@MISC{Estimation_appendixa, author = {The Gradient Estimation}, title = {Appendix A Gradient estimation}, year = {} }

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Abstract

gradient at any time can be computed numerically . use nonparametric regression to estimate a bias-correcting curve (the mean exact gradient as a function of the estimated gradients) . un-bias the original gradient estimates by applying the estimated bias-correcting curve. The bias correction is quite small (at most about 10% for the data sets here) but in simulation studies it can visibly improve the accuracy of fitted rate equations (Ellner & Seifu, 2000). The gradient is estimated from the whole time series, but in all analyses here the estimates at the first two and last two observation times were deleted. Local polynomial fits tend to "wag" at the "tails" of the data, because they are constrained on only one side and therefore can chase after measurement errors in initial and final data points. The region where this occurs can be identified by comparing the gradient estimates to those obtained from local linear regression, which wags less due