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We say that IN has asymptotic level 1 − α. Remarks 1. By analogy to the Gaussian linear regression case, in the nonlinear regression model with homogeneous variance, we define an alternative confidence interval for λ. 2), we replace να with n/(n − p)tα , where tα is the α percentile of a Student variate with n − p degrees of freedom: IT = λ − 2 n t1−α/2 S; λ + n−p n t1−α/2 S . 3) The α percentile of a variate with distribution function F is the value of u, say uα , such that F (uα ) = α and 0 < α < 1.
3, in which we estimated two ELISA response curves. Our concern in this experiment was to estimate the relative potency of the two different sera. 7), is true. If it does exist for all values of x, then the parameters satisfy that θ1May = θ1June , θ2May = θ2June , θ3May = θ3June . In this case, β = θ4May −θ4June is the horizontal distance between the two curves at the inflection point. To determine parallelism we will first 30 2 Accuracy of Estimators, Confidence Intervals and Tests test whether these relations between the parameters are true or, more exactly, if they do not contradict the data.
2. The intervals IN and IT are symmetric around λ. In some applications, a part of the symmetric confidence interval might not coincide with the set of variations of the parameter λ. For example, consider λ = exp θ3 in the pasture regrowth example. If the estimate of the standard error of λ, say S, is bigger than λ/ν1−α/2 , then the lower bound of IN is negative even though λ is strictly positive. In that case, it is easy to see that it is more appropriate to calculate a confidence interval for θ3 and then to transform this interval taking the exponential of its limits to find a confidence interval for λ.