Bias in nonlinear regression

Bias correction for exponential family nonlinear modles

“…is approximately linear and when the expected difference between the linear and quadratic approximation of f (x;/?) is close to zero (Cook et al, 1986). Furthermore, b(b) will be small when is orthogonal to the columns of WX, For a particular reparameterization 6 = g(P), where 6 is a scalar, the O(n-l) bias becomes given by where G is a p x 1 vector with the derivatives aglaj?, and N is a p x p matrix with elements d2gldPra~,, r, s = 1, .…”

“…Ratkowsky (1983) uses various examples of normal nonlinear models to relate bias to the parameter effects curvature. Also for this class of models, Cook et al (1986) show that the bias may be due to the explanatory variables position in the sample space. Young & Bakir (1987) use bias correction to improve several pivotal random variables for a generalized log-gamma regression model.…”

Nearly unbiased estimation in a biparametric exponential family

“…From the log-likelihood defined in equation (2), we obtain the following moments: (2,0) , κ θ,τ = nρ (1,1) , κ τ,τ = nρ (0,2) , κ θθθ = −nρ (3,0) , κ θθτ = −nρ (2,1) , κ θτ τ = −nρ (1,2) , κ τ τ τ = −nρ (0, 3) , κ θθ,θ = κ θθ,τ = κ θτ,θ = κ θτ,τ = κ τ τ,θ = κ τ τ,τ = 0.…”

Jackknife-Based Estimators and Confidence Regions in Nonlinear Regression

“…The righthand side of (3.1) is of order n-'. Cook, Tsai, and Wei (1984) investigated the influence of individual cases on bias and derived the following result:…”