estimator are not affected by such data points. Simulations on a small population illustrate these ideas.

Point-Poisson, point-pps, and modified point-pps sampling: efficiency and variance estimation

Modified point-pps (probability proportional to size) sampling selects at least one sample tree per point and yields a fixed sample size. Point-Poisson sampling is as efficient as this modified procedure but less efficient than regular point-pps sampling in a simulation study estimating total volume using either the Horvitz–Thompson (ŶHT) or the weighted regression estimator (Ŷwr). Point-pps sampling is somewhat more efficient than point-Poisson sampling for all estimators except ŶHT, and point-Poisson sampling is always somewhat more efficient than modified point-pps sampling across.all estimators. For board foot volume the regression estimators are more efficient than ŶHT for all three procedures. Point-pps sampling is always most efficient, except for ŶHT, and point-Poisson sampling is always more efficient than the modified point-pps procedure. We recommend using Ŷgr (generalized regression estimator), Ŷwr, or ŶHT for total volume and Ŷgr for board foot volume. Three variance estimators estimate the variances of the regression estimates with small bias; we recommend the simple bootstrap variance estimator because it is simple to compute and does as well as its two main competitors. It does well for ŶHT, too, for all three procedures and should be used for ŶHT in point-Ppisson sampling in preference to the Grosenbaugh variance approximation. An unbiased variance estimator is given for ŶHT with the modified point-pps procedure, but the simple bootstrap variance is equally good.