George M. Furnival

Regressions by leaps and bounds

This paper describes several algorithms for computing the residual sums of squares for all possible regressions with what appears to be a minimum of arithmetic (less than six floating-point operations per regression) and shows how two of these algorithms can be combined to form a simple leap and bound technique for finding the best subsets without examining all possible subsets. The result is a reduction of several orders of magnitude in the number of operations required to find the best subsets.

sampling methods to estimate foliage and other characteristics of individual trees

The total foliar area or mass of a tree is difficult to measure, as is its bark or cambial area, and various other components of aboveground biomass. A variety of sampling methods is proposed and estimators of these characteristics are presented. Based on probability precepts, all estimators are unbiased. An unbiased estimator of variance for each estimator also is presented. The basis in probability rather than a fitted regression equation provides some important safeguards, and is a useful alternative when fitted re- gression functions are unavailable for a particular species and physiographic condition.

All Possible Regressions with Less Computation

Two methods are given for computing all possible regressions for a set of independent variables. One produces all the usual regression statistics; the other gives only the sums of squares of residuals. Both require less computation than other methods of computing all possible regressions and the second may compare favorably with the procedure suggested by Hocking and Leslie for finding the best subset without evaluating all possible subsets.

Modeling crown rise in even-aged stands of Sitka spruce or loblolly pine

Abstract A ‘crown-rise’ model that estimates average height to the base of a crown in an even-aged, monospecific stand is derived and fitted to loblolly pine and Sitka spruce data. Estimated standard errors are less than 1 m. The driving variables are average tree height and either tree count per unit area or average inter-tree distance. Two potential uses of the crown-rise model are (1) a component of an empirical or mechanistic forest model, and (2) and alternative to stocking charts for stand density management.

Sampling methods for estimating stem volume and volume increment

Abstract Probability sampling is proposed as an alternative to reliance on models for the estimation of tree stem volume and volume increment. A number of methods, which are in a class of procedures known in the simulation literature as variance reduction techniques, are presented with their corresponding estimators. Variance reduction is achieved by the ancillary use of a tree stem model such as a taper function, but unbiasedness does not depend on the validity of the model.

Confidence intervals and significance tests for a single trial

Confidence intervals are developed for the location parameter of a continuous, symmetric, unimodal distribution in the casev where only a single observation from the distribution is available. These intervals are similar to those given by Abbott and Rosenblatt (1963), but shorter. The result is extended to include distributions which can be standardized to have unit scale. The procedure is exemplified for the normal distribution and the power of one- and two-sided significance tests are computed under normality.