Recent results in growth analysis

Abstract

After a brief historical review of the development of growth function analysis recent results of the Rostock research group are presented. These results are based on the asymptotic covariance matrix of the least squares estimator θ of the parameter vector θ of the intrinsically nonlinear regression (growth) function. For eight functions the first kind risks R and the robustness of tests and confidence estimations based on an analogue to the t-statistic were investigated by simulation experiments. Minimum sample sizes n(γ1, γ2) so that |_{N R}|<0,2_N (α_Nnominal risk of the first kind) if n >n(γ1, γ2) for seven pairs of γ1 (skewness) and γ2 (kurtosis) are given. Furthermore results obtained by mathematical derivations or by search procedures with respect to locally D-optimum designs for these functions are presented