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Composite Estimators for Forest Growth Derived from Symmetric, Varying-Length Observation Intervals

Estimates of growth or change in a forest population parameter for a specific length of time, such as cubic meters of wood per hectare per year, are often made from sample observation intervals of different lengths of time. For instance, a basic building block of growth estimators in forest inventory systems is often the annual mean of the first differences of all observations for a particular year, regardless of observation interval length. The aggregate differences between successive observations on re-measured forest sample plots can be viewed as a linear combination, while forest growth is usually assumed to be non-linear. Bias can be assumed to exist whenever a linear combination is used to estimate a specific segment of an underlying non-linear trend. The amount of bias will depend upon the relationship of the intended estimation interval relative to the set of observation intervals. Here, three specific segments, relative to each year of interest, form the bases for a standard set of three estimands. Bias-ratio-adjusted composite estimators for use with observations made on alternative sets of symmetric interval lengths are compared in a simulation against this standard set of estimands. The first estimand has a one-year basis, the second has a five-year mid-interval basis, and the third has a five-year end-of-period basis. For the first and second bases, the initial results clearly show a logical ordering of bias and mean-squared error by observation interval length relative to the target interval length. As expected, some deviance from these clear trends are shown for the end-of-period basis. In the presence of three simple distributions of symmetric measurement intervals, the bias-ratio adjustments and subsequent composite estimators are shown to usually be effective in reducing bias and mean-squared error, while being most obviously effective for the most disparate distribution of intervals and for the end-of-period basis.