KURTOSIS AND CURVATURE MEASURES FOR NONLINEAR REGRESSION MODELS

摘要: An expression for the second-order approximation to kurtosis asso- ciated with least squares estimate of an individual parameter in a nonlinear regression model is derived, and connections between this various other mea- sures curvature are made. Furthermore means predicting reliability commonly-used Wald confidence intervals parameters, based on measures skewness kurtosis, developed. Numerous examples illustrating theoretical results provided. There has been considerable interest over past twenty years devel- oping models which some way quantify deviation from linearity. Specifically, landmark paper 1980, Bates Watts built seminal work Beale (1960) in- troduced relative intrinsic parameter-effects curvatures provide global nonlinearity model. However these not al- ways helpful when parameters (see e.g., Cook Witmer (1985)) as consequence number researchers have developed specifically associated parameters. In particular Ratkowsky (1983) suggested examining estimates by simulation Hougaard (1985) reinforced idea deriving formula skewness. Further Goldberg (1986) Hamilton extended ideas (1980) accommo- date while Clarke (1987) introduced marginal measure derived profile likelihood. The list seems rather daunting diverse uncon- nected. fact (1987), more recently Kang Rawlings (1998),